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Colleen Morgan
Research in digital archaeology, heritage, and marginalia
Tag: Catalhoyuk
A Very Neolithic Halloween
Mornings at the Çatalhöyük dig house were a chaos of tools and tea cups. Too many archaeologists were crammed into a small outpost in the middle of the dusty Anatolian plain and civility came later in the day, after breakfast. It is a very particular way of living that not everyone can cope with; in print I've compared it to Goffman's Total Institution:
"a place of residence and work where a large number of like-situated individuals cut off from the wider society for an appreciable period of time together lead an enclosed, formally administered round of life"
The specialists would retreat to their respective labs–paleobot, osteo, zooarch, lithics, pottery, finds–but the excavators would climb up the tell to escape, pushing squeaky wheelbarrows full of tools. The real prize was to be the first to get away, as you got the best tools and a wide open vista of blue sky and long, golden-brown grass. For a moment you could imagine that you were alone on that big hill, fat with archaeology and promise. And quiet. A little wind flapping the tent, but otherwise, gorgeous, gorgeous quiet.
Of course the chaos of the dig house would eventually clamor up the hill after you, and the day would roll on, but you'd hardly notice by then as you were stuck in, troweling, drawing, taking photos, bagging samples and artifacts. We were digging in Building 49, a smallish mudbrick building that fit onto a sheet of permatrace–so under 5m square, almost bijoux, but full of paintings and people buried underneath the floor.
All archaeologists are atheists, but we are all atheists with ghost stories. Actually, that is not even remotely true, I've met my share of witches and christians in the trench, and we are a profession ripe with superstition. I take it as part of my professional ethics not to believe in ghosts or anything remotely supernatural but if you study humans, then you must acknowledge a sort of placebo-effect of religiosity–if you believe it is true, then it is true for you. This is a convoluted way of saying that if you deal with the remains of people for long enough, you will eventually come across things that creep you the fuck out. Sometimes it's not even in the ground.
So on that sunny, slightly misty morning in July, I pushed my rusty wheelbarrow up to the side of the trench. There was a fine layer of dew covering the archaeology, plaster floors, low, muddy walls, and pits where we'd dug several of the eventual 15 bodies to come out from beneath the floors of the house. I was preoccupied with a series of scrappy paintings layered on top of each other, black lines, then squiggles, then hands, then red.
That morning, there in the dew, a line of footprints snaked across the floors and platforms that we'd carefully uncovered the day before. I was digging with two other archaeologists that year and we all stood at the edge of the trench, staring down at the footprints. The feet that had made the prints were bare, medium sized, and it was obvious where they'd came out of the trench and left the tent. What wasn't obvious is where they'd entered the trench.
You see, nobody was allowed on the tell outside of working hours. I'd worked on projects before where people had illicitly come in the night and messed around in the archaeology to hunt for whatever treasure they thought we were after. In this instance, nothing was out of place. Someone probably just had a sunrise amble across the tell. Barefoot. Yeah.
So after a little while we just got on with it, took out our tools and went to work. But we never figured out who took a stroll through the Neolithic that night and I remember wondering if we should have recorded the prints before I used a small brush to gently whisk them into oblivion.
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Author colleenmorganPosted on October 31, 2016 October 31, 2016 Categories ArchaeologyTags Archaeology, Catalhoyuk, excavation, field work, ghost stories, ghost story, neolithic1 Comment on A Very Neolithic Halloween
New Publication: Dig Houses, Dwelling, and Knowledge Production in Archaeology
I was tempted to title our article, "protracted conversational barking" in honor of this hilariously cantankerous quote from Petrie. Dan and I just published a new article in the Journal of Contemporary Archaeology titled Dig Houses, Dwelling, and Knowledge Production in Archaeology which was probably the most fun I've ever had writing an article. Here's a link to the final draft, as it seems that most people don't have access to JCA yet, and I couldn't find the budget to publish it OA. Sorry.
Sadly a lot of the historical research did not quite make it into the article, but we managed to get in a wide range of archaeological dig houses, from Petrie's tomb to the "palace" headquarters of the Tell Asmar excavation, barasti huts in Bahrain, Villa Ariadne and Harriet Boyd Hawes' sanctified bone yard. We also looked at modern dig houses, often hotels, and tried to make a case for more lively places of knowledge production on excavations. And we sneaked in a bit about dig houses hearkening to Goffman's total institution. But maybe that's just Çatalhöyük.
Speaking of Çatalhöyük, our case study in the article describes the destruction of a re-purposed building on the project called the "Chicken Shed," which we argued was an example of what Stewart Brand calls a "low road building"–good to think in, and a great place to come together and remove structural barriers in a project. It was torn down in 2011, in a way that became very symbolic to much of the former team as the end of an era. The virtual reconstruction of the Chicken Shed shared a similar fate, after the end of Okapi Island in Second Life.
Anyway, give it a read and let me know what you think about our "archaeology of us." If you'd like a copy with the figures, drop me a line.
Morgan, C. & Eddisford, D. (2015) Dig Houses, Dwelling, and Knowledge Production in Archaeology. Journal of Contemporary Archaeology 2.1 169-193.
Author colleenmorganPosted on September 12, 2015 September 12, 2015 Categories ArchaeologyTags Archaeology, archaeology dig house, bibbey, Catalhoyuk, dig house, excavation house, expedition house, petrieLeave a comment on New Publication: Dig Houses, Dwelling, and Knowledge Production in Archaeology
50 Years of Visualization at Çatalhöyük
As I previously mentioned, Jason Quinlan and I co-presented a poster at this year's EAA in Istanbul. While it isn't quite as brilliant as Alison Akins' Plague Poster, I enjoyed putting something together about the photography at Çatalhöyük, especially with one of the primary photographers involved!
Regardless, I've put our poster below. Of particular note is the immense increase in the size of the archive after Photoscan was introduced at Çatalhöyük.
Jason and I collaborated on this remotely, and so there is some funny bits with converting between iterations of Illustrator, most notably in the wandering photo code above.
Author colleenmorganPosted on October 7, 2014 October 7, 2014 Categories Archaeology, photographyTags Archaeology, Catalhoyuk, photography2 Comments on 50 Years of Visualization at Çatalhöyük
EAA Istanbul: A Blast from the (Çatalhöyük) Past
Tea on the Ferry across the Bosphorus, taken in 2006 (!)
For the first time ever, I'm attending the European Association for Archaeology (EAA) meetings, 10-14 September in Istanbul. Istanbul is probably my favorite city in the world, so full of chaos and color, heady intellectualism, romanticism and a past that stretches deep beneath the Bosphorus. I don't think my Turkophilia sits all that well with my Turkish friends, who have to struggle with the conservatism of Erdoğan's government and have to fight in the streets to protect themselves from his police state. I worry about my friends in Turkey, I worry about Turkey's slide into militancy, but I also believe in them and their passionate resistance and refusal to be silenced.
So my joy to be returning to Turkey is somewhat tempered by the ongoing struggles of the Gezi protesters and Erdoğan's move from prime minister to president, with the accompanying fears of a cult of personality that will elevate him into an autocratic regime.
Whew–after that fairly heavy-handed politicizing, I'll be presenting in two sessions, both about previous (slightly old & moldy) work that I did regarding Çatalhöyük that I need to publish.
First is a paper: The Life and Death of Virtual Çatalhöyük in Second Life
Abstract: From 2007 until 2011, OKAPI Island in Second Life hosted a virtual reconstruction of the Neolithic village of Çatalhöyük. This simulation included reconstructions of current excavations, past and present lifeways at the site, a virtual museum, and hosted several forums and open days. Using the reconstruction we hosted a mixed reality session,filmed machinima, held university lectures, and collaborative virtual building sessions. OKAPI Island in Second Life was an incredibly fertile proving ground for re-thinking our assumptions about archaeological interpretation and outreach.When Linden Labs, the makers of Second Life, decided to end the educational discount that made OKAPI Island affordable, a team of students and professors at the University of California, Berkeley made the effort to preserve the virtual reconstruction by record, a process that is familiar to archaeologists. After the "death" of a virtual reconstruction of an archaeological site, what lessons can be learned about digital materiality and preservation? How can we use the example of Çatalhöyük in Second Life to inform our future reconstructions? What is next for collaborative virtual work in archaeology?
Since my fairly effusive 2009 work in Archaeologies, (Re)Building in Second Life: Changing Virtual Reality in Archaeology, I wanted to add a coda–so many virtual reconstructions and digital projects are built, published, and we are left to puzzle out what happened later, so I wanted to wrap up all the work that we'd done and the eventual fate of the reconstruction.
I'm also very happy to be putting together a poster with my good friend and colleague Jason Quinlan:
Title: Fifty Years of Visualization at Çatalhöyük
Abstract: Çatalhöyük, a spectacular archaeological site in central Turkey, has been the subject of visual interpretation for half a century. From Ian Todd's photography performed during James Mellaart's 1960s excavations to Ian Hodder's work since 1993, a vast visual record has accumulated of over 100,000 images. The collection records not only site excavation and finds but also embedded changes recorded in the archive's collective "metadata" in both technical and theoretical approaches to site photography over time.
In this poster we explore the changes in technology, methodology and theory at the site as seen in the changing modes of visualization at Çatalhöyük. Through quantitative and qualitative analyses of the visual record, we provide insights regarding the contrasting archaeological processes at the site. Finally, we look to the future of visual interpretation at Çatalhöyük.
I'm happy to finally be able to draw a line underneath my work at Çatalhöyük and get more of my dissertation research out the door!
Author colleenmorganPosted on August 12, 2014 August 12, 2014 Categories academia, ArchaeologyTags Archaeology, Catalhoyuk, eaa, istanbul, photography, second life, turkey, virtual worlds2 Comments on EAA Istanbul: A Blast from the (Çatalhöyük) Past
Open Access Article: An Archaeology of the Contemporary: A Standing Buildings Survey of "The Chicken Shed" at Catalhoyuk
Rainbow over the Chicken Shed by Jason Quinlan
One of the primary goals of this report is to preserve by record the physical nature and some of the history associated with what is now the oldest modern building on the site. A secondary goal is to make visible a rarely-discussed aspect of an otherwise exhaustively recorded enterprise…the study of the use of architecture and space in archaeological dig houses, while secondary to the primary research goals of an excavation, remains an oral tradition on even the most reflexive of excavations. Recording the chicken shed at Catalhoyuk allowed us to consider the history of the site and the reuse of buildings as well as reconsider the social space we live and work in while conducting research on the lifeways of people in the past.
Dan and I wrote a short piece for the 2011 archive about the beloved chicken shed at Catalhoyuk, something that I hope we can expand upon in a more formalized article. You can read the rest here (starting on page 138):
Archive Report 2011
It is all a little bittersweet now that the team has been fully turned-over and the chicken shed is slated for destruction. Anyway, enjoy!
Author colleenmorganPosted on April 2, 2012 Categories ArchaeologyTags Archaeology, Catalhoyuk, contemporary archaeology, dig house2 Comments on Open Access Article: An Archaeology of the Contemporary: A Standing Buildings Survey of "The Chicken Shed" at Catalhoyuk
Pseudoscience, Archaeology, and the Public
There's a minor tussle going on over at Aardvarchaeology and Archaeological Haecceities over a public lecture at Linnaeus University in Sweden. The lecture is by Semir Osmanagich, a fringe "archaeologist" who claims to have found pyramids in Bosnia. I actually posted about this back in 2008 with photos of some of the nice geological sections that have been gouged into the hill:
https://middlesavagery.wordpress.com/2008/10/12/the-bosnian-pyramids/
When I saw the invite to the lecture "The Bosnian Valley of the Pyramids in Context," I have to admit that I cringed–surely a university wouldn't lend any credibility to this obvious hoax. In the comments over at Aardvarchaeology, Cornelius Holtorf explains, courtesy of Google Translate:
We invite him, not because we are his interpretations of scientific seriousness, but because we think we have to discuss his work and its effects. The Bosnian pyramids have affected not only tourism and the perception of cultural heritagein Bosnia, but is also how we look at the cultural heritage of the wider community. Can fictional heritage have the same (or greater) power than genuine cultural heritage? What is it that the tourists are really looking for when they visit cultural heritage sites and how they present archeology and heritage to the world media so that it has an impact? What is Osmanagich himself at his critics within the scientific archeology and the archaeologists who work in Bosnia?"
