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The Stars Align, Send Chargers to the Playoffs
December 31, 2013 by Andy Cohen
NFL admits that a penalty should have been called on the Chargers for illegal formation on Chiefs' game winning FG attempt. New rule mandates no more than six defenders on either side of the ball.
Image Source: NFL.com
After a series of fortuitous, near impossible events, the Bolts are on their way to the NFL playoffs for the first time since 2009.
By Andy Cohen
Sometimes it's better to be lucky than good. And the 2013 San Diego Chargers certainly are very lucky.
Against all probability, the Chargers are headed to the playoffs after completing a 9-7 regular season. Two weeks ago I wrote a column calling the talk of the Chargers making the playoffs nonsense, even after their dominant week 15, Thursday night win over the #1 overall AFC playoff seed Denver Broncos in Denver. The Chargers, it seemed, had finally gotten their act together and were playing some of the best football in The League. The problem was that it took them 13 weeks to get there.
The best the Chargers could hope to finish was 9-7, and with both Baltimore and Miami (who the Chargers lost to in week 11) ahead of them in the playoff standings, and with both teams coming off of impressive week 15 wins—Baltimore against Detroit, and Miami against Tom Brady (is there any other player on the Patriots 2013 roster that really matters?)—their chances at extending their season beyond week 17 were slim to none.
In order to make the playoffs, the Chargers not only had to win their final two games against Oakland and Kansas City, but they had to hope against hope that both the Ravens and the Dolphins dropped their final two games. Even if the Ravens lost to both New England and Cincinnati—both very good teams—there was little chance that the Dolphins would succumb to both Buffalo and the New York Jets—two not so very good teams. And even after the Dolphins lost 19-0 in Buffalo, you had to figure that they'd regroup against a pretty hapless Jets team at home to secure their playoff future, right?
Source: ESPN Stats & Info
The Chargers' playoff hopes were less than dim. Nothing more than a flicker. With the roll that they were on, it seemed likely that the Bolts would finish the season on a four game win streak after losing 17-10 to the Bengals in week 13. But SOOOOOO many things had to go right for the Chargers to even have a whiff at a chance at the playoffs. In week 14, their chances stood at a paltry 1.7%, falling to 1.4% after the week 15 results were in. But hey, at least the Chargers would finish on a high note with momentum heading into 2014 with a win and a season sweep of Kansas City. With so many blown opportunities earlier in the season, at least the Chargers faithful would have some positive mojo, giving some real substance to the dreaded phrase "wait 'til next year."
But the football gods were smiling on the Chargers. Having both lost the week before, first the Ravens fell to Cincinnati (not all that surprising). All eyes turned toward Miami, where the Jets pulled off the upset (completely and totally SHOCKING!). Against all odds, everything was going the Chargers' way. All they had to do now was beat a Kansas City team they had already beaten in Arrowhead Stadium five weeks prior, and who, having already secured the 5th seed in the AFC playoffs, was sitting 20 of their 22 starters, employing a backup QB who had never started an NFL game. Win and they're IN! Piece of cake!
And then kickoff happened. And the Chiefs marched 80 yards in five plays to take a 7-0 lead on their opening drive. As well as the Bolts' defense had played since the Cincinnati debacle, they reverted back to their early season ways where they would have struggled to keep Mission Hills High School out of the end zone. Offensively they weren't a whole lot better. The offensive line struggled to protect their QB, and the unit as a whole sputtered despite the valiant effort of a hobbled Ryan Mathews—who was clearly not himself even while tallying 144 yards on 24 carries.
With the sixth and final playoff spot offered up on a golden platter, the Chargers were treating it like an infectious disease. What happened to the team that rolled Peyton Manning and the Broncos? What happened to the team that manhandled Eli Manning and the Giants, and then the hated Oakland Raiders?
But again, the football gods were smiling on the Chargers: When Ryan Succop pushed the game winning 41 yard field goal as the fourth quarter clock ticked down to four seconds wide right; when the officials missed an illegal formation by the Chargers that would have given Succop a second chance at sealing the game from 36 yards, sending the Pittsburgh Steelers, and not the Chargers, to the playoffs. And yet again when, in overtime, the officiating crew blew Eric Weddle's forward progress dead on a fake punt, awarding a fresh set of downs and negating a fumble and return for a Chiefs game winning touchdown. Mathews and Philip Rivers proceeded to move the team into position for a Nick Novak 36 yard field goal to take the lead, and the defense bowed, holding the Chiefs just out of range for Succop to attempt to tie it up, forcing a fourth down illegal forward pass by Chase Daniel to seal the win and a playoff berth for the Bolts.
Any honest observer would have to admit that the Chargers don't deserve to be playoff bound after such a subpar effort against the Kansas City JV squad. Then again, the Chiefs' JV effort shouldn't be all that surprising. There is precedent: In the 2004 finale, with the roles reversed and the Chargers sitting all of their stars having already secured the division title and the fourth seed in the playoffs, the Bolts' backups took care of business against the Chiefs 24-17, a result few expected; an exhilarating effort that ranked among the most satisfying of a magical turnaround season. The Chargers should have expected this kind of game from a group of reserves looking to prove a point.
But they're in, for the first time since 2009, and it doesn't matter how they got there. All that matters is what they do with the opportunity. The question is which Chargers team will show up on Sunday in Cincinnati: The team that is maddeningly inept and continually shoots itself in the foot, or the team that's seemingly capable of beating anyone in The League? Fortune swung in the home team's favor, and now it's up to them to prove they belong.
But still, sometimes it truly is better to be lucky than good.
Andy Cohen
Andy spent 15 years working in the highest levels of the San Diego professional sports world, including both the Padres and the Chargers. He began his foray into writing while a volunteer for Francine Busby's 2010 Congressional campaign, eventually becoming a contributor to the now defunct SDNN. He has reported on local and national politics for both the OB Rag and the San Diego Free Press. When not reporting news and events, he offers political and policy commentary from a liberal perspective, occasionally turning back to his sports roots.
Latest posts by Andy Cohen (see all)
Aztecs Fall to 13 in AP, Coaches Poll After UNM Loss. Time to Panic Yet? - February 25, 2014
The Carl DeMaio as Moderate Fallacy - February 18, 2014
Faulconer Victory Brings Back Business as Usual - February 12, 2014
« San Diego Mayor Bob Filner's World Starts to Fall Apart: Looking Back at July 2013
A New Day (Opening David Alvarez's Office on Imperial Avenue) »
Truly, the whole thing, but especially the wide field goal attempt, was a dumbfounding series of accidents and tumbling dice. In the aftermath there was one more dumbfounding thing: the agreement of all sportswriters and their networks that the failed field goal should have been replayed, which would have give life to Pittsburgh's Steelers if KC's second attempt had been successful. All day long the network flashed the news that the Chargers only needed a tie to make it into playoffs.
What's the deal with that.
As in life, the luckiest team, not always the best team, wins. Will the officials who blew it be taken to the woodshed and spanked? Incompetence combined with a little luck beats hard work any day.


