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Not the Best Idea; A Tale of Temperance
By Megan Cutler | December 1, 2017 | Comments 1 comment
And, we're back! I've done two rounds of Seven Deadly Sins prompts, mostly because I have such a large pool of characters to draw from. While flipping through other prompt suggestions, I happened to find a list of the Seven Heavenly Virtues (which seem to get a lot less press). In case you've never heard of them, they are: Chastity, Temperance, Charity, Diligence, Patience, Kindness and Humility. So now that we've seen the darker sides of my characters, why don't we take a peek at their virtues? Next up is Domerin, whose virtue is actually the exact opposite of his vice.
Temperance; moderation or self-restraint in action, statement, etc.; self-control.
Every time someone asked Domerin Lorcasf if it was really the best idea to raise a child on a mercenary ship, he answered no. He didn't hesitate. He didn't think about it. He didn't really need to. Mercenaries tended to be a ragtag group of outcasts to begin with – it was practically a requirement of the job. But Domerin's were rowdier than most and he was never more keenly aware of that distinction than when his daughter was around.
Whenever the question came up, Domerin expected a lecture about stability, consistency and ethics. But instead the inquirer inevitably pressed their lips into a thin line and went on as if the topic had never come up. Perhaps the school officials and doctors who dealt with him were so used to push back from wildly confident parents, secure in the knowledge that they knew best for their child, they were simply unprepared to deal with someone who knew they were in over their head.
On the one hand, it was a relief. He was ill-equipped to handle lectures, more used to delivering them these days. On the other, he would have appreciated some advice. He was always the first to admit that the safety and stability of her aunt's ranch would have suited Robin's upbringing best. But the girl thrived off of their blood connection, and sending her back to all the bad memories of her mother's end seemed more damaging than a few crass statements and the tendency of those surrounding her to solve their problems with punches.
"Her test scores are high," this particular school clerk said to change the topic of conversation. She was an older woman thick glasses perched on the tip of her nose. The tips of the ear rests were attached to a polished silver chain, to keep her from losing them perhaps. They way they jiggled every time she moved only seemed to enhance the slight sag of her jowls. "She'll excel in the sciences if she sticks with it."
"I encourage her," Domerin replied, not sure what else he was supposed to say. It was up to Robin what she ultimately decided to study. He wasn't going to push her, even if experts thought he should. As far as he knew, she wanted to be a veterinarian, and since that was likely to take her back to the out of the way foothills of her home planet, Domerin certainly wasn't going to stop her.
The clerk made a soft sound that might have been approval, but Domerin was too distracted by the severe bunching of her lips to say for sure. She spent entirely too much time straightening the sheets of paper which contained his daughter's official reports – a copy of which had already been emailed to him, but would not be accepted by other schools. For some reason, they all wanted hard copies, a bizarre and illogical throwback to an older age. At last, the clerk was satisfied all the pages corners lined up and she slid the plastic sheets into a bright red envelope, so colored – he imagined – so that he'd never be able to lose it.
After accepting the packet, he stood for several seconds, expecting to be interrogated further as to whether or not he was certain he could handle a child his daughter's age, if he wanted to enroll her permanently in boarding school, or perhaps simply give her up to adoption and admit he was entirely inadequate as a parent. But when the woman said nothing else, he thanked her and left.
It wasn't as if he didn't have other things to worry about. They were due for liftoff in less than three hours and he had spent more time than he anticipated navigating the school's office. Luckily Rilan had been able to take Robin back to the ship, or Domerin might have gone half-mad trying to answer all of her impatient questions while the hours ticked away. He knew how to prepare soldiers for the situations they were likely to encounter during combat, what to do if someone needed first aid and how to disassemble and reassemble most of the systems on his ship, but he had no idea how he was supposed to answer the curious questions of a thirteen year old girl. Especially when he knew almost nothing about girls at that age.
They were on a tight timeline, expected to rendezvous with their latest client in forty hours, and their late departure didn't leave them much time to deal with unexpected delays. But this was hardly his first rodeo and there were ways to stretch their travel window, if he had to.
He expected the last cargo shipment to be loaded by the time he arrived. With three shuttles transporting supplies into orbit, the crew should have been able to finish early. But two of the shuttles sat empty, their doors open and their ramps extended, the boxes they were meant to carry still sitting on pallets nearby.