This should be an interesting talk–I'd very much like to see the lecture and the discussion afterwards. Osmanagich's work is fascinating in this respect; how did he get so far with such an obvious hoax? Why is the idea of pyramids in Bosnia so compelling to so many people? I admire Dr. Holtorf's work and would like to be as high-minded, inclusive and controversial as he is–I mean, why not discuss the implications of imaginary heritage when compared to actual cultural heritage? Sadly I think I would have a problem getting past Osmanagich's wanton destruction of actual archaeological sites while bulldozering for imaginary architecture, and I hope someone at Linnaeus University takes him to task for that. A full rundown of the situation is available on wikipedia:
http://en.wikipedia.org/wiki/Bosnian_pyramids
Oddly enough, an interesting parallel popped up on the Catalhoyuk facebook page–a handful of posts by Artūras Jazavita, projecting a "proportional grid" on many of the photographs of artifacts and architecture:
His proposition is that the Catalhoyuk "proportional grid" is the same as Gobekli Tepe, a claim that oddly echos some of the recent academic literature about Gobekli. By posting his photos on my blog, am I giving him undue credence? Or am I putting it into context, much like the invited lecture above? Should the Catalhoyuk Facebook page owner delete the posts? I actually find the inscribed photographs strangely beautiful, though completely imaginary in their claims:
By offering high-quality digital images to the public, there is a risk of our photographs being co-opted by pseudoscientists who use them to advance these specious claims. We could restrict access to the photographs, or not invite controversial speakers to our universities, but perhaps this would rob us of the chance to counter the claims, or even for us to draw inspiration from their imaginations. As I understand the situation, Dr. Holtorf wants to know why Osmanagich's work is so compelling, and perhaps then try to refocus this public interest back to actual cultural heritage. Artūras' images made me want to take out my drawing tablet and sketch on some archaeological photographs. Can we co-opt the co-opters? Can we steal back the imaginations of the public from the psuedoscientists?
Author colleenmorganPosted on October 17, 2011 October 17, 2011 Categories academia, Archaeology, ethics, new mediaTags Archaeology, Catalhoyuk, gobekli tepe, pseudoscience8 Comments on Pseudoscience, Archaeology, and the Public
Is it all Macabre? Recent Murals from Çatalhöyük
Ian Hodder and Lynn Meskell published a piece titled "A 'Curious and Sometimes a Trifle Macabre Artistry': Some Aspects of Symbolism in Neolithic Turkey" in the April 2011 issue of Current Anthropology. It's paywalled, sadly, but you can read the abstract for free, which I'll copy here:
Comparison of two Turkish Neolithic sites with rich symbolism, Çatalhöyük and Göbekli, suggests widespread and long-lasting themes in the early settled communities of the region. Three major symbolic themes are identified. The first concerns an overall concern with the penis, human and animal, that allows us to spread of a phallocentrism in contrast to the widely held assumption that the early agriculturalists in the Middle East emphasized the female form, fertility, and fecundity. The second theme concerns wild and dangerous animals, even in sites with domesticated plants and animals, and particularly the hard and pointed parts of wild animals, such as talons, claws, horns, and tusks. We interpret this evidence in relation to providing food for large-scale consumption and the passing down of objects that memorialize such events within specific houses. The third theme is that piercing and manipulating the flesh were associated with obtaining and passing down human and animal skulls. The removal of human heads was also associated with symbolism involving raptors. Overall, we see a set of themes, including maleness, wild and dangerous animals, headlessness, and birds, all linked by history making and the manipulation of the body.
This summer about half of the excavators read the article and it became a hot topic of discussion, discussions that obviously quickly degenerated into "finding cock" on site. I don't necessarily have a huge problem with the article, but I think it is an interesting example of just how different interpretations can be on site. I don't have a lot to say about Göbekli, though I'd love to work there, but I find myself mystified at some of the central arguments regarding the Çatalhöyük imagery.
There is little doubt that there are a lot of little penis figurines. They're really cute, and though they're not prominently featured, you can check them out here:
http://figurines.stanford.edu/repository/index.php?cat=27
There are also a whole lot of cute little fat people. Are they ladies? Are they guys? Does the sex or gender matter? You'd have to ask a figurine expert. I have to say that I generally prefer the little animals:
So cute! There is little doubt that there is a variety of imagery coming from the figurines. To be fair, the Macabre article cited above is also ambiguous about the figurines, though they state that a lot of the zoomorphic figurines are represented by horns which they link to maleness. But female aurochs and sheep/goats had horns too…perhaps that is beside the point. In contrast to the hard things that are emphasized in the article, the horns, claws, beaks, etc, I can't help but remember the soft curves of the benches, pillar caps, ovens, and the voids of the crawl-holes and niches that are often nearby in the same house.
I should probably just skip to the heart of what is bothering me–the murals. In the 1960s Mellaart's team excavated a stunning array of murals, a few of which I had the pleasure of seeing up close and personal a couple of days ago in the Museuem of Anatolian Civilizations. A couple of these murals depict hunting scenes and wild animals, but the majority of the murals on site are geometrical patterns, solid blocks of red, or hands, many of them child-sized. These former hunting scenes are what dominate the article, with no mention of the geometric patterns found in a majority of the paintings uncovered.
This year an extraordinary large panel was uncovered (by a fantastically dedicated team of undergraduates and conservators!) in the South shelter area. This painting was similar to a painting that I excavated in building 49 in 2008, with twisting, cellular shapes that look like an M.C. Escher-esque interpretation of a mudbrick village.
Photo by Jason Quinlan, click through to see the detail.
A few days ago ten red hands were discovered in the 4040 area, again by a trusty group of undergraduates who had to pick away at the plaster layer by layer to reveal the paintings. Hands are everywhere on the site–tiny, large, red, orange, white–yet they are only mentioned in reference to their redness, which Hodder and Meskell link to the representation of blood.
So, while I'm not a big fancy famous archaeologist by any means, I am dissatisfied with the picture that Hodder and Meskell paint of the imagery at the site. I have little doubt that blood, sex/penises, and wild animals were very much a part of life in the Neolithic, and I know that Hodder and Meskell were not trying to provide a holistic view of imagery at Çatalhöyük. But I feel like they miss other, perhaps more interesting aspects of the abstract imagery in their focus on the figural/phallic.
What are people doing when they are creating geometric shapes and connecting them in patterns? Even as they were excavating the latest panel, the students were speculating that the patterns were bricks, roads, or…"just doodles." While the last suggestion is tempting, there was too much preparation involved in priming the surface and mixing the paint. Do they represent weaving, as was speculated by Mellaart, or counting, or even architecture–the cellular forms look like bricks, after all. Just what is the brain doing when it is creating abstract designs? What kinds of synaptic paths are formed? Many of these paintings are overlaid, time and time again, often directly on top of one another. Why? And if there are disruptions in the continuity, can they be linked to other stratigraphic "events"?
I'd also like more a more systematic study of the hand paintings. Where do they occur? How many are created with an actual hand? What sizes/shapes are they? Why are there so many of them? Can they be tied to other archaeological "moments" in the stratigraphy? Do these moments correlate across buildings?
There are seven responses to the Macabre article, and then a response to the criticism from Hodder and Meskell. All of the responding professors are better equipped than I am to provide a larger perspective to the article–I can only mention what I've read over the years, what I have uncovered with my hands, and what my fellow excavators have shown me. These moments, by the way, are the best–when the person in the next trench over catches my eye and waves me over. The discussion in low tones over a discovery, sometimes only just beginning to be revealed, before the conservators, the directors, and certainly the news media get to see it. That simple shared wonder over the stuff of the past. To get back to the article, while this sense of discovery does not necessarily privilege my interpretation over that of more experienced archaeologists, I cannot help but feel like this part of the past is erased when omitted from larger narratives constructed about the site.
(edited March 4, 2013, after Stanford decided to break all of my image links.)
Author colleenmorganPosted on August 17, 2011 March 3, 2013 Categories academia, anthropology, Archaeology, ArtTags ancient art, Archaeology, Catalhoyuk, interpretation, multivocality, wall paintings5 Comments on Is it all Macabre? Recent Murals from Çatalhöyük
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There are schools offering film programs in Texas!
Click to browse online film schools >
Schools Offering Film Programs in Texas
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See All Schools in Texas
Schools in TX
Each year, roughly 0.0% of Texas students graduate with degrees in film. In other words, every year an estimated 117 film professionals graduate from Texas' 12 film schools.
The top-ranked school in Texas that has a film program is Southern Methodist University. Southern Methodist University, which was ranked 63rd in the country in 2010, is located in Dallas. 40 students graduated with a degree in film from Southern Methodist University in 2010. Southern Methodist University charged in-state students $37,230 in tuition fees per year.
South University-The Art Institute of Dallas, which was ranked 77th nationwide in 2010, is the second-ranked school in Texas that has a film program. It is located in Dallas. In 2010, 20 students graduated from South University-The Art Institute of Dallas film program. Tuition at South University-The Art Institute of Dallas was $17,618 per year.
The third-ranked school in Texas with a film program is K D Studio, which is located in Dallas. In 2010, it was ranked 79th nationwide. Students at K D Studio paid $15,215 per year in tuition fees.
Tuition at Texas' film schools ranges from $37,230 per year to $1,394 per year. But, the average tuition is $8,235 per year. In 2010, the following Texas film schools had the highest tuition rates:
Southern Methodist University - located in Dallas, students are charged $37,230 per year
South University-The Art Institute of Dallas - located in Dallas, students are charged $17,618 per year
The Art Institute of Austin - located in Austin, students are charged $17,568 per year
The film schools that charged the lowest tuition rates in Texas were:
Houston Community College - located in Houston, students are charged $1,394 per year
San Jacinto Community College - located in Pasadena, students are charged $1,410 per year
South Plains College - located in Levelland, students are charged $1,468 per year
A film degree from a Texas school... what next?
The following counties have the largest number of Texas film professionals:
Collin County - 370 film professionals
Austin County - 170 film professionals
Atascosa County - 70 film professionals
According the US Bureau of Labor Statistics, the number of film professionals is expected to grow by 8% by 2018. There are projected to be 2,330 film professionals working in Texas then. Of these 2,330 film professionals, the government predicts that 620 will be exhibit designers, 1,460 will be camera operators, and 250 will be camera equipment repairers.
film professionals in Texas make an average of $38,990 per year. But, salaries for film professional can vary. In 2010, film professional made as little as less than $15,630 per year or as much as more than $69,820 per year in Texas. Film professionals in the following Texas counties make the highest salaries on average:
Atascosa County - $47,540 per year
Collin County - $43,365 per year
Johnson County - $42,485 per year
On average, film professionals earn the least in the following Texas counties:
El Paso County - $27,460 per year
Bastrop County - $31,610 per year
Austin County - $37,045 per year
On average, the highest paid film professionals in Texas were:
Exhibit Designer - $42,180 per year
Camera Equipment Repairer - $39,170 per year
Camera Operator - $35,620 per year
On average, the lowest paid film professionals in Texas were:
For more data regarding a career in film in Texas and to compare salaries with various related fields such as design or art, take a look at the graphs and charts below.
Associate's Degree in Film in Texas
Bachelor's Degree in Film in Texas
Master's Degree in Film in Texas
Certificate in Film in Texas
Curious what studying Film gets you?
Check out the different options and how they're looking in Texas
Camera Operators, Television, Video, and Motion Picture 890 $35,620 41.3%
Set and Exhibit Designers 500 $42,180 -51.9%
Camera and Photographic Equipment Repairers 130 $39,170 85.7%
Below are film related jobs in Texas