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PARTNER ORGANISATIONS >
PS is a documentary film production and media consulting company based in Berlin. Campaigns, image films and lectures about storytelling are part of the consultation. PS Media is focused on social policy projects (foundations, social clubs) and businesses and is well connected to German TV stations (Arte, ARD, ZDF). PS Media's documentary films focus on inter-religious and current social issues - in Berlin, Germany and Europe. The company's aim is to confront and break stereotypes, racism and discrimination.
https://www.ps-stories.com/
PS MEDIA
Founded in 1683, Brill is a publishing house with a rich history and a strong international focus. The company's head office is in Leiden (The Netherlands) with branch offices in Boston (Massachusetts, USA), Singapore, and Paderborn (Germany). Brill's publications focus on the Humanities and Social Sciences, International Law and selected areas in the Sciences. Brill publishes over 800 books per year in both print and electronic format. Titles are often collated in Brill's E-Book Collection. Brill publishes 200 journal. In addition to its journals and books publishing programmes, Brill also offers reference works and primary source materials. Primary sources usually refer to original material, which scholars study and interpret as a basis for their own academic works. Brill's Primary Source Collections Online include scanned printed or handwritten texts, e.g. pre-modern archival documents, Oriental manuscripts, but also printed art sales catalogues and contemporary human rights reports. Brill hosts the electronic versions of its product range on its own dedicated platforms:
brillonline.com
The Al-Jazeera Media Institute (AJMI) focuses on providing quality media training and development to all employees in media related fields, as well as designing and executing media development initiatives and first class consultancy by transforming its media expertise into knowledge for others to benefit from it. AJMI develops many training programmes, among which a yearly training curricula with training courses and diplomas on 96 topics, with a total of 169 training courses and diplomas scheduled for 2018, both public and private. It has special training courses with strategic partners such as United Nations (UN-AJMN Training Program for Palestinians Journalists 2016), The Norwegian Center for Human Rights (Media and Human Rights workshop 2014), New York Film Academy, among others.
https://institute.aljazeera.net/en
AL-JAZEERA MEDIA INSTITUTE
Casa Árabe is a public institution created in 2006 by the Spanish Ministry of Foreign Affairs and Cooperation. Its objectives are to promote mutual relations and knowledge between Spain and Arab countries at all levels and to offer a space for analysis and debate on Arab world affairs today. It is a centre of reference in Spain for all matters related to Arab countries, organising seminars and conferences of a public, academic and business nature in collaboration with institutions, think tanks and universities from Spain, Europe and the Arab world. It hosts the Centre of Arabic Language, holds art exhibitions and runs a weekly Arab film showing. Casa Árabe runs a broad training and education programme in collaboration with Spanish universities and centres, the Diplomatic School and international organisations (WTO, UNRWA, UNICEF, UNESCO), including courses in Arabic language, calligraphy, Arab world and culture, diplomacy, Islamic law, Andalusian history. It is part of the Anna Lindh Foundation Spanish Network and a participant in its translation project (ALF-CFT/2012704/Translation Programme).
Casa Árabe Cordoba http://en.casaarabe.es/sedes/show/casa-arabe-cordoba-2
Casa Árabe Madrid http://en.casaarabe.es/sedes/show/casa-arabe-madrid
CASA ÁRABE
The National Museum of World Cultures has four locations: the Tropenmuseum (Amsterdam), Museum Volkenkunde (Leiden), Wereldmuseum (Rotterdam) and the Afrika Museum (Berg en Dal). Its internationally renowned collections comprise over 500,000 objects and almost one million photographs, cataloguing the diversity of world cultures. Every year, the Museum hosts a variety of exhibitions and public events addressing historical and contemporary questions around issues of heritage, society, cultural identity and belonging. The museum heads the Research Center for Material Culture (RCMC), based in Leiden, which serves as a focal point for research on ethnographic collections.
http://materialculture.nl
NATIONAL MUSEUM OF WORLD CULTURES 'TROPENMUSEUM'
The Gotha Research Library of the University of Erfurt is a library with a focus on the history of culture and knowledge of the early modern and modern period. As part of the German research infrastructure it is active in research on its collections and delivers research-based services to scholars from around the world. Gotha Research Library hosts Germany's third largest collection of Oriental manuscripts, comprising more than 3,500 codices, mostly in Arabic, Persian and Ottoman. It offers up-to-date library facilities and services: a comprehensive reference library, a digitisation centre, a digital library, and an exhibition hall and venues for workshops and conferences. Platforms for digital exhibitions and digital editions are currently under development.
https://www.uni-erfurt.de/en/library/welcome-to-the-gotha-research-library/
FORSCHUNGSBIBLIOTHEK GOTHA DER UNIVERSITÄT ERFURT
The Centre Pompidou is one of the world's foremost institutions of modern and contemporary art. The Centre Pompidou is recognised for its expertise as the world's premier producer of temporary exhibitions. In collaboration with other leading museums of the world, the Centre Pompidou's exhibitions tour the globe. With more than 120,000 works, the Musée National d'Art Moderne holds one of the most extensive collections in the world, and the finest in Europe.
https://www.centrepompidou.fr/en
The EHESS was founded in 1947 as a section of the école Pratique des Hautes Études from which it became independent in 1975. It functions similarly to a doctoral or graduate school covering the whole spectrum of humanities and social sciences. Its 250 chair professors and associate professors have the task of training their Masters and Doctoral students in research but also conduct graduate-level seminars on topics directly linked to their own research. While upholding an open intellectual debate with hundreds of seminars, invited talks and conferences held annually, the École's main objective is the promotion of leadership in research with an emphasis on interdisciplinarity.
https://www.ehess.fr/en
ÉCOLE DES HAUTES ÉTUDES EN SCIENCES SOCIALES
The Department of Arabic and Islamic Studies was created in the early 1970s, and focuses on the modern and contemporary Arab and Islamic worlds. In 2010, due to the EHEA process of transformation, a new degree was offered on African and Asian Studies, counting with an itinerary in Arabic. In 2009, together with researchers from the CSIC, a new master's programme began, the Master's in Contemporary Arabic and Islamic Studies. The UAM has more than 20 years of experience in managing European and International funds, mainly coming from the Framework Programmes of the EU. It has a European and International Projects Office which is in charge of the promotion and management of European and International funds. In FP7, the University participated in 48 projects worth almost €11m. In H2020, UAM had 27 projects granted in the first round of calls worth more than €15.7m. In other International calls, it has had 13 proposals accepted, worth €1.3m. The Department of Arabic and Islamic Studies participates in two consolidated research groups, Taller de Estudios Internacionales Mediterráneos and Ideologías y Expresiones Culturales.
http://www.uam.es/UAM/Home(en)/1242662784079.htm?language=en
UNIVERSIDAD AUTÓNOMA DE MADRID
The University of Granada (UGR), founded in 1531, is one of the largest and most important universities in Spain. It has received the "Human Resources Excellence in Research (HRS4R)" award, which reflects UGR's commitment to continuously improve its human resource policies in line with the European Charter for Researchers and the Code of Conduct for the Recruitment of Researchers. UGR is also a leading institution in research, being one of the few Spanish universities listed in the Shanghai Top 500 ranking (http://www.arwu.org/), in which its Engineering/ Technology and Computer Science Faculty is positioned at the top of the 50 best universities in the world. With 3,500 teaching staff and more than 2,000 auxiliary personnel, UGR offers a total of 75 degrees through its 123 departments and 27 centres. Library aims to help EC-funded projects at UGR in implementing the Horizon 2020 Open Access and Open Data requirements: The University library offers assistance through its institutional repository. In terms of academic production, UGR publishes annually more than 2,500 publications, with a percentage higher than 50% in the first quartile, having a relative growth ratio of production well above of the average for Spain and the EU.
https://www.ugr.es/en/
Universitat de Barcelona (UB) was founded in 1450. Today it boasts of a student body of 84,370 and a research staff of 4,548. Degrees are offered in 73 different areas of teaching with numerous postgraduate and doctorate programmes as well as continuing education courses. UB is ranked the top Spanish university, and the 23rd European institution for academic quality and productivity, it is the largest of Barcelona's six universities and of the ten in Catalonia and manages an average of 150 European projects per year.
https://www.ub.edu/web/ub/en/
Formed in 1971, Paris I University is a leading university for social sciences and humanities, as well as law and economics. The University is ranked #3 in France by the Times Higher Education ranking, and #91 in the world. It hosts 40,000 students (20% from overseas) in 14 faculties and institutes. It delivers 360 PhDs each year. The University hosts the sole Doctoral School in Art History (ED 441) at national level. In the field of research, it has developed 7 International Chairs, and clusters of excellence, including the Labex CAP (Creation, Arts and Heritage), a collaborative initiative involving museums, libraries and higher education organisations that aims to facilitate the employability of graduates.
https://www.pantheonsorbonne.fr/
UNIVERSITÉ DE PARIS 1 PANTHÉON SORBONNE
The Faculty of Islamic Studies of the University of Sarajevo was established in 1977. The Faculty is a heir to the Higher School of Islamic Theology and Shari'ah (est. 1887). In 2006, the Faculty became a member of the University of Sarajevo. In addition to three undergraduate degrees (BA in Islamic Theology, BA in Islamic Pedagogy and BA for Imams), the Faculty offers postgraduate studies at masters' and doctoral levels. So far over 1,000 students have graduated from the Faculty, including 110 at MA and 42 at PhD level. https://www.unsa.ba/en At present the Faculty employs 29 teaching staff. The Faculty owns a small library focused on Islamic studies. More importantly, its students have access to Gazi Husraw bey Library and its collections which include over ten thousand oriental manuscripts:
http://www.ghb.ba/eng.
UNIVERSITET U SARAJEVU
ABOUT ITN-MIDA 2019
Evaluation report

redpajama_set_name: RedPajamaCommonCrawl


To develop infrastructure in the field of Information Technology.
To employ people with talent and having clear vision in the field of I.T. Industry.
To develop business as software developers, BPOs, I.T. Training Institute, Call centers and all I.T. related businesses and product based develpment to give best opportunity in the campus proposed in Gujarat.
To create I.T. awarness at grass root level co-ordinate businesses.
Group company has a plan to develop in different service and infrastructure sector such as Hospitality Industry.
Stock related terminals business (Shares and Commodity) Estate and building development.
The visionary MD of the co. Shree Naresh Bhojwani in the field of new ventures in construction developed the best sites in ahmedabad with all possible qualitative norms and structural designs so his all buildings in ahmedabad apreiciated by its users and industry tycoons it may be a housing / commercial / industrial and common. The best example of the quality conciseness is that in earth quake in 2001 non of the building made any threat of life to the occupiers of such complexes and no damage done to it the same way the MD of the company once to put up R & D department for Info Co. which should give the best chance to searchers in the field and quality conciseness people will always give the best.


Dr. DAI-Do DO – Swiss Cardiovascular Center, University of Bern, Switzerland.
Important – Should we target sympathetic nervous system or parasympathetic nervous system?
Dr. Prof. Amal K. Banerjee – Fellow of American College of Cardiology, European Society of Cardiology, American College of Physicians, Asian Pacific Society of Cardiology, Indian College of Cardiology, Cardiological Society of India and Indian College of Physicians. Cardiology Division, Institute of Cardiovascular Sciences, IPGME&R and SSKM Hospital, Kolkata. Past President of Cardiological Society of India.


The Olmsted is located on a 81 acres site that was the former Masonic Widow & Orphans Home. The facility is owned and operated by Masterson's Catering. Rental of the venue includes the entire facility and the grounds can be rented for use for an additional fee. The Olmsted's General Manager and Facility Director, Jeri Payne, can assist you in planning the perfect wedding.


First shoes, now diapers. Amazon is reportedly about to announce on Monday the acquisition of Quidsi, the New Jersey-based ecommerce company behind Diapers.com, Soap.com, and, most recently, BeautyBar.com. Fortune's Dan Primack, who broke the story from a maternity ward in Boston where his daughter was just born (no joke), puts the price of the all-cash deal at $540 million. A year ago, Amazon bought online shoe retailer Zappos for $1.2 billion.
Update: the deal was confirmed – read more here.
Founded by Vinit Bharara and Marc Lore, Quidsi has raised a total of $78.5 million. Its most recent funding was a $20 million debt round last April from investors including Accel, Bessemer, MentorTech, and New Enterprise Associates.
Diapers.com is the company's flagship brand, with an estimated $300-million revenue run rate this year. Soap.com just launched in June, and BeautyBar.com launched last week. So the vast majority of revenues is still coming from Diapers.com, which would value the deal at less than 2X revenues. Feeling threatened, Amazon recently started undercutting Diapers.com on price, a strategy which may have helped convince them to sell.
If the deal goes through, it would just go to show that you can still build an ecommerce startup if you go after the right niche. But it would also prove that if you get big enough, Amazon will notice and either buy you or try to squash you.


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What does Girls for Gender Equity do?
We pass the mic to girls and young women of color.
We know cisgender and transgender girls and young women of color face disturbing patterns of policing, interpersonal violence, and institutional violence in their schools and communities. We work locally and nationally to disrupt school-to-prison and sexual-assault-to-prison pipelines through participatory action research, coalition building with dedicated allies, and most importantly, listening to and supporting youth as they hone their own organizing and self-advocacy skills.
We call gender-based violence by its name.
From the social justice curriculum that young people in our three signature programs experience, to the workshops they go on to lead themselves, Girls for Gender Equity engages folks of all genders and ages in the work of unlearning and undoing the practices and policies that perpetuate gender-based violence. As our executive director Joanne Smith said at the 2016 United State of Women White House Summit, gender-based violence intersects with the issues of racial justice, state-sanctioned violence, sexual and reproductive justice, education, and economics. So does GGE's work.
A gift to GGE will allow the organization to continue the important work that has given critical support to over 9,000 young people of color over the past fifteen years. With your support, GGE can provide programming to even greater numbers of young people and strengthen the talents of a new generation of gender and racial justice advocacy and leadership in the 21st century.
Latest Posts from Girls for Gender Equity
GGE Programming: Soon To Be Back In Session! We hope you've all had a great summer! The new school year is just around the corner and so is GGE annual youth ...	more
Andrea Ritchie is an attorney, organizer, and the author of Invisible No More: Police Violence Against Black Women and Women of Color. Ritchie spoke with GGE ...	more
GGE and 'me too.' movement Launching an Online Community for Survivors
This summer, the me too. movement and Girls for Gender Equity are launching an online community for survivors, allies, and advocates to provide resources for ...	more