Domerin glanced at his watch and then rubbed his temples, hoping to stave off the first hint of a headache lurking beneath his skin.
"What the hell is this?" he demanded as his first officer approached, waving at the lack of activity surrounding his shuttles, realizing only belatedly that his daughter had peeked around an open door frame to observe the conversation. Not that he was good at resisting the urge to cuss even on a good day. "I told you we had to be ready to go by the time I got back."
"I know." Rilan held up both hands at shoulder height, palms facing outward. "But we ran into a problem."
"It can't be a bad shipment if everything's sitting right here." He indicated one of the stacked pallets. Then he noticed something out of the corner of his eye and turned to examine it. His lips formed a frown. "Is that horse droppings?"
"Yes," Rilan replied, as if this was what he had been trying to explain all along.
"What are they doing on my shuttle?"
A few feet away, Robin cringed and disappeared back into the shuttle cockpit. Not that it would prevent her from hearing the rest of the conversation if she really wanted to.
"I'm pretty sure that's how it works for horses. I mean, they can't control that sort of thing, can they?"
"Rilan, I do not have time for games right now." More than just the warning hint in his tone, Domerin narrowed his eyes and took a half-step closer to his second in command so the man would know how close he was to his breaking point. Not that he would have punched Rilan, but the next member of his crew to pass within arm's length might not be so lucky.
It was altogether more difficult to keep from cracking skulls since Robin had come aboard. And coincidentally, the situations which caused him to lose patience with his crew often originated with her.
"It's not that big a deal," Rilan insisted, though Domerin could tell from the look in his eyes that he was somewhat frantic. "I guess Robin really missed her horses so she tried to bring a few along. I don't know where she thought she was going to hide them."
Domerin bit the inside of his lip. Moments like this made him think he should ship her back to her aunt's ranch and have done with the whole idea of parenthood. "But the poop gave them away, I take it?"
"That and the mild panic they experienced when she tried to march them over the grating, yeah. It took about half an hour to get the creatures calm enough we could approach them and now, well, they're on their way back home."
"Excellent," Domerin grumbled. It would take an hour to load the shuttles by the time his crew got back and that wouldn't leave them enough time for both the preflight checks and the inspection. And he had long ago learned never to skip a preflight check unless his life depended on immediate departure.
"Are you mad?" Robin's small voice startled him out of his temper.
Domerin lifted one hand to rub his forehead again. "I'm not happy."
Robin swallowed hard; she had long since learned to read her father's moods from his behavior. "Am I in trouble?"
"You bet your ass you're in trouble," Domerin's voice was low and a tad cold but no more so than any other parent's would be. Or so he hoped. "Get the rest of this mess cleaned up and then go strap yourself in. I don't want to hear any excuses. We've all got work to do."
Robin slunk to the far end of the room to retrieve a large shovel, and Domerin got the impression she had already been forced to clean quite a few messes before his arrival.
He didn't like to consider himself a superstitious man but, since bringing his daughter home with him, he had learned that bad luck formed a string. A seemingly innocuous delay without children often passed with relatively little fuss, but combining the same scenario with a single child compounded the trouble significantly. Sometimes it took several days for everything to settle back down, as he suspected the case was likely to be this time.
So he was prepared for the haughty inspector, who found problems where there were none and wanted to ground his shuttles an extra three hours before he would agree to let them launch. And Domerin bit his tongue, held onto his polite nature and managed to talk some sense into the man without having to slip him a bribe – one practice he didn't want to become known for.
And he was ready for the engine diagnostic gone awry that kept one of his ships from departing at full power when he finally did get back into space, his errant daughter in toe.
He was not prepared for the conversation about why Robin had tried to smuggle horses onto his ship and why, subsequently, she would be grounded for the next two weeks. He hated the way she pouted at him, her eyes wide like a puppy that's just been kicked. Her unhappiness never sat well with him, but he couldn't be her friend when she'd done something wrong.
By the time the fight broke out in the mess – and in front of his impressionable daughter to boot – Domerin's temper was on its last thin thread. He wanted nothing more than to grab the instigator by the collar and bash his head against the nearest table to prove his point. His fingers curled into a fist at his side just thinking about it.