redpajama_set_name: RedPajamaCommonCrawl


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Себастья́н Алеха́ндро Батта́лья (; родился 8 ноября 1980 в Санта-Фе) — аргентинский футболист, победитель Кубка Либертадорес в составе «Боки Хуниорс» (2000, 2001, 2007). Игрок сборной Аргентины. Один из самых титулованных футболистов в современном футболе.

Биография
Себастьян Алехандро Батталья родился в 1980 году в Санта-Фе, но начал заниматься футболом в академии столичного гранда «Боки Хуниорс». За основу он дебютировал 31 мая 1998 года, и с 1999 года стал играть важную роль в игровых порядках «Боки». Он был одним из тех людей, которые прошли с командой период роста конца 1990-х годов, когда «сине-золотые» только начинали выходить из многолетнего застоя, до громких побед в чемпионате Аргентины и на международной арене, вместе с такими звёздами мирового футбола, как Мартин Палермо, Хуан Роман Рикельме, Роберто Аббондансьери, Оскар Кордоба, Гильермо Баррос Скелотто и другими.

После побед в трёх чемпионатах Аргентины, трёх Кубках Либертадорес, двух Межконтинентальных кубках, посреди сезона 2003-2004 годов Батталья присоединился к испанской команде «Вильярреаль», в которой тогда был чёткий уклон на покупку бывших игроков «Боки» — помимо Палермо и Рикельме, там также выступали Диего Канья, Родольфо Арруабаррена, Фабрицио Колоччини. «Вильярреаль» выкупил 50% прав на Батталью за 2,8 миллиона евро. Но в Испании Батталья выступал лишь полтора сезона. Он не смог приспособиться к непривычному для себя европейскому футболу. Кроме того, его семья тяжело переживала переезд в чужую страну. После травмы, которая вывела Батталью из строя на полгода, Себастьян в июле 2005 года вернулся в родной клуб.

В «Боке» Батталья постепенно вернул утраченную форму и вскоре стал одним из самых опытных и уважаемых игроков основы, что привело к его избранию капитаном команды. Он вновь стал вызываться в сборную Аргентины, чего не было в испанский период карьеры.

По возвращении в Аргентину к Баталье вновь стали приходить самые разнообразные титулы: четвёртый Кубок Либертадорес, Южноамериканский кубок, три Рекопы, ещё три победы в чемпионате Аргентины. 23 декабря 2008 года, когда Бока стала победителем Апертуры, Батталья сравнялся по количеству титулов в составе «генуэзцев» с предыдущим абсолютным рекордсменом, Густаво Барросом Скелотто (по 16 за профессиональную карьеру).

Почти весь 2011 год у Баттальи ушёл на лечение. Он сыграл лишь в одном матче Апертуры, который в результате выиграла «Бока». Этот трофей стал в карьере Баттальи 17-м, выигранным с «Бокой». Также из-за травмы левого колена Себастьян пропустил всю Клаусуру 2012 и розыгрыш Кубка Либертадорес того же года, в котором «Бока» дошла до финала.

В апреле 2013 завершил карьеру игрока.

17 августа 2021 года назначен исполняющим обязанности главного тренера «Бока Хуниорс» после увольнения Мигеля Анхеля Руссо.

Титулы
 В качестве игрока
  Чемпион Аргентины (8): Апертура 1998 (не играл), Клаусура 1999, Апертура 2000, Апертура 2003, Апертура 2005, Клаусура 2006, Апертура 2008, Апертура 2011
  Обладатель Кубка Аргентины (1): 2011/12 (не играл)
 Обладатель Кубка Либертадорес (4): 2000, 2001, 2003, 2007
 Обладатель Южноамериканского кубка (1): 2005
 Обладатель Рекопы (3): 2005, 2006, 2008
  Обладатель Кубка Интертото (1): 2004
 Обладатель Межконтинентального кубка (2): 2000, 2003

 В качестве тренера
  Обладатель Кубка Аргентины (1): 2019/20
  Обладатель Кубка Профессиональной лиги (1): 2022

Примечания

Ссылки

 Статистика в чемпионате Аргентины
 Статистика

Футболисты Аргентины
Игроки сборной Аргентины по футболу
Игроки ФК «Бока Хуниорс»
Игроки ФК «Вильярреал»
Футбольные тренеры Аргентины
Тренеры ФК «Альмагро»
Тренеры ФК «Бока Хуниорс»

redpajama_set_name: RedPajamaWikipedia


text:
Home » Pratoni 2022 eventing entry list is bursting with talent
Pratoni 2022 eventing entry list is bursting with talent
FEI Eventing World Championship will be underway on September 15-18 in the beautiful surroundings of Pratoni del Vivaro, Italy, and it promises to be a thrilling competition
Julia Krajewski (GER) oro individuale ai Giochi di Tokyo con Amande de B'Neville - © FEI/Christophe Taniére
Bologna, August 19th 2022 – In just four weeks' time, the FEI Eventing World Championship will be underway on September 15-18 in the beautiful surroundings of Pratoni del Vivaro, Italy, and it promises to be a thrilling competition.
Nominated entries closed this week and an impressive number of nations – 27 – will be represented, with 17 of them potentially fielding a team.
The complete list of nominated riders includes such well-established and famous names as Australia's triple Olympic gold medallist Andrew Hoy, dual European champion Pippa Funnell (GBR), former world number one William Fox-Pitt (GBR), a European team gold medallist at Pratoni in 1995, Phillip Dutton (USA), who could be contesting his ninth consecutive World Championship, and Karin Donckers who has been representing Belgium at championship level for three decades.
The last three individual World Champions from 2010, 2014 and 2018 respectively are listed – Michael Jung (GER), Sandra Auffarth (GER) and Ros Canter (GBR) – plus Nicolas Touzaint (FRA), who won the European title at Pratoni in 2007, and world number one Oliver Townend (GBR), a member of the winning British team in 2007 and the reigning Olympic champion, Julia Krajewski (GER).
Alongside such legendary names are a brand-new generation Felix Vogg, the first Swiss CCI5*-L winner for 71 years, his compatriot Robin Godel, who won the Pratoni Test Event in May, Japanese rider Kazuma Tomoto, fourth individually at Tokyo Olympic Games, and Lissa Green (AUS), whose mother, Lucinda, won the 1982 title for Great Britain.
New Zealand, the country that dominated the last World Championship at Pratoni, in 1998, through Blyth Tait, Mark Todd, Vaughn Jefferis and Andrew Nicholson, now has a new generation of riders headed by power couple Jonelle and Tim Price, number two and three on the FEI World Rankings for Eventing, plus Amanda Pottinger, whose mother, Tinks, competed in the 1986 World Championships.
Tim Price (NZL) on Falco at the Test Event in May at Pratoni – © Massimo Argenziano
Great Britain, who won both FEI European Eventing Championships at Pratoni, in 1995 and 2007, also has new names in the form of Olympic gold medallists Tom McEwen and Laura Collett, plus Yasmin Ingham, second on her CCI5*-L debut this year.
«With such an incredible range of talent this promises to be a very competitive World Championship which will result in some truly deserving medallists,» commented Giuseppe Della Chiesa, Event Director and Course Designer for cross country. «It is very exciting to see so many nations competing and I think we are all intrigued to see who will be standing on the podium at the end.»
Definite entries are due on September 5. At this stage, the following nations could enter teams: Australia, Austria, Belgium, Brazil, Canada, France, Great Britain, Germany, Ireland, Italy, Japan, New Zealand, Poland, Spain, Switzerland, Sweden and USA.
Ten nations will be represented by individual riders: China, Czech Republic, Denmark, Ecuador, Hungary, India, Lithuania, Mexico, Netherlands and Thailand.
For details of tickets and timetabling, visit www.pratoni2022.it
English / 24 Settembre 2022
Fise4All, the 'special' service to the sport
In the occasion of the FEI World Championships 2022, the 'special' assistance service Fise4All enabled people with mobility impairments to follow the action
Eventing / 17 Settembre 2022
Germany takes charge on a thrilling cross-country day
It was anticipated that cross-country day at the FEI Eventing World Championship at Pratoni del Vivaro, Italy, would be thrilling, and it did not disappoint. Jung in the lead
Pratoni 2022: did you know that…
Facts and figures that can drive attention on the World Eventing. Things you probably didn't know about competitors at Pratoni 2022
Michael Jung and British Team smash all records
Records are there to be broken and that is what happened on a thrilling second day of dressage at the 15th FEI Eventing World Championship, at Pratoni del Vivaro, Italy
The cross-country course at Pratoni 2022
The track for the Fei World Championship Eventing cross-country at Pratoni 2022 has good sandy going and is a clever mix of let-up fences and challenging combinations. Giuseppe Della Chiesa is the course designer


For Spring 2019, the Capucines BB handbag graduates in colour from deep Lie de Vin red at its base to a vivid pink at the top. Crafted from supple Taurillon leather, its strap allows it to be worn over the shoulder or across the body. Alternatively, the strap may be removed in order to carry it by the dainty top handle.