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Government/Institutional HVAC
NREL Researchers Point Toward Energy Efficiency for Achieving 100% Renewable Grid
Oversizing renewable capacities by a factor of 1.4-3.2 and aiming for 52%-68% in energy savings through building energy efficiency measures lead to cost-optimal paths depending on region of the country.
Incorporating energy efficiency measures can reduce the amount of storage needed to power the nation's buildings entirely with renewable energy, according to analysis conducted by researchers at the U.S. Department of Energy's (DOE's) National Renewable Energy Laboratory (NREL).
As more communities plan to eventually rely on 100% renewable energy, the researchers offer a strategy that could guide their paths — one that shifts away from long-duration storage.
"Minimizing long-duration storage is a key element in trying to achieve the target cost-effectively," said Sammy Houssainy, co-author with William Livingood of a new paper that outlines an approach to 100% renewables. The research paper, "Optimal Strategies for a Cost-Effective and Reliable 100% Renewable Electrical Grid," appears in the Journal of Renewable and Sustainable Energy.
The researchers considered solar and wind as the source of renewable energy, given that most plans for meeting the 100% target take those into account. They also used the Department of Energy's EnergyPlus and OpenStudio building energy modeling tools to simulate energy demand, considering such factors as building size, age, and occupancy type. Data from the U.S. Energy Information Administration informed the scientists about the existing building stock characteristics and energy load used by the buildings.
Further, the researchers separated the country into five climate zones, ranging from the hot and humid (Tampa, Florida) to the very cold (International Falls, Minnesota). The other zones encompassed the cities of New York, El Paso, and Denver. Knowing the extremes of heating and cooling demands in each zone enabled the researchers to select the appropriate mix of renewable power sources to minimize any needed storage.
While varying definitions exist in the literature, for purposes of this study the researchers define long-duration storage as energy storage systems that meet electricity demands for more than 48-hour durations. Therefore, long-duration energy storage provides power days or months after the electricity is generated. However, most long-duration storage technologies are either immature or not available everywhere. The two NREL researchers calculated reaching the last 75% to 100% of renewable energy would result in significant increases in costs associated with long-duration energy storage. Instead of focusing on storage, the researchers emphasized the optimal mix of renewable resources, oversized generation capacities, and investments in energy efficiency. The researchers note that multiple pathways exist to reach 100% renewable and, as the costs and performance of technologies change, new pathways will emerge, but they identified a key pathway that is achievable today.
They also determined that oversizing renewable capacities by a factor of 1.4-3.2 and aiming for 52%-68% in energy savings through building energy efficiency measures lead to cost-optimal paths depending on region of the country. Houssainy said making homes and offices more energy-efficient reduces the amounts of renewable resources needed, decreases the amount of storage, and cuts transmission costs, ultimately supporting the implementation of a carbon-free energy system.
"What's included in the paper is really a multistep process to follow," Livingood said. "That process is applicable to large cities as well small cities. Now, the end result will change, city to city, as this multistep process is followed to cost-optimally achieve the target."
For example, Tampa would generate all of its electricity from solar panels, while International Falls would receive 100% from wind turbines, the researchers calculated, in order to have the least reliance on storage.
"It is not intended to replace the need for site-specific, detailed engineering design and planning processes for buildings, electric grid, and energy infrastructure," Livingood said. "But, we believe our novel calculation methodology yields overarching concepts and conclusions that are broadly relevant and applicable. For cost-effectively achieving 100% renewable scenarios, our newly developed calculation methodology provides general principles that help guide these detailed engineering design and planning processes."
DOE's Building Technologies Office funded the research, under the advisement of Andrew Burr (formerly DOE).
NREL is the U.S. Department of Energy's primary national laboratory for renewable energy and energy efficiency research and development. NREL is operated for DOE by the Alliance for Sustainable Energy LLC.
KEYWORDS: NREL renewable grid renewables
NREL's OptGrid is Designed to Control Distributed Energy Resources for Grid Optimization
The Center for Energy Efficiency and Renewable Energy
LG Pledges to Transition to 100% Renewable Energy by 2050
Low Energy Cooling for Sustainable Buildings
Top 100 HVAC/R Tips
Energy Systems Engineering: Evaluation and Implementation, Third Edition


SERBIA: A €943m agreement for the modernisation of the 108 km section of the Beograd – Budapest corridor between Novi Sad and the Hungarian border at Subotica was signed by Serbia's Ministry of Construction, Transport & Infrastructure, China Railway International and China Communications Construction Co on July 7.
The work to raise speeds and capacity on the route is expected to start in 2019.
Serbia had secured beneficial terms after negotiating the contract for more than a year, Minister Zorana Mihajlović said after the signing ceremony on the sidelines of the seventh China & Central & Eastern European Countries '16+1' summit in Sofia.
CRI and CCCC had previously been appointed main contractors for the modernisation of the 75 km Beograd – Stara Pazova section of the route from the capital to the border.
RZD International is modernising and double tracking the 40 km Stara Pazova – Novi Sad section of the corridor under a US$248m contract which includes the construction of three viaducts, 19 bridges, and a new station at Beška. The Russian Railways subsidiary is also building the new Čortanovci tunnel under a US$350m project financed from a Russian loan (75%) and the Serbian budget (25%), with opening expected in early 2022.
On July 10 the Western Balkans Investment Framework announced a €2·0m grant to support planning of the Niš railway bypass, and €3·5m to plan modernisation of the Niš – Prеšеvo (– Skopje) line.
Read more about Chinese involvement in the Beograd – Budapest upgrading project in the January 2018 issue of Railway Gazette International magazine, which subscribers can access in the digital archive.


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With Christian Ramirez on a roll, Loons return to an old house of horrors in KC
By Jeff Rueter May 31, 2018 3
Creating a schedule in a 23-team league has its challenges. Continued expansion (congrats, Cincinnati) has ended the days when every team could fill the schedule by playing the rest of the league home-and-away. There are some common rules — play every conference opponent twice, non-conference sides once, and a wild-card match or two — but the timing of matches also becomes tricky.
Last year, it meant playing Sporting Kansas City on May 7 and June 3 in 2017 league play with a June 14 Open Cup match to boot. Similarly, Minnesota United will play its I-35 rivals for the second time in the span of 14 days this Sunday. After Wednesday's team training, players and coaches alike admitted it seemed bizarre, but knew it was out of their power.
"I feel like it happens every summer," Christian Ramirez told The Athletic after training on Wednesday. "Last year, we played them two or three times in a month. For whatever reason, the...


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\section{Introduction}

The fascination with magnets can be traced back as far as the antiquity in China, but it was only with the discovery of spins that we developed a better understanding of magnetism.~\cite{discoverSpin,Ohanian1986} Insulating solids with magnetic properties, in particular, can be viewed as lattices of atomic or ionic magnetic moments, each localized to one site.~\cite{MattisBook,NoltingRamakanthBook,ParkinsonBook} The total magnetic moment of the atom or ion depends, in general, on the spins of the electrons in incomplete shells and their orbital angular momenta. Here we refer to this total angular momentum simply as spin. The interactions between the spins may lead to collective behaviors with macroscopic effects, such as ferromagnetism, where the spins line up parallel to each other, and antiferromagnetism, where neighboring spins point in opposite directions. The source of such spontaneous magnetization is the so-called exchange interaction, introduced by Heisenberg and Dirac in the end of the 1920's.~\cite{MattisBook,NoltingRamakanthBook} This interaction has a quantum mechanical origin. It is the manifestation of the Coulomb repulsion between the electrons and the Pauli exclusion principle, being therefore strong and short range. A magnetic dipolar interaction is also present, but it is too small to explain magnetism at room temperature.

The exchange interaction between particles of spin 1/2 and higher is usually described by the Heisenberg model. This is one of the most important models of magnetism and has been investigated for decades.~\cite{MattisBook,NoltingRamakanthBook,ParkinsonBook}  In 1931, Bethe found an exact analytical solution to the one-dimensional spin-1/2 Heisenberg model with coupling between nearest-neighbor sites.~\cite{Bethe1931,BetheIntro} This was a breakthrough in the studies of exactly solvable quantum many-body systems.~\cite{SutherlandBook} In 1983, Haldane suggested a remarkable difference between one-dimensional antiferromagnetic systems of integer and half-integer spins,~\cite{HaldanePLA1983,HaldanePRL1983} namely that the first should be gapped and the latter gapless.~\cite{Affleck1989} A necessary condition for a material to be insulating is the presence of an energy gap between the ground state and the first excited states. The prediction of the Haldane gap was confirmed numerically and experimentally, and a rigorous proof was soon provided for a similar model.~\cite{Affleck1987,Affleck1989}

The present work is restricted to the one-dimensional spin-1/2 Heisenberg model. Despite being a simplified theoretical model, it describes quantitatively well real materials found in nature or synthesized in laboratory, such as magnetic compounds. In some of these systems, unusual high transport of heat has been verified,~\cite{Sologubenko2000PRB,Hess2007,Hlubek2010} which has highly motivated the current interest in the subject. Such anomalous transport behavior has been associated with a macroscopic number of conserved quantities characterizing the model.~\cite{Zotos1997}

The spin-1/2 Heisenberg model finds applications in several other contexts. It is a key model in studies of quantum phase transition,~\cite{Chen2007} superconductivity,~\cite{MattisBook} localization in disordered systems,~\cite{Dukesz2009} as well as the dynamics~\cite{Santos2009JMP,Santos2011,Santos2012PRL} and thermalization~\cite{RigolARXIVBook} of correlated one-dimensional lattice systems. In quantum information, Heisenberg systems are used as models for quantum computers, each spin-1/2 representing a quantum bit (qubit), \cite{NielsenBook} in the analysis of entanglement, \cite{Amico2008} and in methods to transfer information in a controllable way.~\cite{Bose2007,Cappellaro2007} In the presence of impurities, disorder, or couplings beyond nearest-neighbors, the system becomes non-integrable and has been employed in the characterization of the crossover from integrability to quantum chaos.~\cite{Hsu1993,Avishai2002,Santos2004,Gubin2012}

There have also been attempts to simulate spin-1/2 Heisenberg chains with cold gases in optical lattices.~\cite{Simon2011}  Optical lattices are crystals of light. Laser beams propagating in opposite directions result in standing waves that confine ultracold atoms to small regions, the atoms playing the role of electrons in solid crystals.~\cite{Greiner2008} These systems are highly controllable, which allows for the simulation of condensed matter models not easily accessible with real solid state systems. Moreover, they are weakly coupled to the environment, which makes it possible to study their evolution for a long time. These factors combined make optical lattices essential tools to advance our understanding of quantum many-body systems far from equilibrium. The behavior of nonequilibrium systems is an outstanding challenge at the forefront of physics.

Motivated by the widely spread interest in spin systems and in the out-of-equilibrium properties of quantum many-body systems, we study here the factors that may limit the time evolution of the one-dimensional spin-1/2 Heisenberg model with couplings between nearest-neighbor sites only. We focus on the effects of an anisotropy parameter and on the symmetries of the system. We rely on the analysis of the eigenvalues and eigenstates of the system to anticipate its dynamics. Our predictions are then confirmed with actual numerical results for the time evolution. Since our studies require all eigenvalues and eigenstates, we use full exact diagonalization.

The paper is organized as follows. Section II provides a detailed description of the
Hamiltonian of the system. Section III analyzes the diagonal elements of the Hamiltonian, as well as its eigenvalues and eigenstates. Section IV investigates the time evolution of the system. Its symmetries and how they can constrain the system dynamics are discussed in Sec. V.