But he could feel his daughter's gaze staring up at him, probably wondering if he was about to ground a chunk of his crew for three weeks for the black eyes and bloody lips they exchanged before his sharp rebuke dragged them apart. He had never been above using force against his crew when he thought a situation warranted it, but he was trying to teach his daughter to fight her battles with words.
"Clean up the mess," he growled instead, forcing himself to flex his fingers. "Then get back to your quarters."
"We're sorry, Commander…" One of the fighters started, but fell silent when Domerin's sharp gaze fell on him.
"We regret causing you trouble," another murmured, head bowed, eyes on the floor.
"You will when you're finished running laps in full combat gear," Domerin growled. He turned and guided his daughter toward the serving line, a clear indication the conversation was at an end.
But his temples throbbed by now, a harder and faster beat than the rhythm housed in his chest. It was all he could do to keep from chewing everyone's ear off; venting his spleen wasn't going to get the work done faster and it was better to save his ire for those who deserved it.
When at last, he got Robin settled into bed for the night, he allowed himself to indulge in a single glass of whiskey – the good stuff – a soothing balm for his building temper. He tried to remind himself that the good days outweighed the bad ones, and that the end result would be worth all the struggle. Not to mention the fact that he had, somehow, survived most of his life without murdering the people who pissed him off.
The trouble, he was forced to admit, was lack of confidence. He never questioned his command decisions, but everything about fatherhood seemed coupled with the imminent threat of ruining his child's life. And it was so much easier to relieve the build of pressure against the smaller issues that seemed so simply cut and dry.
But it wouldn't have set a good example. Nor would it have been fair. And while Domerin Lorcasf was more keenly aware than most of how unfair the universe could be, he wasn't about to compound the problem. He would just have to find his way through, keep a tight rein on his temper and hope for the best.
Bolstered by the slight taming of his headache, Domerin poured himself one more glass of whiskey. If nothing else, it would help him sleep.
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Top 10 Minnesota sports stories of the year
PUBLISHED: December 30, 2011 at 11:01 pm | UPDATED: November 13, 2015 at 1:29 am
1) Killebrew dies – When Harmon Killebrew announced at the end of 2010 that he had been diagnosed with esophageal cancer, we hoped for the best. When he announced in May that he had ceased treatment and entered hospice care, we knew the end was near. But he had helped teach us the value of hospice care, having been through it in 1990 when a staph infection almost killed him, and became a hospice advocate. When he died, it spurred an outpouring of affection not just in Minnesota but through the baseball world.
2) Mauer has what? – It was bad enough Adrian Peterson and Trevor Mbakwe blew out their knees during this painful sport year; we can deal with those. But what was the deal with Joe Mauer? And how did it come to symbolize everything bad about the Twins and their clubhouse?
3) Lynx reign – Finally, there was a reason to celebrate major professional sports in Minnesota. Women's basketball hasn't been this big here since what's-her-name was the point guard for the Gophers' Final Four team. (Yeah, we know, it was Lindsay Whalen, too.)
4) Vikings flop – We were happy Leslie Frazier got the coaching job, but nobody thought the Vikings would be THIS bad. They still could tie Les Steckel's 3-13 1984 team for the worst 16-game record in franchise history. Not the way to ring in 2012, though.
5) Twins collapse – Which was more shocking? Going from 94 wins to 99 losses? Or firing GM Bill Smith? So much for The Twins Way. We did have Francisco Liriano's no-hitter. And Jim Thome's 600th home run. But an on-field celebration for avoiding 100 losses? Really?
6) Vikings seek home – We spent the year counting down to the end of the Metrodome lease in February (we think), wondering if the team will find a new home here (Arden Hills? Minneapolis?) or elsewhere (gulp). Will we regret the stalemate of 2011 in 2012?
7) Kill Era begins – The drama. The seizures. The drubbings. The upsets. That was just Year One of football under Jerry Kill. But he bred optimism after other high-profile Gophers sports had tanked. Now men's basketball and men's hockey are winning again. And Kill Year Two awaits.
8) Blyleven elected – On his 14th attempt, the great curveball pitcher finally made Cooperstown. Bert Blyleven's statistics were too much to ignore, especially compared to today's six-inning starters. Meanwhile, ex-teammates Tony Oliva and Jim Kaat still wait.