Place butterflied shrimp in a shallow dish.
Combine all the remaining ingredients except the oi and pour over the shrimp.
Cover and refrigerate one to two hours, turning shrimps occasionally.
Take shrimp out of the marinade and deep fry at 365 degrees for about one minute, or until shrimp are just cooked through.
Serve with spanish rice while hot.


text:
Leighton Buzzard teenager who failed breath test jailed for two years after fatal collision at Linslade pedestrian crossing
Benito Mattei
Published: 13:16 Monday 17 June 2019
A drink-driving Leighton Buzzard teenager has been jailed after a pensioner sustained fatal injuries in a collision at a pedestrian crossing in Linslade last year.
Benito Mattei, 19, of Garland Way, was sentenced at Luton Crown Court on Thursday to two years imprisonment, of which he has to serve at least half, after he pleaded guilty to causing death by dangerous driving. He was also disqualified from driving for three years.
At approximately 10.30pm on August 31, 2018, Mattei was driving a dark coloured Ford Fiesta when he struck a 72-year-old man on the pedestrian crossing. Mattei was arrested shortly after the incident after failing a roadside breath test.
The victim was transported to hospital, but passed away two days later on September 2, 2018.
Mattei admitted to consuming alcohol prior to driving and, even after two-and-half hours, he provided a sample which proved to be over the limit.
PC Matthew Jacob, from the Bedfordshire, Cambridgeshire and Hertfordshire Roads Policing Unit, said: "This was a tragic incident in which a man sadly lost his life. Mattei immediately admitted his wrongdoing to the officer who arrested him at the scene and later during a police interview.
"At no point did he make any excuses for his actions, and took full responsibility for the tragic consequences of them.
"This case is a grim reminder of the devastating impact of drink driving.
"A man has lost his life, a family have lost a loved one, and a young man has, for the rest of his life, got to carry the weight of that burden on his shoulders.
"I would like to ask everyone who considers driving after consuming alcohol to think twice. Even if you feel fine, there is no point taking this risk. Be safe and take a taxi home."
Alcohol is one of the main causes of death on the roads and is a one of the Fatal Four, those being alcohol/drugs, speeding, not wearing a seatbelt and using a mobile phone behind the wheel. If you believe someone is about to drive following consumption of alcohol or drugs call 999 immediately - this may save someone's life.
Beds Police chiefs call for tougher sentences for attacks on police officers


text:
<?php

declare(strict_types=1);

namespace Sonata\PageBundle\Page\Service;

use Sonata\PageBundle\Model\PageInterface;
use Symfony\Component\HttpFoundation\Request;
use Symfony\Component\HttpFoundation\Response;

/**
 * Interface for a page service responsible for the management of pages from a given type.
 *
 * This class acts as a page controller that manages the life-cycle of a page type. It may handle pages that do not
 * necessarily have a symfony route or a symfony controller, such as pure cms pages, but that still require some
 * processing such as data loading or http headers.
 *
 * For other page types, this service may contain the action that would normally be set within a controller, and may
 * also provide additional information or behavior related to this type of pages.
 *
 * @author Olivier Paradis <paradis.olivier@gmail.com>
 */
interface PageServiceInterface
{
    /**
     * Returns the page service name.
     *
     * @return string
     */
    public function getName();

    /**
     * Executes the page. This method acts as a controller's action for a specific page and is therefor expected
     * to return a Response object.
     *
     * @param PageInterface $page       Page to execute
     * @param Request       $request    Request object
     * @param array         $parameters An array of view parameters. In the case of hybrid pages, it may have a
     *                                  parameter "content" that contains the view result of the controller
     * @param Response|null $response   Response object
     *
     * @return Response
     */
    public function execute(PageInterface $page, Request $request, array $parameters = [], ?Response $response = null);
}

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}

In the past decade, the negatively charged nitrogen-vacancy (NV) centre in diamond \cite{Doherty_RPP_2013}
has emerged as a very versatile solid-state system for studies of quantum information \cite{Toyli_MRS_2013}.
The main characteristics that make it unique \cite{Doherty_RPP_2013} are its paramagnetic ground state
\cite{Loubser_RPP_1978}, bright luminescence, extremely long spin coherence times \cite{Balasubramanian_NM_2009},
coupling to nearby nuclear spins \cite{Childress_Science_2006}, and the ability to initialize and read out the spin
using optical techniques \cite{Jelezko_PRL_2004a,Jelezko_PRL_2004b}. Increasingly, NV centres in bulk crystals and
nanodiamonds are used for metrological applications at the nanoscale, i.e., for measuring local magnetic \cite{Taylor_NP_2008}
and electric \cite{Dolde_Nature_2011} fields, temperature \cite{Acosta_PRL_2010,Toyli_PRX_2012,Toyli_PNAS_2013}, and pressure
\cite{Doherty_PRL_2014}.

The negatively charged NV centre possesses $C_{3v}$ symmetry and consists of a substitutional nitrogen atom
adjacent to a nearby carbon vacancy (figure \ \ref{fig-NV}(a)) with an additional trapped electron, the total electric
charge thus being $-1$. The electronic structure of the ground and the lowest excited states of the centre
is mainly determined by four electrons in atomically localized states of $a_1$ and $e$ ($e_{x}$ and $e_{y}$)
symmetries; the energy level diagram of the many-electron system is shown
in figure \ref{fig-NV}(b) \cite{Doherty_NJP_2011,Maze_NJP_2011}. The basics of NV physics is understood in terms
of the ground-state triplet $^3\hspace{-0.5mm}A_2$ state (configuration $a_1^2e^2$), the excited state
triplet $^3\hspace{-0.5mm}E$ state (configuration $a_1^1e^3$), and two singlet ``dark'' states $^1E$
and $^1A_1$ (configuration $a_1^2e^2$). The singlets play a crucial role in both initialization and
read-out of the ground-state spin \cite{Doherty_RPP_2013}.

\begin{figure}
\begin{center}
\includegraphics[width=15.5cm]{fig1.eps}
\caption{
(a) Schematic representation of the NV centre. Green: carbon atoms; blue: nitrogen atom.
The dashed circle indicates the position of the carbon vacancy.
The pink isosurfaces depict the wavefunctions of the single-electron $a_1$ and $e$ states.
(b) Energy-level diagram of the negatively charged NV centre. The luminescence occurs
between triplet states $^3\hspace{-0.5mm}E$ and $^3\hspace{-0.5mm}A_2$. $E_{ZPL}$ is the energy of
the zero-phonon line. (c) One-dimensional cc diagram illustrating luminescence.
$\Delta E_{\{e,g\}}$ are relaxation energies in the excited and the ground state.
}
\label{fig-NV}
\end{center}
\end{figure}

Nearly all of the applications of NV centres rely on measuring photoluminescence between
$^3\hspace{-0.5mm}E$ and $^3\hspace{-0.5mm}A_2$ electronic states as a function of other
experimental parameters \cite{Doherty_RPP_2013}. At low temperatures the luminescence band \cite{Davies_PRS_1976}
consists of a sharp zero-phonon line (ZPL) at $E_{ZPL}=1.945$ eV (637 nm), and $\sim 4$ increasingly broad phonon
replicas with a phonon energy of $\sim63$-$65$ meV, as schematically shown in figure \ref{fig-NV}(c). A detailed
analysis of the experimental phonon sideband was performed by Davies \cite{Davies_RPP_1981}. In particular,
he determined the weight of the ZPL $w_{ZPL}\approx2.4$ \% and a Huang-Rhys (HR) factor
\cite{Huang_PRCL_1950}, in essence the average number of phonons emitted during the optical
transition (see Section \ref{theory} for a quantitative definition), $S=3.73$.

The relevance of the NV centre to a variety of applications and the crucial importance
of the luminescence band in all these applications raises a question: can the luminescence
lineshape, i.e., the electron-phonon coupling during the optical transition, be calculated using
first-principles calculations that require no experimental input? Such calculations should
address an accurate determination of the Huang-Rhys factor, frequencies of dominant phonon
modes, as well as the fine structure of the phonon sideband, including the coupling to long-range
acoustic phonons. Previous work \cite{Gali_NJP_2011,Zhang_PRB_2011}
has addressed the vibrational structure of NV centres to some extent; however, because
of finite-size effects the results of these calculations are somewhat ambiguous.
No first-principles calculation of the luminescence lineshape has been performed to date. Such a
calculation would provide valuable information about electron-phonon coupling at NV centres, which at present
is incompletely understood \cite{Doherty_RPP_2013}. In addition, if the theory is \emph{predictive}, it can
be applied to other defects, for example alternative systems that are currently being actively considered for
quantum information and metrology applications \cite{Weber_PNAS_2010,Koehl_Nature_2011,Gali_pss_2011,Baranov_PRB_2011},
or defects that play an important role in light-emitting diodes \cite{Reshchikov_JAP_2005,Brgoch_JPCC_2013}.

In this work we present accurate calculations of the vibronic structure pertaining to the triplet luminescence
band of the NV centre in diamond. We demonstrate that the combination of state-of-the-art first-principles methods,
in particular hybrid density functional theory \cite{Heyd_JCP_2003}, and computational techniques to address
electron-phonon coupling at large enough length scales to accurately include long-wavelength
acoustic phonons, is very successful in describing the luminescence lineshape and all the related parameters.
The experimental luminescence spectrum which serves as a benchmark for the theoretical study has been measured
in our laboratory.
The measured luminescence band is of a comparable quality to those of Refs.\
\cite{Santori_NT_2010} and \cite{Kehayias_2013}.

This paper is organized as follows. In Section \ref{theory} we outline the general theory to calculate
the vibrational structure of luminescence bands and describe our computational approach. In Section
\ref{experiment} the details of acquiring and processing the experimental spectrum are presented.
The results are presented in Section \ref{results} and analyzed in Section \ref{analysis}. Section \ref{conclusions}
contains our conclusions. The paper is supplemented with four appendices that discuss specific technical
issues in more detail.

\section{Theory and computational methodology \label{theory}}

\subsection{Luminescence \label{theory2}}

The excited state $^3\hspace{-0.5mm}E$ is an orbital doublet that forms an $E\otimes e$
Jahn-Teller system via coupling to $e$ phonon modes \cite{Davies_RPP_1981,Fu_PRL_2009,Abtew_PRL_2011}.
The Jahn-Teller effect is dynamical, since the energy splitting between the vibronic sub-levels
is larger than the barrier in the adiabatic potential energy surface $\delta \approx 10$ meV
\cite{Abtew_PRL_2011}. The presence of this effect is manifest in the broadening of the
ZPL that follows a $\sim T^5$ rather than the usual $\sim T^7$ dependence at low temperatures
\cite{Fu_PRL_2009,Abtew_PRL_2011}. However, the effect is weak \cite{Abtew_PRL_2011},
and we will neglect it when calculating the phonon sideband. One way to judge the validity of this
approximation is via an \emph{a posteriori} comparison \cite{Davies_RPP_1981}. If a linear model of
electron-phonon interactions, such as the one employed in this work, accurately describes the lineshape
of the optical transition, then the Jahn-Teller effect can be considered negligible for this particular
transition. As we show below, this turns out to be the case for the triplet luminescence at NV centres.