\section{Spin-1/2 chain}

The description of a system composed of a single spin-1/2 requires the use of the spin operators
$\hat{S}^{x,y,z} = \hat{\sigma}^{x,y,z}/2$, where
\[ \hat{\sigma}^x \equiv \left(
\begin{array}{cc}
0 & 1  \\
1 & 0
\end{array}
\right) ,
\hspace{0.5 cm}
 \hat{\sigma}^y \equiv \left(
\begin{array}{cc}
0 & -i  \\
i & 0
\end{array}
\right) ,
\hspace{0.5 cm}
 \hat{\sigma}^z \equiv \left(
\begin{array}{cc}
1 & 0  \\
0 & -1
\end{array}
\right)
\]
are the Pauli matrices and $\hbar$ has been set to 1. The quantum state of the spin is represented by a two-component vector, known as the spinor. This state is commonly written in terms of basis vectors corresponding to the eigenstates of $\hat{S}^z$, which are the spin pointing up in the $z$ direction $|\uparrow \rangle = \binom{1}{0}$ and the down-spin $|\downarrow \rangle = \binom{0}{1}$. The eigenvalue associated with $|\uparrow \rangle$ is +1/2 and that of  $|\downarrow \rangle$ is -1/2, which justifies referring to the first as the excitation. The operators $\hat{S}^{x}$ and $\hat{S}^{y}$ flip the up- or down-spin according to
\[
\hat{S}^{x} |\uparrow \rangle = \frac{1}{2} |\downarrow \rangle \hspace{0.7 cm} \hat{S}^{x} |\downarrow \rangle = \frac{1}{2} |\uparrow \rangle
\]
\[
\hat{S}^{y} |\uparrow \rangle = \frac{-i}{2} |\downarrow \rangle \hspace{0.7 cm} \hat{S}^{y} |\downarrow \rangle = \frac{i}{2} |\uparrow \rangle .
\]

Here, we study a one-dimensional system (chain) composed of $L$ coupled spins-1/2 described by the Heisenberg model,
\begin{equation}
\hat{H} = \sum_{n=1}^{L-1} \left[ J \left(
\hat{S}_n^x \hat{S}_{n+1}^x + \hat{S}_n^y \hat{S}_{n+1}^y \right)  +
J_z  \hat{S}_n^z \hat{S}_{n+1}^z \right] .
\label{ham}
\end{equation}
The operators $\hat{S}^{x,y,z}_n$ act only on the spin placed on site $n$. The couplings are limited to nearest-neighbor spins; $J$ is the strength of the flip-flop term $\hat{S}_n^x \hat{S}_{n+1}^x + \hat{S}_n^y \hat{S}_{n+1}^y$, $J_z$ is the strength of the Ising interaction $\hat{S}_n^z \hat{S}_{n+1}^z$, and the ratio $\Delta=J_z/J$ is the anisotropy parameter. The model is isotropic when $\Delta=1$, in which case it is known as the XXX model, and it is anisotropic when $\Delta \neq 1$, usually referred to as the XXZ model (XYZ also exists when the coupling strengths in the three directions are different). A natural basis for the system is the set of $2^L$ states where the spin on each site is either pointing up or down, such as  $|\downarrow_{1} \uparrow_{2} \uparrow_{3} \dots \downarrow_{L} \rangle$. In quantum information, these states are known as quantum computational basis vectors. We refer to them as site-basis vectors.

We note that the one-dimensional spin-1/2 Heisenberg model can be mapped onto a system of hard-core bosons, that is bosons that cannot occupy the same site.~\cite{RigolARXIVBook} This system, in turn, is equivalent to the Bose-Hubbard model in the limit of strong repulsive interaction.~\cite{Cazalilla2011} The Bose-Hubbard model is used to describe interacting bosons on a lattice and the Hubbard model treats interacting fermions. The latter was introduced in 1963, \cite{Hubbard1963}  and since then these models have been extensively studied, especially for describing superconductivity and the transition from an insulator to a superfluid. \cite{Quintanilla2009,EsslerBook}

The flip-flop term in Hamiltonian~(\ref{ham}) interchanges the position of neighboring up and down spins according to
\[
J(\hat{S}_n^x \hat{S}_{n+1}^x + \hat{S}_n^y \hat{S}_{n+1}^y)|\uparrow_n \downarrow_{n+1} \rangle =
(J/2) |\downarrow_n \uparrow_{n+1} \rangle .
\]
It is also commonly written with raising $\hat{S}^{+} = \hat{S}^{x} + i \hat{S}^{y}$ and lowering $\hat{S}^{-} = \hat{S}^{x} - i \hat{S}^{y}$ spin operators,
\[
(J/2) (\hat{S}_n^+ \hat{S}_{n+1}^- + \hat{S}_{n+1}^+ \hat{S}_{n}^-)|\uparrow_n \downarrow_{n+1} \rangle =
(J/2) |\downarrow_n \uparrow_{n+1} \rangle .
\]
The flip-flop term therefore couples site-basis vectors that differ only by the orientation of the spins in two adjacent sites. In this basis, it constitutes the off-diagonal elements of the Hamiltonian matrix. This term plays a key role in the evolution of the system by moving the excitations through the chain.

In the case of open boundary conditions (open chain), as in Eq.~(\ref{ham}), where the sum goes from site $n=1$ to site $L-1$, an excitation on site 1 can move only to site 2 and from site $L$ to $L-1$. The scenario of a ring (closed chain), where an excitation on site $L$ can also move to site 1 corresponds to closed boundary conditions and will be discussed briefly in this paper.

The Ising interaction contributes to the diagonal part of the Hamiltonian matrix written in the site-basis. It causes a pair of adjacent parallel spins to have different energy from a pair of anti-parallel spins, because
\begin{equation}
J_z \hat{S}_n^z \hat{S}_{n+1}^z |\uparrow_n \uparrow_{n+1}\rangle =+(J_z/4) |\uparrow_n \uparrow_{n+1}\rangle,
\label{upup}
\end{equation}
while
\begin{equation}
J_z \hat{S}_n^z \hat{S}_{n+1}^z |\uparrow_n \downarrow_{n+1}\rangle =-(J_z/4) |\uparrow_n \downarrow_{n+1}\rangle.
\label{updown}
\end{equation}

A Hamiltonian containing only the Ising interaction, $\hat{H}_{zz}=J_z \hat{S}_n^z \hat{S}_{n+1}^z $, constitutes the Ising model and was employed in the first attempts to describe the phase transition from paramagnetism to ferromagnetism.~\cite{Cipra1987} As one can infer from Eqs.~(\ref{upup}) and (\ref{updown}), the ground state of this model depends on the sign of the interaction strength; it is ferromagnetic, with all spins aligned in the same direction, when $J_z<0$,  and it shows an antiferromagnetic arrangement with antiparallel neighboring spins when $J_z>0$.

The state in which all spins align in the same direction is also an eigenstate of the Heisenberg model, because the flip-flop term has no effect on it. When the Heisenberg model is ferromagnetic ($J_z<0$), this state is a ground state. For the antiferromagnetic Heisenberg model ($J_z>0$), on the other hand, the ground state is more complicated than the simple configuration of antiparallel spins (details about it may be found, for instance, in \cite{ParkinsonBook}).

Here, we are interested not only in the ground state, but in all eigenvalues and eigenstates of the finite antiferromagnetic XXZ model with open boundary conditions. They are computed numerically and used to compare the static and dynamic properties of the system in two scenarios, when $\Delta \lesssim 1$ and when $\Delta \gg 1$. We address the role of the anisotropy parameter, as well as border effects and symmetries.

Our Hamiltonian commutes with the total spin in the $z$ direction, ${\cal \hat{S}}^z=\sum_{n=1}^L \hat{S}_n^z$, that is, $[\hat{H},{\cal \hat{S}}^z]=0$. This means that the system is invariant by a rotation around the $z$-axis, or equivalently, it conserves ${\cal \hat{S}}^z$. As a result, the Hamiltonian matrix of a system with $L$ sites is composed of $L+1$ independent blocks (or subspaces), each with a fixed number $N\in [0,L]$ of up-spins. Therefore, even though the total dimension of the Hilbert space is $2^L$, we can diagonalize a single subspace at a time, each of dimension $D=\binom{L}{N}$. When $L$ is even, the largest subspace has $N=L/2$. In this case, full exact diagonalization can be carried out for $L\leq 14 $ with the {\it Mathematica} computer codes we provide.~\cite{www} For larger systems, we recommend using a high-level computer programming language, such as {\it Fortran} or {\it C$^{++}$}. Full exact diagonalizations have been performed for matrices with up to $D \sim 3 \times 10^4$. \cite{Santos2010PRE}

Other symmetries may also be present, but this discussion is left for Sec.~V. In the next two sections, we focus on the analysis of the spectrum of a particular ${\cal \hat{S}}^z$-subspace and the structure of its eigenstates written in the site-basis, as a way to predict the dynamics of the system, and then confirm our expectations by investigating the actual time evolution of different initial states.

\section{Spectrum}

Before diagonalizing the XXZ Hamiltonian matrix, which we write in the site-basis, let us first look at its diagonal elements. They correspond to the eigenvalues of the Ising part, $\hat{H}_{zz}$, of the Hamiltonian~(\ref{ham}) and are split into sets of degenerate energies. Here, we refer to separated sets of energies as energy bands. The bands are determined by the number of pairs of adjacent parallel spins in the basis vectors. For each ${\cal \hat{S}}^z$-subspace, the larger the number of pairs, the larger the energy of the basis vector. For example, in an open chain with $L=4$ and $N=2$, the highest energy, $J\Delta/4$, occurs for the states with two pairs of parallel spins, $|\uparrow \uparrow \downarrow \downarrow \rangle$ and $|\downarrow \downarrow \uparrow \uparrow \rangle$. The band that precedes this one in energy has the states with only one pair of parallel spins, $|\uparrow  \downarrow \downarrow \uparrow \rangle$ and  $| \downarrow \uparrow \uparrow \downarrow \rangle$, yielding an energy of $-J\Delta/4$, while the states of the band with the lowest energy, $-3J\Delta/4$, have no pairs of parallel spins, $|\uparrow  \downarrow \uparrow \downarrow  \rangle$ and $| \downarrow \uparrow \downarrow \uparrow  \rangle$. One sees that the energy difference between consecutive bands is $J\Delta/2$, since we move down in energy by breaking a pair, thus adding the factor $J\Delta/4$ one less time and subtracting it one more time. In an open chain, where there are $L-1$ coupling bonds, the general expression for the energy of each band is therefore
\begin{equation}
E_{zz}^{\text{open}} = [2 p - (L-1)] J\Delta/4,
\end{equation}
where $p$ is the total number of pairs of adjacent parallel spins.

In a closed chain, on the other hand, the energy difference between successive bands is $J\Delta$. In this case, there are $L$ bonds and always an even number of antiparallel pairs, because there is no border to absorb any of them. We move down in energy by breaking necessarily two pairs of parallel spins, the factor $J\Delta/4$ thus being added two less times and subtracted two more times. The diagonal energies are then given by
\begin{equation}
E_{zz}^{\text{closed}} = [2 p - L] J\Delta/4.
\end{equation}
Clearly, the closed chain has fewer bands than the open one, as shown in Table~\ref{table:numberofbands}  (Note: $\lfloor x \rfloor $ is the integer part of $x$).
\begin{table}[h]
\caption{Number of energy bands formed with the diagonal elements of the XXZ Hamiltonian written in the site-basis.}
\begin{center}
\begin{tabular}{ccc}
N & open & closed \\ [2pt]
\hline \\ [-7pt]
$<\lfloor \frac{L}{2} \rfloor$ & 2N & N \\ [2pt]
\hline \\ [-7pt]
$\lfloor \frac{L}{2} \rfloor$ and $\lfloor \frac{L+1}{2} \rfloor$ & (L-1) & N \\ [2pt]
\hline \\ [-7pt]
$>\lfloor \frac{L+1}{2}  \rfloor$ & 2(L-N) & (L-N) \\ [2pt]
\hline
\end{tabular}
\end{center}
\label{table:numberofbands}
\end{table}

From now on, our analysis focuses solely on open chains. Notice, however, that extending the studies to the case of closed systems is straightforward and the codes for it are provided.~\cite{www}