We also assume that the transition dipole moment $\vec{\mu}_{eg}$ between the excited and the ground
state depends weakly on lattice parameters (the Franck-Condon approximation). At $T=0$ K the absolute luminescence
intensity $I(\hbar\omega)$ (i.e., photons per unit time per unit energy) for a given photon energy $\hbar\omega$
and for one emitting centre is given by (in SI units) \cite{Stoneham}:
\begin{equation}
I(\hbar\omega)=\frac{n_{D}\omega^3}{3\varepsilon_0\pi c^3 \hbar}\left|\vec{\mu}_{eg}\right|^2
\sum_m\left| \left \langle \chi_{gm}|\chi_{e0} \right \rangle \right |^2
\delta \left(E_{ZPL}-E_{gm}-\hbar\omega\right).
\label{Lum-int}
\end{equation}
Here $n_D=2.4$ is the refractive index of diamond; $\chi_{e0}$ and $\chi_{gm}$ are
vibrational levels of the excited and the ground  state; $E_{gm}$ is the energy of the state $\chi_{gm}$,
being the sum over all vibrational modes $k$, i.e., $E_{gm}=\sum_{k}n_{k}\hbar\omega_k$; and
$n_k$ is the number of phonons of type $k$ in this state. The absolute angle-averaged value of $\mu_{eg}$
is $\sim 5.2$ Debye, as extracted from the radiative lifetime $\tau=13$ ns of the $m_s=0$ spin state of the $^3 E$
manifold \cite{Doherty_RPP_2013}. A prefactor $\omega^3$ in equation (\ref{Lum-int}) arises from the density of states
of photons that cause the spontaneous emission ($\sim\omega^2$), and the perturbing electric field of those
photons ($|\vec{\cal{E}}|^2\sim\omega$). This prefactor has to be taken into account
when determining parameters pertaining to the luminescence lineshape, and this will be discussed in Section \ref{HR3}.
Since in both the excited and the ground electronic state the system has $C_{3v}$ symmetry,
only fully symmetric $a_1$ phonons contribute to the sum in equation (\ref{Lum-int}).

The experimental determination of the absolute luminescence intensity given in equation (\ref{Lum-int}) is difficult.
Thus, in this work we will consider the normalized luminescence intensity, defined as
\begin{equation}
L(\hbar\omega)=C\omega^3\hspace{-0.5mm}A(\hbar\omega),
\label{Norm-lum-int}
\end{equation}
where
\begin{equation}
A(\hbar\omega)=
\sum_m\left| \left \langle \chi_{gm}|\chi_{e0} \right \rangle \right |^2
\delta \left(E_{ZPL}-E_{gm}-\hbar\omega\right)
\label{spectral}
\end{equation}
is the optical spectral function, and $C$ is the normalization constant: $C^{-1}=\int A(\hbar\omega) \omega^3 d(\hbar\omega$).
$I(\hbar\omega)$ is related to $L(\hbar\omega)$ via $I(\hbar\omega)=n_{D}/(3C\varepsilon_0\pi c^3 \hbar)L(\hbar\omega)$.

The evaluation of the overlap integrals $ \left \langle \chi_{gm}|\chi_{e0} \right \rangle $
immediately poses a challenge. Vibrational modes that enter into equation\ (\ref{spectral}) are not those of the
pristine bulk, but rather those of the solid with a defect.  The use of bulk modes can lead to large discrepancies
with experiment, as we will show in Section \ref{results}. Lattice imperfections induce
localized or quasi-localized vibrational modes that depend on the local electronic structure; in addition, the normal
modes in the excited state and the ground state can be in principle quite different \cite{Duschinsky_AP_1937}. This
results in highly multidimensional integrals that can in practice be evaluated only for molecules \cite{Borrelli_JCP_2003},
small atomic clusters \cite{Patrick_NC_2013}, or model defect systems \cite{Alkauskas_PRL_2012}.

Some kind of approximation is thus unavoidable.  Here we assume that (i) the normal modes that
contribute to the luminescence lineshape are still those of the solid with a defect, but (ii) the modes in
the excited electronic state are identical to those in the ground state. Such an assumption is implicit in
virtually all studies of defects in solids \cite{Markham_RMP_1959,Lax_JCP_1952}. First-principles calculations
\cite{Gali_NJP_2011,Zhang_PRB_2011},
as well as a comparison of experimental absorption and emission spectra \cite{Davies_PRS_1976}, indicate that
the assumption does not strictly hold for the NV centre. Since the more exact calculation is not feasible, the validity
of this approximation has to be checked by comparing the results with the experimental spectrum.

When vibrational modes in the ground and the excited state are identical, the optical spectral function $A(\hbar\omega)$
(equation\ (\ref{spectral})) can be calculated using a generating function approach proposed by Lax \cite{Lax_JCP_1952},
as well as Kubo and Toyozawa \cite{Kubo_PTP_1955}. The fundamental quantity that has to be calculated is the spectral function
(also called spectral density) of electron-phonon coupling \cite{Miyakawa_PRB_1970}
\begin{equation}
S(\hbar\omega)=\sum_k S_{k} \delta(\hbar\omega-\hbar\omega_k),
\label{e-ph1}
\end{equation}
where the sum is over all phonon modes $k$ with frequencies $\omega_k$, and $S_k$ is the (partial) Huang-Rhys factor
for the mode $k$. It is defined as \cite{Markham_RMP_1959}
\begin{equation}
S_k=\omega_k q_k^2 /(2\hbar)
\label{Sk}
\end{equation}
with
\begin{equation}
q_k=\sum_{\alpha i}m_{\alpha}^{1/2}(R_{e;\alpha i}-R_{g;\alpha i})\Delta r_{k;\alpha i}.
\label{qk}
\end{equation}
$\alpha$ labels atoms, $i=\{x,y,z\}$, $m_{\alpha}$ is the mass of atom $\alpha$ (carbon or nitrogen,
average atomic masses of naturally occurring isotopes were used),
$R_{\{e,g\};\alpha i}$ is the equilibrium position in the initial (excited) and the final (ground)
excited state, and $\Delta  r_{k;\alpha i}$ is a normalized vector that describes the displacement of
the atom $\alpha$ along the direction $i$ in the phonon mode $k$. One can use an alternative expression for $q_k$:
\begin{equation}
q_{k}=\frac{1}{\omega_k^2}\sum_{\alpha i}\frac{1}{m_{\alpha}^{1/2}}(F_{e; \alpha i}-F_{g; \alpha i}) \Delta r_{k;\alpha i},
\label{qk2}
\end{equation}
where $F_{e; \alpha i}-F_{g; \alpha i}$ is the change of the force on the atom $\alpha$ along the direction $i$
for a fixed position of all atoms when the electronic state of the defect changes from $^3\hspace{-0.5mm}E$ to
$^3\hspace{-0.5mm}A_2$. The latter equation directly follows from the relationship
$(\vec{R}_{e}-\vec{R}_{g})=-\hat{H}^{-1}(\vec{F}_{e}-\vec{F}_{g})$, where $\hat{H}$ is the Hessian matrix,
different from the dynamical matrix only because of additional mass prefactors in the latter.
The two formulations are completely equivalent in the harmonic approximation. In \ref{1D} we show
that if the dynamical Jahn-Teller effect is neglected the anharmonicities are indeed minute. While being
in principle equivalent, the use of equation\ (\ref{qk2}) instead of equation\ (\ref{qk}) offers a huge
advantage when dealing with large systems, i.e., when extrapolating $S(\hbar\omega)$ to the dilute limit,
and this is discussed in Section \ref{ab-initio} and \ref{supercell}.

Once $S(\hbar\omega)$ is determined, the spectral function $A(\hbar\omega)$ (equation\ (\ref{spectral})) is given as the
Fourier transform of the generating function $G(t)$ \cite{Lax_JCP_1952,Kubo_PTP_1955}:
\begin{equation}
A(E_{ZPL}-\hbar\omega)=\frac{1}{2\pi}\int_{-\infty}^{\infty}G(t)e^{i\omega t-\gamma|t|}dt.
\label{spectral2}
\end{equation}
The generating function $G(t)$ itself is defined as
\begin{equation}
G(t)=e^{S(t)-S(0)},
\label{spectral6}
\end{equation}
where
\begin{equation}
S(t)=\int_{0}^{\infty}S(\hbar\omega)e^{-i\omega t}d(\hbar\omega)
\label{spectral7}
\end{equation}
and
\begin{equation}
S\equiv	S(t=0)=\int_0^{\infty}S(\hbar\omega)d(\hbar\omega)=\sum_k S_k
\label{HR}
\end{equation}
is the total HR factor for a given optical transition. In equation\ (\ref{spectral2}) the parameter $\gamma$ represents
the broadening of the ZPL. In real situations this broadening has two contributions: the homogeneous broadening due to
anharmonic phonon interactions \cite{Silsbee_PR_1962,McCumber_JAP_1963} and the inhomogeneous broadening due to ensemble
averaging. Since neither of these two effects is modeled in our approach, $\gamma$ is chosen to reproduce the
experimental width of the ZPL.

\subsection{Huang-Rhys and Debye-Waller factors \label{HR3}}

The partial HR factor $S_k$ defined in equation\ (\ref{Sk}) is the average number of phonons of type $k$
emitted during an optical transition \cite{Huang_PRCL_1950}. The total HR factor, defined in equation\ (\ref{HR}),
is then the number of phonons off all kinds that are emitted during the same transition.
The HR factor is thus an important parameter that characterizes the vibrational
structure of the luminescence band. If (i) there was no additional prefactor
$\sim\omega^3$ in the expression for the luminescence intensity in equation\ (\ref{Norm-lum-int})
and (ii) the vibrational modes in the excited and the ground state were indeed identical,
then the weight of the zero-phonon line would be given by \cite{Davies_JPC_1974,Davies_RPP_1981,Markham_RMP_1959,Lax_JCP_1952}
$w_{ZPL} = e^{-S}.$ Since this line corresponds, by definition, to zero absorbed or emitted phonons,
$w_{ZPL}$ is often called the Debye-Waller factor, in analogy with x-ray scattering, where it represents
the ratio of the elastic to the total scattering cross section. Therefore, we also use this nomenclature
to comply with the accepted practice.

The Debye-Waller factor $w_{ZPL}$
is a quantity that is directly measurable in experiment, and its determination is therefore unambiguous.
In practical situations the HR factor is often deduced from the relationship $\widetilde {S} = -\ln (w_{ZPL})$,
where we have added a ``tilde'' to distinguish this quantity from the actual HR factor $S$, which is
defined by equation\ (\ref{HR}). $\widetilde {S}$ differs from $S$ because of the additional assumption (i).

The spectral weight in $L(\hbar\omega)$ (equation\ (\ref{Norm-lum-int})) moves to slightly higher energies
in comparison to $A(\hbar\omega)$ due to the prefactor $\omega^3$. This increases the weight of the
ZPL, $w_{ZPL}$, if determined from $L(\hbar\omega)$, and thus decreases the value of $\widetilde S$
with respect to $S$. This distinction has to be borne in mind when comparing different experimental
papers. In this paper we will consistently use $w_{ZPL}$ and $S$ in their original definitions.