For an open chain with an even number of sites and $N=L/2$, the diagonal elements of the XXZ Hamiltonian matrix form $L-1$ bands with energies ranging from $-(L-1)J\Delta/4$, when $p=0$, to $(L-3)J\Delta/4$, when $p=L-2$. The total number of states $\eta_B$ contained in an arbitrary band $B$, with $B\leq L/2$ being a positive integer, is equal to the number of states $\eta_{L-B}$ contained in the band $L-B$, that is the band structure is symmetric.
The number of states in each band grows as we approach the middle of the spectrum. For example,
\begin{eqnarray}
L=6: &&  \eta_1=\eta_{5}=2 \hspace{0.34 cm} \eta_2=\eta_{4}=4 \hspace{0.34 cm} \eta_3=6, \nonumber \\
L=8: &&   \eta_1=\eta_{7}=2 \hspace{0.34 cm} \eta_2=\eta_{6}=6 \hspace{0.34 cm} \eta_3=\eta_4=\eta_5=18, \nonumber \\
L=10: && \eta_1=\eta_{9}=2 \hspace{0.34 cm} \eta_2=\eta_{8}=8 \hspace{0.34 cm} \eta_3=\eta_7=32\nonumber \\
&& \eta_4=\eta_6=48 \hspace{0.34 cm} \eta_5=72. \nonumber
\end{eqnarray}
The case for $L=10$ is illustrated  with histograms in Figs.~\ref{fig:histograms} (a) and (b) for two values of $\Delta$. The least populated bands are always the ones in the extremes containing only two states each, $\eta_1=\eta_{L-1}=2$. If $L \! \! \mod 4 \neq 0$, as in Fig.~\ref{fig:histograms}, $B=L/2$ is the most populated band, whereas if $L$ is divisible by 4, the three bands in the middle are the most populated with $\eta_{L/2-1}=\eta_{L/2}=\eta_{L/2+1}$. By studying the three examples above and larger system sizes, we arrived at the general equation,
\begin{equation}
\eta_B = \eta_{L-B}= 2 \prod_{k=1}^B \frac{N- \lfloor k/2\rfloor}{N\delta_{k,1}+\lfloor k/2\rfloor}.
\end{equation}

\begin{figure}[htb]
\includegraphics[width=0.4 \textwidth]{JoelKollmarSantosFig01.eps}
\caption{(Color online) Histograms of the diagonal elements [panels (a) and (b)] and of the eigenvalues [panels (c) and (d)], and IPR averaged over all eigenstates vs $\Delta$ [panel (e)], for the antiferromagnetic XXZ Hamiltonian with open boundaries, $L=10$, and $N=5$. The site-basis is used. Panels (a) and (c): $\Delta=0.5$; panels (b) and (d): $\Delta=10$. Panel (c): bin width = 0.2 and panel (d): bin width = 1.0.}
\label{fig:histograms}
\end{figure}

Contrary to the diagonal elements, the eigenvalues of the total Hamiltonian (\ref{ham}) may or not form bands of energy depending on the interplay between the Ising interaction and the flip-flop term. Figures~\ref{fig:histograms} (c) and (d) show the histograms for the spectrum of the XXZ chain obtained with the same parameters considered in the top panels. In Fig.~\ref{fig:histograms} (c), where $\Delta \lesssim 1$, the band structure is lost. This happens because the energy difference between the basis vectors is $\lesssim J$, so the flip-flop term can couple intra- and also inter-band states, broadening significantly the range of energy values. In contrast, the band structure is preserved in Fig.~\ref{fig:histograms} (d). There, since $\Delta \gg 1$, states from different bands are too far off-resonance and the flip-flop term can effectively couple only states belonging to the same band. Each band then acquires a small width, which does not erase the energy gap between them.~\cite{substructure}

The competition between the Ising and the flip-flop term of the Hamiltonian is reflected also in the structure of the eigenstates. As the Ising interaction increases, limiting the role of the flip-flop term, the eigenstates become less spread in the site-basis. This can be quantified, for example, with the so-called inverse participation ratio (IPR).~\cite{Izrailev1990,ZelevinskyRep1996} Consider an eigenstate
\begin{equation}
|\psi^{(j)} \rangle =\sum_{k=1}^{D} a_{k}^{(j)} |\phi_k \rangle
\label{PsiBasis}
\end{equation}
written in terms of arbitrary orthonormal basis vectors $|\phi_k\rangle$. IPR is defined as
\begin{equation}
I^{(j)} \equiv \frac{1}{\sum_{k=1}^{D} |a_{k}^{(j)}|^4}.
\label{IPR}
\end{equation}
This quantity is proportional to the number of basis vectors which contribute to each eigenstate. It is small when the state is localized and large when the state is delocalized in the chosen basis. In our studies, $|\phi_k\rangle$ corresponds to the site-basis.

Figure~\ref{fig:histograms} (e) shows IPR averaged over all eigenstates, $\langle I \rangle$, for various values of the anisotropy parameter. The maximum delocalization occurs at $\Delta=0$. As the anisotropy increases,  $\langle I \rangle$ decays monotonically until the energy bands cease overlapping and $\langle I \rangle$ approaches a constant value.~\cite{Dukesz2009} In this latter scenario, the eigenstates become superpositions involving only intra-band basis vectors.

\section{Dynamics}

We now analyze the time evolution of different initial states, each corresponding to a specific site-basis vector, $|\Psi(0)\rangle = |\phi_k\rangle$. The source of the dynamics is the flip-flop term, which couples $|\phi_k\rangle$ with other states, transforming $|\Psi(t)\rangle$ into an evolving superposition of site-basis vectors. From the results for the eigenvalues and eigenstates described in the previous section, we expect the initial state to spread over several basis vectors when $\Delta \lesssim 1$, whereas the dynamics should be confined to states belonging to the same energy band as $|\Psi(0)\rangle$ when $\Delta \gg 1$.

To confirm the above predictions, we study two quantities, the magnetization of each site,
\begin{equation}
M_n(t) = \langle \Psi(t) | \hat{S}^z_n| \Psi(t) \rangle ,
\end{equation}
and the probability $P_l(t)$ for finding a basis vector $|\phi_l\rangle $ at instants of times $t$. Since the Hamiltonian matrix (\ref{ham}) in the site-basis is real symmetric, one can find a set of orthonormal real eigenstates. This is indeed what we obtain from our numerical diagonalization. Furthermore, since the initial state is a single basis vector, we have $|\phi_k\rangle = \sum_{j=1}^D a_k^{(j)} |\psi^{(j)}\rangle$, where the coefficients $a$'s are real. This leads to
\begin{eqnarray}
|\Psi(t)\rangle &=& \sum_{j=1}^D a_k^{(j)} |\psi^{(j)}\rangle e^{-i E_j t} \nonumber \\
&=&  \sum_{l=1}^D \left( \sum_{j=1}^D a_k^{(j)} a_l^{(j)} e^{-i E_j t} \right) |\phi_l\rangle ,\nonumber
\end{eqnarray}
and the probability is then given by
\begin{equation}
P_l(t) = \left| \sum_{j=1}^D a_k^{(j)} a_l^{(j)} e^{-i E_j t} \right|^2.
\end{equation}

The panels in Fig.~\ref{fig:dynamics} show the magnetization of each site for an open chain that has a single excitation initially placed on site 1, $|\Psi(0) \rangle=| \uparrow \downarrow \downarrow \ldots \downarrow \rangle $. In panels (a) and (c), where $\Delta =0.5$, the up-spin leaves the edge and gradually spreads through the chain by hopping successively from one site to the next in intervals of time $\sim J^{-1}$. The probability of finding it on a single site decreases from site 2 to $L-1$, but it finally reaches the other edge with high probability. The preference for the edges is a border effect that occurs only in open chains, because the border states $|\uparrow \downarrow \downarrow \ldots \downarrow \rangle $ and $|\downarrow \downarrow \ldots \downarrow \uparrow \rangle$ are in resonance. This effect decreases with system size, as seen by comparing panel (a), where $L=6$, with panel (c), where $L=12$. Since the energy difference between the border states and the states with the up-spin on sites $2\leq n\leq L-1$ is only $J\Delta/2=0.25J$, the latter can still take part in the dynamics. For comparison, we show in panels (b) and (d) the case where this energy difference is large, $J\Delta/2=5J$. There, only the border states are effectively coupled. The intermediate states, being so different in energy, have negligible participation in the evolution of the initial state. In perturbation theory, they are referred to as ``virtual states''. \cite{ShankarBook} The order of perturbation theory in which the border states are coupled is determined by the number of virtual states separating them, and their effective coupling strength, $ J_{\text{eff}}$, is inversely proportional to the order of perturbation theory and to the energy difference between coupled and intermediate states.  Therefore, the time $t\sim J_{\text{eff}}^{-1}$ for the excitation to move from $n=1$ to $n=L$ is long and increases with system size, as seen by the time scales in panels (b) and (d), where two different chain sizes are considered.
\begin{figure}[htb]
\includegraphics[width=0.4 \textwidth]{JoelKollmarSantosFig02.eps}
\caption{(Color online) Magnetization of each site versus time; initial state $| \uparrow \downarrow \downarrow  \ldots \downarrow \rangle$. The sites are indicated with numbers.  Panels (a), (c): $\Delta=0.5$ and panels (b), (d): $\Delta=10$. Top panels: $L=6$ and bottom panels: $L=12$. All panels are for open chains.}
\label{fig:dynamics}
\end{figure}

The different time scales associated with the order of perturbation theory in which states are effectively coupled are well illustrated in the top panel of Fig.~\ref{fig:probability}. There we have 6 sites and 2 excitations initially placed away from the borders, but next to each other. Since the anisotropy considered is large, $\Delta=10$, the up-spins will tend to move through the chain as a bound pair. The figure shows the probability in time for each basis vector. The initial state $|\Psi(0) \rangle=| \downarrow \uparrow \uparrow \downarrow  \downarrow \downarrow \rangle$ (whose probability is indicated with a solid line) is in resonance with the basis vectors $| \downarrow \downarrow \uparrow \uparrow  \downarrow \downarrow  \rangle $ (circles) and $| \downarrow \downarrow \downarrow \uparrow \uparrow   \downarrow  \rangle $ (triangles), both of which have up-spins next to each other. It is also in resonance with state $| \uparrow \downarrow \downarrow \downarrow  \downarrow \uparrow \rangle $ (cross), which compensates for the absence of a bound pair of up-spins by placing each excitation on a border site. This resonance is therefore a border effect. The four states belong to the same energy band, which is well separated from the other bands. Thus, only these four states should be able to mix, as confirmed by the figure.