\subsection{First-principles approach \label{ab-initio}}

In this work the spectral function of electron-phonon coupling $S(\hbar\omega)$ (equations\
(\ref{e-ph1})-(\ref{qk})) is calculated within density functional theory (DFT).  The electronic,
atomic, and vibrational properties of the NV centre are calculated in the supercell approach
\cite{Freysoldt_RMP_2014}, whereby one defect is embedded in a sufficiently large piece of host
material, which is periodically repeated. We take a conventional cubic cell with 8 carbon atoms
as the building block for larger supercells. The cubic supercell $N$$\times$$N$$\times$$N$,
for example, contains $M$=$8N^3$ atomic sites.

To study the electronic and vibrational structure of defects we use two different exchange-correlation
(XC) functionals: the generalized gradient approximation (GGA) in the form proposed by Perdew, Burke, and
Ernzerhof (PBE) \cite{Perdew_PRL_1996} and the screened hybrid functional of Heyd, Scuseria, and Ernzerhof
(HSE) \cite{Heyd_JCP_2003}. PBE is known to describe structural properties of many materials with high
accuracy, but the calculated band gaps of semiconductors and insulators agree poorly with experiment,
and this also affects the position of defect levels within the band gap. The HSE functional overcomes
this problem by incorporating a fraction $a=1/4$ of screened Fock exchange (screening parameter $\omega=0.2$ \AA$^{-1}$).
HSE calculations yield excellent results for excitation energies for the spin-triplet optical transition
in NV centres \cite{Gali_PRL_2009}.

The properties of the excited state $^3\hspace{-0.5mm}E$ have been calculated using the constrained
occupation method of Slater \cite{Slater}, as first applied to the NV centre by Gali \emph{et al.}
\cite{Gali_PRL_2009}. In this method one electron from the $a_1$ orbital is promoted to one of the $e$
orbitals. The electronic and the atomic structure is optimized with a hole in the $a_1$ state.
To circumvent the problems with the Jahn-Teller distortion in the excited state, resulting from
the degeneracy of the nominal $a_1 e_x^2 e_y^1$ and $a_1 e_x^1 e_y^2$ configurations, the coordinate
dependence of the total energy in the excited state is studied here by constraining the
configuration to $a_1 e_x^{1.5} e_y^{1.5}$. This is a practical solution to restrict the excited state
density to be the average of the two degenerate configurations, retaining a $C_{3v}$ symmetry.

We find that while the integrated parameters, for example the total HR factor $S$ (equation\ (\ref{HR}))
converge quickly when the size of the defect supercell is increased, the convergence
of the spectral function $S(\hbar\omega)$ (equation\ (\ref{e-ph1})) is significantly slower.
This is a particular concern for the spectral function at lower energies, i.e., coupling
to long-range acoustic phonons. As an example, let us consider a $2$$\times$$2$$\times$$2$ simple cubic
supercell, containing 64 lattice sites. Without a defect, the lowest energy $\Gamma$-point vibration of such a
supercell corresponds to the bulk transverse acoustic (TA) mode at the $\Lambda$ point with an energy of
about $68$ meV. This is even higher than the experimentally determined energy of the dominant phonon mode at
the NV centre, being $\hbar\omega_0$=$63$-$65$ meV. Clearly, supercells of this size are insufficient to
determine $S(\hbar\omega)$.

To obtain converged results and determine the nature of vibrational states, we have performed
calculations for a series of supercells: from $2$$\times$$2$$\times$$2$  (64 sites)
up to $11$$\times$$11$$\times11$  (10648 sites). Since a direct approach for supercells
containing more than a few hundred atoms is computationally too demanding,
we have developed a special methodology to achieve this goal. First, in \ref{1D} we show that it
is an excellent approximation to calculate vibrational properties at the PBE level, since the relevant
vibrational modes are very similar in the PBE as compared to the HSE functional. This presents huge computational
savings, since HSE calculations are up to two orders of magnitude more expensive. Then in \ref{supercell}
we present a methodology to calculate vibrational spectra and spectral functions $S(\hbar\omega)$ for very
large systems. In short, the procedure is as follows. Partial Huang-Rhys factors for large systems are
determined from equation (\ref{qk2}). Forces $\vec{F}_{\{e,g\}}$ in the large supercell $N$$\times$$N$$\times$$N$
($N>3$), needed in that approach, are obtained from the calculation of a smaller supercell ($4$$\times$$4$$\times$$4$)
via a suitable embedding procedure, explained in \ref{supercell}. For these large defect supercells, vibrational
modes and frequencies, that also appear in expression (\ref{qk2}), have been determined by diagonalizing the
dynamical matrix constructed from dynamical matrices of bulk diamond and NV centre in the $3$$\times$$3$$\times$$3$
supercell. The validity of the procedure relies on the fact that the dynamical matrix of diamond is rather
short-ranged. Specific parameters of the procedure are determined from accurate convergence tests, and are
discussed in \ref{supercell}.

Defect calculations have been performed with the {\sc vasp} code \cite{VASP1,VASP2}, and the interaction
with ionic cores was described via the projector-augmented wave (PAW) formalism \cite{Bloechl_PRB_1994}.
A kinetic energy cutoff of 400 eV (29.4 Ry) has been used for the expansion of electronic wavefunctions.
For the $2\times 2 \times 2$ supercell the Brillouin zone was sampled using a $2\times2\times2$ $k$-point
mesh, and $\Gamma$-point sampling was used for larger supercells.

To produce additional insights, we have also calculated $S(\hbar\omega)$ (equation\ (\ref{Sk})) and $L(\hbar\omega)$
(equation\ (\ref{Norm-lum-int})) with an additional assumption, namely that phonon modes that contribute to the
luminescence lineshape are those of the unperturbed host \cite{Kretov_JL_2012,Kretov_RJPCA_2013}. For this purpose we
have determined the vibrational modes of bulk diamond using density functional perturbation theory \cite{Baroni_RMP_2001},
reproducing earlier calculations \cite{Pavone_PRB_1993}. Vibrational modes were determined on a very fine $27\times27\times27$
$k$-point grid close to the Brillouin zone centre, and a courser $9\times9\times9$ grid elsewhere. These calculations
have been performed using the {\sc quantum espresso} code \cite{QuantumEspresso} within the local density approximation
\cite{Perdew_PRB_1981}; this XC functional describes phonons modes of \emph{bulk} diamond very well \cite{Pavone_PRB_1993}.
To evaluate $S(\hbar\omega)$, the modes were mapped  to the $\Gamma$-point of the desired supercell. The contributions
from the vacancy site are set to zero in equations\ (\ref{qk}) and equation\ (\ref{qk2}), while the mass of the nitrogen
atom was set to be equal to that of the carbon atom
in this case.

\section{Experimental spectrum \label{experiment}}

The NV centre photoluminescence (PL) spectrum was taken at 8 K on an ensemble of NV centres using a home-built
confocal setup.  The diamond sample used was a {\sc Sumitomo} high-pressure, high-temperature grown Ib
{\sc Sumicrystal} with a specified nitrogen content of $30-100$ parts per million.  The sample was irradiated with
2 MeV electrons at a dose of $1\times10^{17}$ electrons/cm$^2$ and annealed at 850 $^{0}$C for 2 hours to generate a
high density of NV centres within the bulk.  The NV centres were photo-excited with 532 nm light with sufficiently low
intensity to suppress the luminescence of neutral (NV$^0$) centres.  Subsequent PL was collected into a spectrometer
with $\sim$0.3 meV spectral resolution.  The spectrum intensity was calibrated by measuring the nominally-known spectrum
of an {\sc OceanOptics} LS-1-LL tungsten halogen light source placed at the same position
of the diamond sample within the optical setup.

The experimentally obtained spectrum was normalized to 1 for comparison with the theoretical calculations.
For normalization purposes the low-energy tail of the spectrum was modeled as an exponential function.
The weight of the zero-phonon line (Debye-Waller factor) was determined to be $\sim3.2$\%.
This corresponds to $\tilde{S}=3.45$, in very close agreement with Ref.\ \cite{Kehayias_2013}.
The actual Huang-Rhys factor can be estimated to be $S\approx 3.85\pm0.05$.

\section{Results \label{results}}

\subsection{Excitation energies \label{prelim}}

For the $4$$\times$$4$$\times$$4$ supercell, the largest system for which we have performed
actual electronic structure calculations, $E_{ZPL}$ was calculated to be 1.757 eV using the PBE functional,
and 2.035 eV using the HSE functional. The latter is thus much closer to the experimental value of 1.945 eV.
Our calculations agree with those of Gali \emph{et al.}\ \cite{Gali_PRL_2009} and
Weber \emph{et al.} \cite{Weber_PNAS_2010}. The HSE functional is clearly superior for describing the local
electronic structure of the NV centre \cite{Gali_PRL_2009}. The difference of about 0.1 eV between the experimental
and calculated ZPL is within the error bar of the HSE calculations, but would complicate direct comparisons between
theoretical and experimental lineshapes. To enable a more meaningful comparison, in all subsequent analysis we set
$E_{ZPL}$ to the experimental value. Thus, the broadening of the ZPL $\gamma$ in equation (\ref{spectral2})
and the value $E_{ZPL}$ are the sole instances where information from experiment has been used in the
theoretical results.

\subsection{Spectral function of electron-phonon coupling $S(\hbar\omega)$ \label{spectral5}}

We first analyze the convergence of $S(\hbar\omega)$ when the size of the supercell is increased.
In addition to providing justification for the computational procedure, such a study provides
insights into the origin of vibrational modes that contribute to the phonon sideband.

In figure \ref{Sw-conv} we show $S(\hbar\omega)$ (equation\ (\ref{e-ph1})) and partial
Huang-Rhys factors (equation\ (\ref{Sk})) as a function of the supercell size,
from $2\times$$2\times$$2$ to $11\times$$11\times$$11$ (results for five intermediate supercells are omitted).
The range of the left vertical axes for $S(\hbar\omega)$ was kept identical for all supercells, but
note that this is not the case for the right vertical axes that apply to $S_k$. For the calculation of $S(\hbar\omega)$
$\delta$-functions in equation\ (\ref{e-ph1}) were replaced by Gaussians with widths $\sigma=6$ meV. HSE
results are discussed here.

\begin{figure}
\begin{center}
\includegraphics[width=12cm]{fig2.eps}
\caption{Spectral functions $S(\hbar\omega)$ (equation\ (\ref{e-ph1})) and partial Huang-Rhys factors (equation\ (\ref{Sk}))
pertaining to the spin-triplet optical transition at NV centres for increasingly larger supercells,
from $2$$\times$$2\times$$2$ to $11\times$$11\times$$11$ (some intermediate results are not shown).
$S(\hbar\omega)$: left vertical axes and black solid lines; to enable a meaningful comparison
the range of these vertical axes is the same for all supercells. $S_k$: right vertical axes and blue bars;
the range of these vertical axes decreases for larger supercells.
}
\label{Sw-conv}
\end{center}
\end{figure}

In the case of the smallest $2\times2\times2$ supercell, only a few phonon modes contribute to $S(\hbar\omega)$.
The most important of these are modes with energies 60.4 meV and 77.8 meV, in complete agreement with the results of
Gali \emph{et al.} \cite{Gali_NJP_2011} (59.7 and 77.0 meV), who studied local vibrational modes for this size of
supercell. While the energy of the first mode is close to the energy of the most pronounced phonon mode seen in
experiment, this agreement is largely fortuitous, since, as mentioned in Section \ref{ab-initio}, the lowest-energy
bulk TA phonon mode in this supercell has a similar energy. The low-energy tail that represents the coupling to
long-range phonons ($<$60 meV) is completely missing for this supercell, and the total HR factor $S=3.02$
(inset of figure \ref{Sw-conv}) is 20\% smaller than the converged value $S=3.67$.

In the case of a larger $3\times3\times3$ supercell, the most dominant vibration is the 45.9 meV mode. This result
is an artifact resulting from the use of a small cell, since this vibration corresponds to the lowest-energy
$\Gamma$-point bulk TA phonon---it is not an actual defect-derived mode. While the total HR factor increases
to $3.27$, $S(\hbar\omega)$ is still far from converged. This emphasizes possible dangers in drawing
conclusions about local vibrational modes from small-size supercells \cite{Zhang_PRB_2011}.

When increasing the size of the supercell further, $S(\hbar\omega)$ slowly attains its converged form.
figure \ref{Sw-all} shows that the spectral function is essentially converged for the two largest supercells
we use, even though there are still apparent changes in individual partial HR factors $S_k$.
The peak of $S(\hbar\omega)$ occurs at $\hbar\omega_0=65$ meV, in excellent agreement with experimental findings (see Sec.\
\ref{comp-lumin}). This is the first time that theoretical calculations yield the energy of the peak decisively.
Interestingly, the \emph{total} HR factor, i.e. the integral of $S(\hbar\omega)$, is within $\sim$1\% of the
converged value already for the $4\times4\times4$ supercell.

Figure\ \ref{Sw-conv} also allows us to draw the following conclusions about lattice distortions or, equivalently,
coupling to phonons, that occur during the $^3\hspace{-0.5mm}E \rightarrow\hspace{0.5mm}^3\hspace{-1mm}A_2$ optical
transition:

\begin{enumerate}
\item The $65$ meV vibration is not a localized phonon mode, but a defect-induced vibrational resonance:
it occurs within the spectrum of bulk phonon modes (0-167 meV). In figure \ref{Sw-conv} this result is
evident from the fact that for larger supercells this mode splits into many closely spaced modes, with a
simultaneous decrease of their absolute contributions. The 65 meV resonance is induced by the NV centre itself,
and cannot be understood solely by considering bulk phonon spectrum. This is demonstrated in Figure \ref{Sw-all}
and discussed in more detail in section \ref{comp-lumin}.

\item In agreement with a general theory of vibrational broadening of luminescence lines \cite{Silsbee_PR_1962},
the spectral function is linear for small energies, i.e., $S(\hbar\omega)=\alpha\hbar\omega$ for $\omega\rightarrow0$.
Indeed, partial HR factors corresponding to acoustic modes scale like $1/\omega$, which, multiplied
with the density of states of acoustic modes $\sim\omega^2$, yields this linear dependence. While this
general behaviour is known \cite{Silsbee_PR_1962}, we emphasize that the {\it prefactor} to the linear dependence is
system dependent, and only accurate atomistic calculations such as the ones presented here can provide the actual
value. In our case we obtain $\alpha\approx3.6\times10^{-4}$ meV$^{-2}=360$ eV$^{-2}$. Interaction via
acoustic phonons has been recently proposed as a promising mechanism to couple two NV centres
in nanodiamonds \cite{Albrecht_NJP_2013}. The coupling of isolated qubits is essential for
any quantum computing protocol. Our calculations provide information about the coupling of NV
centers to acoustic phonons in bulk diamond, and can be useful pursuing the ideas proposed in Ref.\
\cite{Albrecht_NJP_2013} ideas further.

\item 99\% of the lattice distortions due to the optical transition, as quantified by their contribution
to $S(\hbar\omega)$, occur within $\sim 12$ \AA$ $ of the NV centre. This follows from our finding that the
total HR factor for the $4$$\times$$4\times$$4$ supercell is within 1\% of the converged value. However, long-range
relaxations, while contributing little to the total HR factor $S$, are manifest in the low-frequency
part of $S(\hbar\omega)$, and are actually observed in the luminescence lineshape (see Section \ref{comp-lumin}).

\end{enumerate}

In figure \ref{Sw-all} we show a comparison of $S(\hbar\omega)$ calculated using three different approaches.
From here on we use the following notation when we refer to our calculations: (i) ``HSE'' refers to calculations
where atomic displacements or forces in equations\ (\ref{qk}) and (\ref{qk2}) are calculated using the HSE hybrid
functional, but vibrational modes are calculated using the PBE functional. As discussed in Section \ref{ab-initio}
and \ref{1D}, calculations for smaller supercells show that vibrational modes calculated at the PBE level are
very similar to HSE results. (ii) ``PBE'' refers to calculations in which all quantities are determined at the PBE level.
In both (i) and (ii), vibrational modes correspond to the defect system. (iii) ``Bulk phonons'' refers to calculations in which
atomic distortions or forces were determined at the HSE level, as in (i), but vibrational modes correspond to those of
the unperturbed host. The comparison of (i) and (iii) should inform us whether the introduction of the defect modifies
the vibrational spectrum, and whether the phonon sideband can be understood by considering bulk modes alone.

\begin{figure}
\begin{center}
\includegraphics[width=10cm]{fig3.eps}
\caption{Comparison of $S(\hbar\omega)$ calculated using three theoretical approaches: (i) the hybrid functional HSE,
(ii) the GGA functional PBE, and (iii) by using bulk phonons, as explained in the text.
}
\label{Sw-all}
\end{center}
\end{figure}

$S(\hbar\omega)$, calculated at the PBE level, is qualitatively very similar to the HSE result. The function has a peak
at $\hbar\omega=64$ meV, but the absolute value of $S(\hbar\omega)$ is smaller for almost all energies.
In particular, the total HR factor is $S=2.78$, a quarter smaller than in HSE. In contrast, when
the bulk phonon spectrum is used, $S(\hbar\omega)$ is even qualitatively completely different. In this case
the spectral function closely follows the density of vibrational states of bulk diamond
\cite{Pavone_PRB_1993,Zaitsev_PRB_2000}, with a pronounced peak at $\hbar\omega\approx$150 meV.
The total HR factor is 4.48 in this case. However, the coupling to low-energy ($<$20 meV) acoustic modes
is very similar to cases (i) and (ii); indeed long-range phonons are expected to be little affected by the presence
of the defect.

\subsection{Comparison with experiment: luminescence lineshape and Huang-Rhys factors}
\label{comp-lumin}

In figure \ref{spectra} we compare the luminescence lineshape $L(\hbar\omega)$ (equations
(\ref{Norm-lum-int}) and (\ref{spectral2})), calculated using the HSE functional,
with the experimental one. The agreement between theory and experiment  is extremely good.
Not only is the overall shape of the luminescence band described correctly, but all the specific features are described very accurately.
In particular:

\begin{figure}
\begin{center}
\includegraphics[width=10cm]{fig4.eps}
\caption{Measured (black solid line) and calculated (blue solid line) normalized luminescence lineshapes for NV
centers in diamond in the energy range 1.5$-$2.0 eV. The calculations have been performed at the HSE level, as explained in the text.
The low-energy tail ($<$1.5 eV) of the experimental spectrum is less reliable because of calibration issues.
}
\label{spectra}
\end{center}
\end{figure}

\begin{enumerate}
\item The weight of the ZPL of the theoretical spectrum $w_{ZPL}=3.8$\% is
very close to the experimental result $w_{ZPL}=3.2$\%. Both of these quantities have been determined
directly from luminescence lineshapes shown in figure \ref{spectra}, as discussed in Section \ref{HR3}.
The theoretical Huang-Rhys factor $S=3.67$ is thus also very close to the experimental HR factor
$S=3.85\pm0.05$; the latter has been extracted from the experimental spectrum as described in Sec.\ \ref{HR3}.

\item
Both the experimental and the theoretical band show about 4 increasingly broad phonon replicas.
The theoretical phonon frequency $\hbar\omega_0$=$65$ meV is in very good agreement
with the experimental value $\hbar\omega_0$=$64$ meV.

\item
The fine structure near the ZPL, which is representative of the coupling to acoustic phonons, agrees closely.

\end{enumerate}

We conclude that calculations based on hybrid density functionals describe the vibrational properties and
the luminescence lineshape of NV centres with a very high accuracy.

\begin{figure}
\begin{center}
\includegraphics[width=10.0cm]{fig5.eps}
\caption{Comparison of luminescence lineshapes calculated using the three different theoretical approaches described in
Section \ref{spectral5} (curves (i)-(iii)) with the experimental one (curve (iv)). (i) and (iv) are the same as in
figure \ref{spectra}.}
\label{spectra-comp}
\end{center}
\end{figure}

In figure \ref{spectra-comp} we present luminescence lineshapes calculated using all the three different theoretical
approaches discussed in Section \ref{spectral5}. The experimental curve and the one that corresponds to the HSE
functional are the same as those in figure \ref{spectra}. The lineshape calculated at the PBE level is qualitatively
similar to the HSE one, but there are quantitative differences. In particular, the weights of the first
two phonon replicas are larger, and the overall band is narrower. Figure~\ref{spectra-comp} also shows that when
bulk phonons are used instead, the calculated luminescence lineshape bears no resemblance to
the experimental curve: it is much broader and has a very different fine structure. This result clearly shows that
the consideration of the bulk phonon spectrum is not sufficient to understand the phonon sideband, challenging the
discussion of Ref.\ \cite{Kehayias_2013}. Taking into account vibrational modes of the defect system is essential.

\section{Analysis: localized vs. delocalized phonon modes \label{analysis}}

In Section \ref{spectral5} we mentioned that the $65$ meV phonon that
dominates the phonon sideband, is not a localized mode, but rather a vibrational resonance.
This means that it is formed by a continuum of vibrational modes, all of which have a larger weight
close to the defect, but none of which are strictly localized in real space. This mode
gives rise to a peak in $S(\hbar\omega)$ with a full width at half-maximum (FWHM) of about
32 meV (figures\ \ref{Sw-conv} and \ref{Sw-all}).

\begin{figure}
\begin{center}
\includegraphics[width=14.0cm]{fig6.eps}
\caption{Partial Huang-Rhys factors $S_k$ ((a) and (c), equation\ (\ref{Sk})),
inverse participation ratios $IPR_k$ ((b) and (d), equation\ (\ref{IPR})),
and vibrational patterns ((e) and (f)) for phonon modes with frequencies $\sim65$ meV
((a), (b), and (c)) and $\sim167$ meV ((d), (e), and (f)) as
a function of the supercell size.}
\label{HR-conv}
\end{center}
\end{figure}

We illustrate the fact that the 65 meV is a vibrational resonance in the following way.
For each defect supercell studied we choose the individual phonon mode that has the largest
Huang-Rhys factor in the energy range $49-81$ meV (right axis, figure \ref{Sw-conv}). The energy
range corresponds to a FWHM of the 65 meV peak in the converged function $S(\hbar\omega)$.
In figure \ref{HR-conv} (a), we plot this largest value of the partial Huang-Rhys factor $S_k$
as a function of the supercell size $N$. The value of $S_k$ for this mode decreases steadily, albeit with some
oscillations, as a function of supercell size. Since the total HR factor does not change much
as the system size grows, the decrease of this particular $S_k$ is
compensated by an increase in other phonon modes (figure \ref{Sw-conv}). This is a signature of a vibrational
resonance, which is also called a quasi-local mode.