State $|\downarrow \uparrow \uparrow \downarrow  \downarrow \downarrow \rangle$ couples with state
$| \downarrow \downarrow \uparrow \uparrow  \downarrow \downarrow  \rangle $ in second order of perturbation theory via an intermediate transition where the pair splits into the virtual state $|\downarrow \uparrow \downarrow  \uparrow  \downarrow \downarrow \rangle$ and then recombines again. Since the energy difference $E_{|\downarrow \uparrow \uparrow \downarrow  \downarrow \downarrow \rangle} - E_{|\downarrow \uparrow \downarrow  \uparrow  \downarrow \downarrow \rangle} =J\Delta $, the effective coupling strength between $|\downarrow \uparrow \uparrow \downarrow  \downarrow \downarrow \rangle$  and $| \downarrow \downarrow \uparrow \uparrow  \downarrow \downarrow  \rangle $ obtained by perturbation theory  is $J_{\text{eff}} \sim J/\Delta$.~\cite{ShankarBook,MerzbacherBook}
The same coupling strength is found between states $| \downarrow \downarrow \uparrow \uparrow  \downarrow \downarrow  \rangle $ and $| \downarrow \downarrow \downarrow \uparrow \uparrow   \downarrow  \rangle $.
These states then hybridize at $t \sim \Delta J^{-1}$.  In contrast, the effective coupling between $|\downarrow \uparrow \uparrow \downarrow  \downarrow \downarrow \rangle$ and $| \uparrow \downarrow \downarrow \downarrow  \downarrow \uparrow \rangle $ occurs in fourth order of perturbation theory. It then takes much longer for the latter state to take part in the dynamics. As seen in the top panel, the probability to find this state is negligible for a long time. Moreover, similar to the discussion in Fig.~\ref{fig:dynamics}, this time further increases with system size and the maximum probability to ever find this state further decreases.

\begin{figure}[htb]
\includegraphics[width=0.35 \textwidth]{JoelKollmarSantosFig03.eps}
\caption{(Color online) Probability in time to find a specific basis vector; open chain, $L=6$, and $\Delta=10$. Top panel: Initial state $| \downarrow \uparrow \uparrow \downarrow \downarrow \downarrow  \rangle $ (solid line) couples effectively with
 $| \downarrow \downarrow \uparrow \uparrow  \downarrow \downarrow  \rangle $ (circles) ,
 $| \downarrow \downarrow \downarrow \uparrow \uparrow   \downarrow  \rangle $ (triangles), and
 $| \uparrow \downarrow \downarrow \downarrow  \downarrow \uparrow \rangle $ (cross).
Bottom panel: initial state $| \uparrow \uparrow \uparrow \downarrow \downarrow \downarrow \rangle $ (solid line)
couples effectively only with $|\downarrow \downarrow \downarrow \uparrow \uparrow \uparrow \rangle  $ (dashed line).}
\label{fig:probability}
\end{figure}

The combination of large anisotropy and border effects can slow down the evolution of the system significantly, to the point that an initial state may look stationary.~\cite{Santos2005exc,Santos2009JMP,Haque2010} This is the case shown in the bottom panel of Fig.~\ref{fig:probability}, where $\Delta =10$ and the initial state, $|\Psi(0) \rangle=| \uparrow  \uparrow \uparrow \downarrow \downarrow \downarrow \rangle$, has a bound triple of up-spins with one excitation on the border. The panel shows the probability in time for each basis vector. The initial state can hybridize only with  $| \downarrow \downarrow \downarrow \uparrow  \uparrow \uparrow \rangle$, because all the other states are very far in energy. The communication between the two states occurs in a very high order of perturbation theory, all three excitations taking a long time to cross the chain from the left to the right side. This makes the initial state look frozen for a long time. Notice that in a closed chain, where the borders are absent, the dynamics would be faster. In this case, the bound triple of excitations $\uparrow  \uparrow \uparrow$ would not be restricted to the edges, but would move together through the whole chain.

Separated energy bands caused by large anisotropy and the presence of borders can then limit the dynamics of the system to a portion of the Hilbert space. Another restrictive factor is the symmetries of the system, as we discuss next.

\section{Symmetries}

Operators that commute with the Hamiltonian have two important properties: their eigenstates are also eigenstates of $\hat{H}$, \cite{GriffithsBook} and they represent physical quantities that are conserved.~\cite{HenleyBook} The latter property comes from the fact that the expectation value of a conserved quantity, $\langle \hat{O} \rangle$, does not change in time, so
\[
\frac{d \langle \hat{O} \rangle}{dt} =\frac{i}{\hbar} \langle \hat{H}\hat{O} - \hat{O}\hat{H} \rangle = 0 \Rightarrow [\hat{H},\hat{O}]=0,
\]
The way to find such constants of motion is by looking for the symmetries of the system. According to Noether's theorem,~\cite{Noether} the invariance of the Hamiltonian under a symmetry operation must necessarily lead to a conserved quantity. For example, invariance of $\hat{H}$ under translation in
space leads to conservation of linear momentum, and invariance of $\hat{H}$ under translation
in time leads to conservation of total energy.

We have already encountered a conserved quantity of our system, the total spin in the $z$-direction. As we saw when studying the dynamics, the eigenvalue of ${\cal \hat{S}}^z$ for the initial state is conserved throughout the evolution. If the initial state has $N$ up-spins, then all the states that take part in its evolution must have the same number of up-spins. But our system shows additional symmetries, as we describe next.

Hamiltonian (\ref{ham}) is invariant under reflection, which leads to conservation of parity, that is, $\hat{H}$ commutes with the parity operator
\[
\hat{\Pi} = \left\{
\begin{array}{ccc}
{\cal \hat{P}}_{1,L} {\cal \hat{P}}_{2,L-1} \ldots {\cal \hat{P}}_{\frac{L}{2},\frac{L+2}{2}} & \text{for} & L=\text{even}\\
{\cal \hat{P}}_{1,L}  {\cal \hat{P}}_{2,L-1} \ldots {\cal \hat{P}}_{\frac{L-1}{2},\frac{L+3}{2}} & \text{for} & L=\text{odd}
\end{array}
\right.
\]
where ${\cal \hat{P}}_{i,j}=(\hat{\sigma}^x_i \hat{\sigma}^x_j + \hat{\sigma}^y_i \hat{\sigma}^y_j + \hat{\sigma}^z_i \hat{\sigma}^z_j +\mathbb{1})/2$ is the permutation operator and $\mathbb{1}$ is the identity operator.  ${\cal \hat{P}}_{i,j}$ permutes the $i^{th}$ and $j^{th}$ vector spaces. For instance, $\hat{\Pi} |\uparrow \downarrow \downarrow \uparrow \downarrow\rangle = |\downarrow \uparrow \downarrow \downarrow \uparrow \rangle $.

Invariance under reflection may be better understood by imagining a mirror at one edge of the chain. If parity is conserved, the probability of each basis vector in the eigenstate is equal to that of its reflection. For example, suppose we have $L=4$ and one excitation. The eigenstates of $\hat{H}$, which are also eigenstates of $\hat{\Pi}$, are
given by
\[
|\psi^{(j)} \rangle = a_{1}^{(j)}|\uparrow \downarrow \downarrow \downarrow \rangle +
a_{2}^{(j)} |\downarrow \uparrow \downarrow \downarrow \rangle +
a_{3}^{(j)} |\downarrow \downarrow \uparrow \downarrow \rangle +
a_{4}^{(j)} |\downarrow \downarrow \downarrow \uparrow \rangle
\]
and the probability amplitudes are either $a_{1}^{(j)}=a_{4}^{(j)}$ and $a_{2}^{(j)}=a_{3}^{(j)} $ for even
parity, $\Pi=+1$, or $a_{1}^{(j)}=- a_{4}^{(j)}$ and $a_{2}^{(j)}=- a_{3}^{(j)} $ for odd
parity, $\Pi=-1$. [Notice that the hat in $\hat{\Pi}$ indicates the operator and its absence indicates the eigenvalue, $\hat{\Pi} |\psi^{(j)} \rangle = \Pi |\psi^{(j)} \rangle$.]

If $L$ is even and $N=L/2$, our Hamiltonian is also invariant under a global $\pi$ rotation around the $x$ axis. The operator that realizes this rotation is
\[
\hat{R}^x_{\pi} = \hat{\sigma}^x_1  \hat{\sigma}^x_2 \ldots \hat{\sigma}^x_L
\]
and one can easily verify that $[\hat{H},\hat{R}^x_{\pi} ]=0$.
As an example, suppose we have $L=4$ and $N=2$. The eigenstate
\begin{eqnarray}
|\psi^{(j)} \rangle &=& a_{1}^{(j)}|\uparrow \uparrow \downarrow \downarrow  \rangle +
a_{2}^{(j)} |\uparrow \downarrow \uparrow  \downarrow \rangle +
a_{3}^{(j)} |\uparrow \downarrow \downarrow \uparrow  \rangle \nonumber \\
&+&
a_{4}^{(j)} |\downarrow \uparrow \uparrow \downarrow  \rangle +
a_{5}^{(j)} |\downarrow \uparrow  \downarrow  \uparrow \rangle +
a_{6}^{(j)} |\downarrow \downarrow \uparrow \uparrow  \rangle , \nonumber
\end{eqnarray}
has either $a_{1}^{(j)}=a_{6}^{(j)}$, $a_{2}^{(j)}=a_{5}^{(j)}$, and $a_{3}^{(j)}=a_{4}^{(j)}$, in which case the eigenvalue of $\hat{R}^x_{\pi}$ is $R^x_{\pi}=+1$, or $a_{1}^{(j)}=- a_{6}^{(j)}$, $a_{2}^{(j)}=- a_{5}^{(j)}$, and $a_{3}^{(j)}=- a_{4}^{(j)}$, in which case $R^x_{\pi}=-1$.

There are two other symmetries, which we will not explore here. One is conservation of total spin, ${\cal \hat{S}}_T = \sum_n \vec{S}_n$, which occurs only in isotropic systems ($\Delta=1$), where $[\hat{H},{\cal \hat{S}}_T^2]=0$. The other is conservation of momentum, which happens in the closed chain due to its invariance by a translation in space.