To gain more insight, we study the inverse participation ratio (IPR) for the mode $k$ \cite{Bell_JPCC_1970}:
\begin{equation}
IPR_k = \frac{1}{\sum_\alpha p_{k;\alpha}^2},
\label{IPR}
\end{equation}
where
\begin{equation}
p_{k;\alpha} = \sum_{i}\Delta r_{k; \alpha i}^2.
\end{equation}
$IPR_k$ defined in this way measures the number of atoms onto which the vibrational mode
is localized. If, e.g., only one atom vibrates for a given mode, $IPR=1$. If all $M$ atoms
in the supercell vibrate with the same amplitude, $IPR=M$.
Note that the definition in equation\ (\ref{IPR}) is different from the one used in Ref.\ \cite{Zhang_PRB_2011}
to analyze vibrational modes of the NV centre in a 216-atom supercell, and is more in line with the traditional
definition \cite{Bell_JPCC_1970}.

In figure \ref{HR-conv}(b), the $IPR_k$ for the most pronounced mode in the energy range
$49-81$ meV is shown as a function of the supercell size $N$. For all supercell sizes
$IPR_k$ is but a fraction of the total number of atoms $M$, but steadily increases with
$N$, albeit with similar oscillations as for $S_k$. This underpins the finding that the 65 meV mode
is a vibrational resonance. This resonance represents the lion's share of the distortion of
the defect geometry (cf.\ equations (\ref{qk}) and (\ref{qk2})). It has the largest amplitude
on the four atoms surrounding the vacancy, and the vibrational pattern is shown in Fig. \ref{HR-conv}(c).
The N atom is vibrating along the defect axis, while the vibrational vectors of the C atoms
form an angle of $\sim$110$^{\circ}$ with this axis.

By analyzing partial Huang-Rhys factors and inverse participation ratios of all the modes we
were able to identify a few other, weaker resonances. These are modes with frequencies
161, 134, and 120 meV (in the order of decreasing localization). All of these weaker resonances
were recently identified in the experiment of Kehayias \emph{et al.} \cite{Kehayias_2013}.
The 153 meV resonance seen in the same experiment is not very pronounced in our calculations.
As a measure of localization we define the ``localization ratio'' $\beta$, which is the ratio
of the number of atoms in the supercell ($M=8N^3$) to the largest $IPR_k$ corresponding to
one of these resonances:
\begin{equation}
\beta_k=8N^3/(IPR_k)
\label{beta}
\end{equation}
We obtain the actual value of $\beta_k$ by fitting the $IPR_k$ for a given mode
with a function $8N^3/\beta_k$ (see figure \ref{HR-conv}(b)).
The larger the ratio $\beta_k$, the more pronounced the resonance. For a truly localized mode in the
limit $M\rightarrow\infty$, $\beta_k$ would be infinite, since for a localized mode $IPR_k$
remains constant as $M$ increases. The results are summarized in Table \ref{table_modes}. For example,
the localization ratio $\beta_k$ for the 65 meV mode is $\sim$11. Values for the ``localization ratio''
should be considered as rough estimates, but they are useful when comparing different modes.

\begin{table}
\caption{Quasi-local and local modes of $a_1$ symmetry that couple to the $^3\hspace{-0.5mm}E\rightarrow^3\hspace{-0.5mm}A_2$ optical
transition.}
\label{table_modes}
\begin{indented}
\item[] \begin{tabular}{@{}c c }
\br
\multicolumn{2}{c}{Quasi-local modes}\\
\mr
Energy  (meV) & Localization ratio $\beta_k$ \\
\mr
65   &  $\sim$11 \\
120  &  $\sim$3  \\
134  &  $\sim$6  \\
161  &  $\sim$8  \\
\br
\multicolumn{2}{c}{Local mode}\\
\mr
Energy  (meV) & $IPR_k$ \\
\mr
167  &  $\sim$80 \\
\br
\end{tabular}
\end{indented}
\end{table}

Together with these vibrational resonances, we \emph{do} find one truly localized defect-induced
phonon mode. In figure \ref{HR-conv}(d) we show $S_k$ as a function of the supercell size for a phonon
mode with a frequency $\approx$167 meV, which is slightly ($\approx$0.2 meV) above the theoretical bulk
phonon spectrum. Increasing the size of the system, $S_k$ approaches a constant value of
$\approx$0.02. When the size of the supercell grows, the $IPR_k$ of this mode also approaches a
constant value of $\sim$80 (figure \ref{HR-conv}(e)). In analogy with shallow defect levels with energies
close to bulk band edges, one could name this mode a shallow defect-localized vibration.
While this mode is ``shallow'', half of its total weight is distributed
over 6 carbon atoms: 3 that are immediately adjacent to the vacancy,
and 3 more that are nearest neighbours of the first trio along the defect axis.
The vibrational pattern associated with this vibration is shown in figure \ref{HR-conv}(f).
It is an optical mode with vibrational vectors of all atoms only slightly off the $z$ direction (by $\sim$14$^{\circ}$)
due to the influence of the defect. The participation of the nitrogen is negligible in this vibration.

The 167 meV mode contributes less than 1 \% to the total HR factor of 3.67, and therefore its role
in the formation of the phonon sideband is not very significant. However, since this is a truly localized
vibrational mode, it can play an important role in other physical processes at nitrogen-vacancy centres.
Kehayias \emph{et al.} \cite{Kehayias_2013} recently found that a phonon mode that has the signature
of a localized vibration and an experimental energy of 169 meV plays a
noticeable role in the infrared transition $^1\hspace{-0.5mm}E\rightarrow^1\hspace{-1.4mm}A_1$.
Due to very similar atomic geometries
of the $^3\hspace{-0.5mm}A_2$, $^1\hspace{-0.5mm}A_1$ and $^1\hspace{-0.5mm}E$
electronic states \cite{Toyli_PRX_2012,Doherty_NJP_2011,Maze_NJP_2011,Kehayias_2013}
we suggest that the localized phonon mode found in our current study is the same
as the one observed in the experiments of Kehayias \emph{et al.} \cite{Kehayias_2013}.

\section{Conclusions \label{conclusions}}

In this work we have developed a first-principles methodology to calculate
the vibrational structure of defect luminescence bands. Both localized, quasi-localized,
and bulk phonons are taken into account on equal footing. The methodology was applied to study the
phonon sideband pertaining to the 1.945 eV spin-triplet transition at
nitrogen-vacancy centres in diamond. Calculations based on hybrid density functional theory yield
a luminescence lineshape and all related parameters that are in excellent agreement with experiment.
The phonon sideband is dominated by a vibrational resonance with an energy of $\sim65$ meV,
but a few other, weaker resonances, are also identified. 99 \% of all atomic relaxations that
contribute to the phonon sideband occur within $\sim$12 \AA $ $ of the defect, but the interaction with
long-range acoustic phonons is also directly manifest in the luminescence spectra close to the zero-phonon line.
We find a truly localized phonon mode slightly above the phonon spectrum of bulk diamond. While this mode,
being localized on $\sim$ 75 atoms, contributes little to the spin-triplet optical transition, it can play
an important role in other physical processes at this defect, as recent experiments suggest \cite{Kehayias_2013}.
Our findings provide a deeper understanding of the coupling of electronic states to
$a_1$ phonon states at nitrogen-vacancy centres. The success of the computational
methodology developed here provides confidence that it can be fruitfully applied to other systems of
high current interest that exhibit a complex vibrational structure of luminescence bands
\cite{Weber_PNAS_2010,Koehl_Nature_2011,Gali_pss_2011,Baranov_PRB_2011,Reshchikov_JAP_2005,Brgoch_JPCC_2013}.

\section*{Acknowledgments}
AA was supported by the Office of Science of the U.S.~Department of Energy (Grant No.~DE-SC0010689),
and by the Swiss NSF (PA00P2$\_$134127) during the initial phase of the project (2011-2012).
Experimental work at UCSB was supported by the Air Force Office of Scientific Research
and the Defense Advanced Research Projects Agency. We thank A. L. Falk and D. M. Toyli for useful comments on the
manuscript. This research used resources of the National Energy Research Scientific Computing centre, which is supported by
the Office of Science of the U.S.~Department of Energy under Contract No. DE-AC02-05CH11231,
and the Extreme Science and Engineering Discovery Environment (XSEDE),
supported by NSF (OCI-1053575 and NSF DMR07-0072N)

redpajama_set_name: RedPajamaArXiv


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text:
La corne de rhinocéros, written and drawn by Franquin, is the sixth album of the Spirou et Fantasio series. The material was first serialised in Spirou magazine in two parts, Spirou et la Turbotraction and the sequel La corne de rhinocéros, and finally merged into one for the release of the hardcover album in 1955.

Story
In The Rhino's Horn, Spirou and Fantasio rescue their friend the racecar driver Roulebille (from Spirou et les héritiers) who has been wounded by murderous thugs. Roulebille's employers, Turbot, have designed a car so spectacular that competitors will stop at nothing to steal its revolutionary plans. In order to find Roulebille's partner Martin and retrieve the car's blueprints, the two reluctantly team up with another journalist, an initially irritating but ultimately priceless young woman called Seccotine. The search for Martin takes them to several regions of Africa - complete with rather dated portrayals of the natives. After retrieving the missing blueprints from the titular body part, Spirou and Fantasio are given the very first prototype of the car, baptised Turbot-Rhino to celebrate their adventure.

Background
Publisher Dupuis had Franquin retouch an early sequence when thugs chase Spirou and Fantasio in the department store, removing their guns.

The introduction of cheeky and quick-witted Seccotine into the Spirou universe was quite ahead of its time for Belgian comic books. She returns in several other stories.

The futuristic-looking Turbotraction:Turbot-Rhino I was not as far-fetched as it looked at the time. Franquin based it on actual prototypes depicted in scientific revues. A life-size model of it and other vehicles created later in the series was created for the World of Franquin exhibition in Paris and Brussels in 2006–2007.

References

 Franquin publications in Spirou BDoubliées
Footnotes

External links
 Spirou official site album index
 Franquin site album index

Comics by André Franquin
Spirou et Fantasio albums
1955 graphic novels
1955 in comics
Africa in fiction
Works originally published in Spirou (magazine)
Literature first published in serial form


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