\begin{table}[htb]
\caption{The first column numerates the eigenstates $|\psi^{(j)} \rangle $ of an open XXZ chain with $\Delta=0.4$, $L=6$, and $N=3$. The second and third columns give, respectively, the eigenvalues of $\hat{\Pi}$ and $\hat{R}^x_{\pi}$ of these eigenstates. Fourth, fifth, sixth, and seventh columns: probability amplitudes $c_{A,B,C,D}^{(j)}$ of the initial states [Eq.~(\ref{initialABCD})] written as superpositions of the eigenstates of the Hamiltonian,
$|\Psi_{A,B,C,D}(0) \rangle = \sum_j c_{A,B,C,D}^{(j)} |\psi^{(j)} \rangle $. The eigenvalues of $\hat{\Pi}$ and $\hat{R}^x_{\pi}$ for these initial states are shown in the second and third rows.}
\begin{center}
\begin{tabular}{ccc||cccc}
\multicolumn{4}{c}
{}  &  &  &  \\ [2pt] \cline{4-7} \\[-7pt]
 & & & \hspace{0.1cm}  $|\Psi_A (0) \rangle $ \hspace{0.2cm}  & $|\Psi_B(0)\rangle $ \hspace{0.2cm} & $|\Psi_C(0) \rangle $ \hspace{0.2cm} & $|\Psi_D(0) \rangle $ \\ [2pt] \cline{4-7} \\[-7pt]
 & & &   $\Pi=+1$                            & $\Pi=-1$                            &         $\Pi=\O$               & $\Pi=-1$ \\ [2pt]
 \cline{4-7} \\[-7pt]
 & & &      $R_{\pi}^x=\O$         &        $R_{\pi}^x=\O$               & $R_{\pi}^x=+1$      & $R_{\pi}^x=+1$ \\ [2pt]
 \hline \\ [-7pt]
 &$\Pi$   &  $R_{\pi}^x$  & $c_A^{(j)}$    &   $c_B^{(j)}$  & $c_C^{(j)}$      & $c_D^{(j)}$   \\ [2pt]
\hline \\ [-7pt]
$\psi^{(1)}$  & -- & -- &   0 & --0.16 & 0 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(2)}$  & + & + &    --0.19 & 0 & --0.19 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(3)}$  & -- & + &    0 & 0.33 & 0.33 & 0.46 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(4)}$  & -- & -- &    0 & --0.07 & 0 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(5)}$  & + & + &   0.19 & 0 & 0.19 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(6)}$  & + & -- &    --0.48 & 0 & 0 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(7)}$  & + & + &    --0.05 & 0 & --0.05 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(8)}$  & -- & + &    0 & --0.28 & --0.28 & --0.40 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(9)}$  & -- & -- &    0 & 0.33 & 0 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(10)}$  & -- & -- &    0 & 0.42 & 0 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(11)}$  & + & + &    --0.50 & 0 & --0.50 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(12)}$  & + & -- &    --0.15 & 0 & 0 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(13)}$  & + & + &    --0.34 & 0 & --0.34 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(14)}$  & -- & -- &    0 & 0.11 & 0 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(15)}$  & -- & -- &    0 & --0.30 & 0 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(16)}$  & -- & + &    0 & --0.56 & --0.56 & --0.79 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(17)}$  & + & -- &    0.50 & 0 & 0 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(18)}$  & + & + &    0.04 & 0 & 0.04 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(19)}$  & -- & -- &    0 & --0.28 & 0 & 0 \\ [2pt]
\hline \\ [-7pt]
$\psi^{(20)}$  & + & + &    --0.24 & 0 & --0.24 & 0 \\ [2pt]
\hline
\end{tabular}
\end{center}
\label{table:symmetry}
\end{table}
In this work, we focus on $\hat{\Pi}$ and $\hat{R}^x_{\pi}$ and analyze how they affect the dynamics of the system. For this, we consider four different initial states corresponding to superpositions of few basis-vectors,
\begin{eqnarray}
|\Psi_A(0) \rangle &=& (|\downarrow \uparrow \uparrow \uparrow \downarrow \downarrow \rangle + |\downarrow \downarrow \uparrow \uparrow \uparrow \downarrow \rangle )/\sqrt{2}, \nonumber \\
|\Psi_B(0) \rangle &=& (|\downarrow \uparrow \uparrow \uparrow \downarrow \downarrow \rangle - |\downarrow \downarrow \uparrow \uparrow \uparrow \downarrow \rangle )/\sqrt{2}, \nonumber \\
|\Psi_C(0) \rangle &=& (|\downarrow \uparrow \uparrow \uparrow \downarrow \downarrow \rangle + |\uparrow \downarrow \downarrow \downarrow \uparrow \uparrow \rangle )/\sqrt{2}, \nonumber \\
|\Psi_D(0) \rangle &=& (|\downarrow \uparrow \uparrow \uparrow \downarrow \downarrow \rangle - |\downarrow \downarrow \uparrow \uparrow \uparrow \downarrow \rangle +  \nonumber \\
&& \hspace{0.17 cm} |\uparrow \downarrow \downarrow \downarrow \uparrow \uparrow  \rangle  - |\uparrow \uparrow \downarrow \downarrow \downarrow \uparrow \rangle)/2.
\label{initialABCD}
\end{eqnarray}
The first two states are not eigenstates of $\hat{R}^x_{\pi}$, but parity is well defined, $|\Psi_A(0) \rangle$ has even parity and $|\Psi_B(0) \rangle$ has odd parity. State $|\Psi_C(0) \rangle$, on the other hand, is an eigenstate of the operator $\hat{R}^x_{\pi}$ with eigenvalue $+1$, but not of $\hat{\Pi}$. The last state, $|\Psi_D(0) \rangle$ is an eigenstate of both $\hat{\Pi}$ and $\hat{R}^x_{\pi}$, with eigenvalues $-1$ and $+1$, respectively.

In Table~\ref{table:symmetry}, we write each initial state as a linear superposition of the eigenstates of the system, $|\Psi_{A,B,C,D}(0) \rangle = \sum_j  c_{A,B,C,D}^{(j)} |\psi^{(j)} \rangle $, so that we can investigate which eigenstates can take part in the evolution. The first column numerates the eigenstates, $|\psi^{(j)} \rangle $. The second and third columns give the eigenvalues of $\hat{\Pi}$ and $\hat{R}^x_{\pi}$, respectively, for each eigenstate. The fourth, fifth, sixth, and seventh columns show the values of the probability amplitudes, $c_{A,B,C,D}^{(j)}$, of the eigenstates for the initial states $|\Psi_A (0) \rangle $, $|\Psi_B (0) \rangle $, $|\Psi_C (0) \rangle $, and $|\Psi_D (0) \rangle $, respectively. The eigenvalues of $\hat{\Pi}$ and $\hat{R}^x_{\pi}$ for each initial state are shown in the second and third rows.

From the table, we can see that only the eigenstates with the same symmetries as the initial state can contribute to the evolution of the latter. For $|\Psi_A (0) \rangle $ and $|\Psi_B (0) \rangle $, eigenstates with both values of $R_{\pi}^x$ are seen, but parity is strictly conserved. In the first case, the probability amplitudes of all odd eigenstates are zero and for the second state, $c_B^{(j)}=0$ for all eigenstates with $\Pi=+1$. For state $|\Psi_C (0) \rangle $, eigenstates with both parities are part of the superposition, but $c_C^{(j)}\neq 0$ only for eigenstates with $R_{\pi}^x=+1$. The last state, $|\Psi_D (0) \rangle $, has both symmetries, so only three of the 20 eigenstates have $c_D^{(j)}\neq 0$, those with $\Pi=-1$ and  $R_{\pi}^x=+1$ simultaneously.

The three eigenstates constituting $|\Psi_D (0) \rangle $ are $|\psi^{(3)} \rangle, |\psi^{(8)} \rangle$, and $|\psi^{(16)} \rangle$. They are more localized in the site-basis than all other eigenstates, {\em i.e.}  they have fewer coefficients $a_k^{(j)} \neq 0$ in  Eq.~(\ref{PsiBasis}). This is because superpositions of some of the basis-vectors cannot satisfy both $\Pi=-1$ and  $R_{\pi}^x=+1$ at the same time. For example, the effect of the two operators $\hat{\Pi}$ and  $\hat{R}_{\pi}^x$ on $b_1 |\uparrow \uparrow \uparrow \downarrow \downarrow  \downarrow \rangle + b_2 | \downarrow \downarrow  \downarrow \uparrow \uparrow \uparrow \rangle $ is the same, so they cannot give different eigenvalues. If $\Pi=-1$, we necessarily have $b_2=-b_1 $, for which case $R_{\pi}^x$ is inevitably -1. These two basis vectors (and similarly for others) cannot, therefore, be part of the contributing eigenstates $|\psi^{(3)} \rangle, |\psi^{(8)} \rangle$, and $|\psi^{(16)}\rangle$; the coefficients $a_k^{(3),(8),(16)}$ associated with these basis vectors can only be zero.

In summary, the larger the number of conserved quantities, the smaller the invariant subspaces. The time evolution of an initial state with many constants of motion is therefore more constrained in the Hilbert space.

\vspace{0.7cm}

\section{Discussion}

We make available online all computer codes used to obtain our data, as well as detailed explanations about them.~\cite{www}. Students and professors should have no difficulty to reproduce our results and to explore further questions. The studies described here can constitute an entire summer project, as in our case, can set the basis for a senior thesis, or give ideas for assignments in courses about Quantum Mechanics. By the time of completion of this work, the two first authors of this paper were undergraduate students who had not had a course on Quantum Mechanics, but had a solid background on Linear Algebra.

\centerline{\bf Acknowledgments}
This work was supported by the NSF under Grant DMR-1147430 and in part under Grant PHY11-25915 and PHY05-51164.
D.~K. thanks Stern College for Women of Yeshiva University for a summer fellowship. K.~J. and D.~K. thank the Kressel Research Scholarship for a one-year financial support.
This work is part of their theses for the S. Daniel Abraham Honors Program. L.~F.~S. thanks the KITP at UCSB for its hospitality.

redpajama_set_name: RedPajamaArXiv


Ripponden-based JLA has today [22nd January 2013] launched a new medical division to capitalise on the UK care and healthcare industry's growing requirement for more of its critical equipment, demonstrating the on-going growth of the West Yorkshire company.
The move to launch JLA Medical as a new sub-brand is expected to net the company more than £1 million in the next 12 months, capitalising on the company's huge growth over the past year.
Stephen Baxter, CEO of JLA, said: "JLA Medical represents another big step forward for JLA in terms of our continuing commitment to meeting our customers' needs and specific requirements. Following other recent advancements in warewashing and detergents provision, it further highlights our significant investment into product development and carefully planned expansion into new areas of commercial equipment supply and servicing.
Based at Meadowcroft Lane in Ripponden, West Yorkshire, JLA employs almost 450 people across its head office, engineering and field sales, and is currently recruiting for a number of roles across its departments.
The new JLA Medical range represents a huge expansion of its products in the care home and healthcare sector. The range includes a set of bedpan washer-disinfector and macerator products, specifically designed to maximise infection control and improve hygiene in care homes and hospitals, while making life easier for staff and operators.
JLA, which will celebrate its 40th year in business this year, has seen its growth strategy pay off over the past few years with turnover in 2011/12 at £62m. Mr Baxter expects the launch of JLA Medical to further boost the company's economic profile, with hundreds of care homes expected to install the new products by the end of 2013.
As reinforcement of Mr Baxter's assertion, JLA's own research reveals that almost 60% of all care homes rely on hand-washing their bedpans and over 90% rely on yellow waste bags for their waste disposal. Using mechanical disposal could save care homes up to £4,000 per year.
JLA is the market-leader in commercial equipment and service provider for care, working with thousands of UK homes to supply and service critical operational processes with washing machines, dryers, dishwashers, detergents, bedpan washer disinfectors, macerators, compliance & safety checks and more.
Its unique, all-inclusive Total Care package offers customers machine supply, 7-day breakdown cover with no wear and tear clause, along with a 24/7 helpline. Available for a simple monthly payment, Total Care also includes an 8-working hour response guarantee, whereby customers are paid £100 if an engineer is not on-site in that time.


Vintage Reworked Levi's 501 dark blue jeans in excellent condition. Button front. Frayed hem. Waist measures 30ins/76cms. Inside leg length is 28ins/71cms. Our model is 5ft 6ins. Measurements are taken before listing as due to the vintage they often don't match the label.Our jeans are tagged with the reference number during our photo shoot so you will receive the item as listed.


Whisk the vinegar, lemon juice, garlic, and thyme in a large bowl to blend. Season with salt and pepper. Gradually whisk in the oil. Spoon 3 tablespoons of the marinade into a small bowl. Cover and set aside. Add the zucchini and yellow squash to the remaining marinade in the large bowl and toss to coat. Transfer the mixture to a 13 by 9 by 2-inch glass baking dish. Cover and marinate at room temperature at least 3 hours or cover and refrigerate up to 1 day.
Prepare the barbecue for medium-high heat. Grill the vegetables until they are crisp-tender and brown, turning occasionally, about 8 minutes. Transfer the vegetables to a platter. Drizzle with the reserved marinade and serve hot or at room temperature.


You are here: Home / Are You an Experienced Bioscience Pro?
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Weather isn't looking too pleasant for tonight and sunday, so I had a little fit and drove to Edale instead! I'm on my way up kinder via Grindsbrook and its lovely if not a little windy. Just stopped for a slice of pizza - real hill food! On the look out for a quite pitch to wild camp sometime in the near future. More later.


text:
West Ham to appoint new fitness coach within weeks
Articles / Conditioning/ West Ham
Left to right: Billy McKinlay, Alan Irvine, David Moyes, Stuart Pearce and Chris Woods
Written by Simon Austin — November 20, 2017
WEST HAM manager David Moyes says he hopes to appoint a new fitness coach 'within the next few weeks'.
The previous incumbent, Miljenko Rak, was sacked along with former boss Slaven Bilic on November 6th.
"I'm happy that we have our coaching staff in place," Moyes said. "We're still looking for a fitness coach and I hope we can appoint someone in the next few weeks. As it is, we have three assistant coaches, Alan Irvine, Billy McKinlay and Stuart Pearce."
West Ham's fitness has been the source of much debate and their stats certainly don't look good, no matter which metric you choose.
Injuries: The Hammers suffered the second-highest number of significant injuries (46) and days lost to injury (1737) last season. This had improved so far this season. As of November 7th, they had lost 237 days to injury, which was only the ninth worst record in the Premier League.
Distance covered: As of November 7th, West Ham had the second worst record in the league for distance covered - 1163km. The fact that second-placed Manchester United were bottom (with 1162km) shows that stats don't tell you everything. West Ham were averaging 105km per game under Bilic. This improved to 115.62km against Watford (Moyes' first game in charge), although it was hard to say that their performance had.
Sprints: West Ham had the worst record for total sprints as of November 7th, with 4942. Manchester City were top with 6198.
Bilic downplayed the stats when they were put to him at the start of the month.
"I have all these statistics and more," he said. "They are not the best but in two of the games we had players sent off in the first half and that changes things a lot.
"The inference from the stats is that the players are not fit enough but I don't see us being over-run. We certainly finished strongly against Spurs and worked hard at Palace. Against Brighton, after the third goal, we quit a little because the game was over.
"We are not flying and the stats don't lie but they don't tell you everything."
Former England physio Gary Lewin was appointed Head of Medical Services by the club in the summer, replacing Stijn Vandenbroucke, who left to "take up a new challenge".
READ MORE: West Brom win 2016/17 injury title
Ben Dinnery from Premier Injuries, who provided the injury stats above, told TGG: "Overall, West Ham are faring considerably better in terms of injuries than they did 12 months ago, due in part to the fact they have no European football.
"Their performance, in terms of injuries, from the last few seasons may well have influenced the decision to appoint Gary Lewin as Head of Medical Services."
Rak, 70, certainly had an interesting back story. He was a former professional long jumper who coached both the Croatian handball team and skier Janica Costelic to Olympic gold before working with Bilic for Croatia, CSKA Moscow, Besiktas and West Ham.
ConditioningWest Ham


text:
Balthasar Waltl (* 3. März 1858 in Kirchdorf in Tirol; † 9. Juni 1908 in Innsbruck) war ein österreichischer Porträt-, Historien- und Kirchenmaler.

Balthasar Waltl besuchte die Kunstgewerbeschule in Innsbruck bei Michael Stolz und Caspar Jele und setzte sein Studium ab dem 9. April 1877 an der Königlichen Akademie der Künste in München bei Alois Gabl und Otto Seitz fort.

1890 heiratete er Anna Mayr und erwarb das Anwesen "Rennfeld" in Kitzbühel. 1894 erbaute er die "Villa Waltl" in der Bahnhofstraße.

Waltl beschäftigte sich hauptsächlich mit der Kirchen-, Porträt- und Landschaftsmalerei sowie mit der Restaurierung der Werke alter Meister, wie z. B. der Fresken von Simon Benedikt Faistenberger in der Pfarrkirche in Ellmau. Er malte auch eine Reihe von Altarbildern. In der Pfarrkirche Hopfgarten im Brixental schuf Waltl von 1891 bis 1893 im Rahmen der Kirchenrenovierung Bilder mit Heiligendarstellungen über dem Hochaltar.

Waltl zeigte seine Werke u. a. auf der Tiroler Landesausstellung 1893 und auf der Weltausstellung in St. Louis.

Balthasar Waltl wohnte ab 1902 in Innsbruck und wurde im Innsbrucker Westfriedhof begraben.

In seinem Geburtsort Kirchdorf in Tirol wurde der Balthasar-Waltl-Weg nach ihm benannt.

Literatur

Weblinks

 Gedenken an Balthasar Waltl. Kitzbüheler Anzeiger vom 11. September 2008
 03398 Balthasar Waltl, Matrikelbuch 1841–1884 der Akademie der bildenden Künste München

Einzelnachweise

Maler (Österreich)
Porträtmaler
Kirchenmaler
Person (Kaisertum Österreich)
Person (Cisleithanien)
Geboren 1858
Gestorben 1908
Mann

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His plea was made before Judge Michael Warren in the 6th Circuit Court in Pontiac.
Five felony counts of False Pretenses, $1,000 or more but less than $20,000 – a maximum sentence of five years and/or $10,000, or three times the value of the money or property involved (whichever is greater).
Carta also pleaded to all charges as a Third Offense Habitual Offender, and therefore his sentence may be double the maximum sentence typically permitted for each offense.
From November 2009 to July 2013, Carta and Freedom by Faith Ministries defrauded approximately 100 victims out of more than $300,000 by employing a Ponzi-type scheme promising short sales, mortgage modifications and other real estate scams. Individuals who sought his assistance in resolving mortgage problems were defrauded of amounts ranging between $1,000 and $24,000. Carta pocketed the money and did nothing to help his customers with their financial troubles.
The Michigan Attorney General's Office launched its investigation in 2013 and subsequently filed charges against Carta in 2014 following a series of complaints made to its office.
As part of his plea, Carta agreed that he would be responsible for paying restitution of $658,626.17.
Carta's sentencing is scheduled for 1:30 p.m. Wednesday, May 15, 2019 before Judge Warren in the 6th Circuit Court.


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Why is this episode(s) one of the best?
To be fair, we're cheating a little bit with this one, as it's a multi-parter. That is going to be the case with a lot of these as Power Rangers really excels when it gets to have a miniseries/TV movie. Dark Wish was one such event.
The episode portrays the young adults who are the Power Rangers as real people. They've been fighting for 4 months, and they've grown tired of it. They have magic, and they abuse that magic not for personal gain, but to do their jobs. They have access to a genie, but they aren't allowed to use it to wish their enemies away. This grates on them, until the enemies trick them into using that genie, get a wish of their own, and never become the Power Rangers in the first place.
Teaming up with their enemy Koragg to set the world back to the way it was (Koragg having been betrayed by the current enemy general in charge, and along the way forming an amazing truce with friendy troll, Phineas) the rangers head to another dimension atop a dragon, fight a horde of zombie knights, and parlay with a tribunal of magical deities to reverse their wish. When their request is denied, they get sent back to their new, colorless world, and instead of falling into despair without their magic, take a stand against the bad guys.
The tribunal awards their courage by returning their old world to them, and eventually granting them new powers and zords to boot.
Dark Wish exceeds because it is essentially a cinematic story told in three parts for television.
For all the good Dark Wish does in one sitting, taking it as separate parts really doesn't do it any favors. While Part 2 is a really engaging episode on its own, and I could have just picked that for 19th place, the plot of the episode doesn't work with just the middle piece.
Part 1 of Dark Wish is unnecessarily slow. The monsters for this episode, the Barbarian Beasts, are extremely forgettable villains. Two of them are subjected to footage burning (i.e. they had dedicated episodes in Super Sentai, but were relegated to cannon fodder for Power Rangers) and two of them, while still effective, are just not fun characters. 50 Below speaks about as fast as Cleveland playing an auctioneer on Family Guy, and Fightoe only becomes useful after being killed and stuffed into a mechanical puppet by Imperious.
No one is really a wooden character in these episodes, and that's great, but the effects used for some of the original footage are cringe-worthy. (Fireheart animation, you kill me every time.) Power Rangers is by no means expected to have great cgi, but it has certainly had better than that.
Ask a fan of Power Rangers what his favorite thing to see on screen is and you may be surprised at the answer. Sure, we love the suits. We love the weapons. We love the zords. But, the thing we most enjoy is seeing the rangers fighting, without their suits. Civilian fights are something that made Mighty Morphin' a power house; it showed that even without their powers, these kids could save the world.
Mystic Force, for these episodes anyway, brought a balance. They had powers, sure, but they needed to rely on their ordinary fighting prowess to get themselves through the battle. That balance is something I'm personally hoping for in the new film, and if the trailers are any indication, they're right on the money.
Tickets are available for regular sale as of tomorrow, March 6th!


Hypertrophic pyloric stenosis – the most common cause of gastric outlet obstruction in infants – is characterized by hypertrophy and hyperplasia of the pyloric sphincter in the first months of life. Clinical manifestations usually appear between three and five weeks of age. The primary symptom is regurgitation progressing to nonbilious, projectile vomiting, which occurs intermittently or after feeding. The infant is irritable and demonstrates a strong rooting and sucking reflex because of hunger. Constant vomiting leads to hypokalemic and hypochloremic metabolic alkalosis. The diagnosis is usually clinical and involves the detection of a palpable "olive-shaped" structure in the epigastrium (a sign of marked hypertrophy of the pylorus) and visible gastric peristalsis proximal to the site of obstruction. The condition may also be diagnosed on ultrasound in the absence of a palpable "olive-shaped" structure. Initial management involves adequate rehydration and correction of electrolyte imbalances. The definitive treatment is Ramstedt pyloromyotomy.
Approx. 40% of cases occur in first‑born infants.
The incidence is higher in white populations.
Nowadays, hypertrophic pyloric stenosis is diagnosed early and infants do not generally present with significant electrolyte imbalances!
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2. Krogh C, Gørtz S, Wohlfahrt J et al. Pre- and perinatal risk factors for pyloric stenosis and their influence on the male predominance. American Journal of Epidemiology. 2012; 176(1): pp. 24–31. doi: 10.1093/aje/kwr493.
3. Krogh C, Biggar RJ, Fischer TK et al. Bottle-feeding and the Risk of Pyloric Stenosis. Pediatrics. 2012; 130(4). doi: 10.1542/peds.2011-2785.
4. Olivé AP, Endom EE. Infantile hypertrophic pyloric stenosis. In: Post TW, ed. UpToDate. Waltham, MA: UpToDate. https://www.uptodate.com/contents/infantile-hypertrophic-pyloric-stenosis. Last updated October 19, 2016. Accessed December 30, 2016.
5. Emmett M, Szerlip H. Causes of metabolic alkalosis. In: Post TW, ed. UpToDate. Waltham, MA: UpToDate. https://www.uptodate.com/contents/causes-of-metabolic-alkalosis. Last updated October 9, 2015. Accessed December 30, 2016.
6. Venkatesan T. Cyclic Vomiting Syndrome. In: Cuffari C. Cyclic Vomiting Syndrome. New York, NY: WebMD. http://emedicine.medscape.com/article/933135. Updated March 9, 2016. Accessed December 30, 2016.
7. Desilets DJ. Cyclic vomiting syndrome. In: Post TW, ed. UpToDate. Waltham, MA: UpToDate. https://www.uptodate.com/contents/cyclic-vomiting-syndrome. Last updated May 17, 2016. Accessed December 30, 2016.
8. Hernanz-schulman M. Infantile hypertrophic pyloric stenosis. Radiology. 2003; 227(2): pp. 319–31. doi: 10.1148/radiol.2272011329.