9) Boogaard dies – Former Wild cult hero Derek Boogaard died accidentally, from an alcohol-painkiller combination. And we learned afterward of the brain issues that had affected him – and perhaps other hockey enforcers – raising questions about fighting in hockey.
10) Wild revamp – Todd Richards? Fired. Brent Burns and Martin Havlat? Traded. The Wild have a new look. And they brought buzz back to the Xcel Energy Center with an early run to the top of the NHL. An eight-game losing streak was deflating, but can Mike Yeo & Co. regroup?
First things first: The Twins' bullpen, as a unit, has not been bad this season, contrary to what some on social media would lead you to believe. Led by Taylor Rogers, who is in the midst of the best season of his career, the Twins' bullpen ranked 11th coming into Monday with a 4.20 earned-run average. The bullpen has a...
Lynx leaders Sylvia Fowles, Odyssey Sims named WNBA All-Star Game reserves
After being snubbed last week when the WNBA announced starters for the All-Star Game, Lynx leaders Sylvia Fowles and Odyssey Sims were named reserves on Monday. This will be the sixth time Fowles has been selected to play in an All-Star Game — her third with the Lynx — and the first time for Sims. It also marks the eighth...
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Two Gophers on watch lists for national college football awards
Going into the 2019 football season, two senior Gopher players were named Monday to watch lists for prestigious awards. Receiver Tyler Johnson was among 80 players up for the Maxwell Award, which is given to the best collegiate player in the nation. The Minneapolis product is one of 12 wideouts on the list. Defensive end Carter Coughlin was selected among...
May annoyed after Twins drop series finale but win 2 of 3 in Cleveland
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Timberwolves' Keita Bates-Diop has improved his game in all the right ways
Timberwolves coach Ryan Saunders had "an honest conversation" with every player on the roster at the end of last season, Keita Bates-Diop included.

redpajama_set_name: RedPajamaCommonCrawl


Gallery-wrapped painted canvas sides. Abstract acrylic painting on canvas. Ready to Hang. Framing optional.
Signed by artist Kiyoshi Otsuka 2016. Gallery-wrapped painted canvas sides. Abstract acrylic painting on canvas. Ready to Hang. Framing optional.


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\section{Introduction}

The first observations of the distinctive asymmetric Fano profile came during the 1930s in the study of molecular photodissociation and atomic photoionization spectra \cite{Brown1932,Beutler1935}. Spurred by the new unexplained experimental evidence, O.K. Rice on the one hand \cite{Rice1933} and Ugo Fano on the other \cite{Fano1935} set out to develop the corresponding theories. The inclusion of pre-dissociated for the first and auto-ionizing states for the second opened an additional pathway towards the fragmentation. The interference pattern between the direct and the (newly included) indirect pathway resulted in the asymmetric lineshape. Although both theories had similar physics, eventually the simplicity of the Fano expression \cite{Fano1961} led to it being more widely used. The Fano profile:
\begin{equation}
f(\epsilon,q)=\frac{(\epsilon+q)^2}{\epsilon^2+1}
\label{eq:Fano}
\end{equation}
where $\epsilon$ is a normalized detuning of the laser frequency with respect to the ground-excited transition energy and $q$ is the lineshape asymmetry parameter that reflects the relative strength of the two pathways to reach the continuum.
The theory was generalized to include more complicated and realistic structures of the energy levels whilst preserving the general idea of competing pathways to a continuum \cite{Fano1961,Glutsch2002}.
Over the course of the years, the Fano profile has been successful in fitting the lineshape in situations far removed from photodissociation or photoionization of molecular or atomic gases experiments \cite{Miroshnichenko2010,Lucky2010,
Nguyen2007,Lombardi2016,Gallinet2010, Harbers2007,Brown2001,Mazumdar2006,Tremblay2010,Bianconi2003,Vittorini-Orgeas2009}. \newline

Descriptions of asymmetric lineshapes in condensed matter systems followed very shortly after 1961 \cite{Baldini1962,Jain1965}. These were found in GaAs semiconductors under a magnetic field, where magneto-excitons resulting from excitation of Landau levels couple Coulombically to the band continuum \cite{Glutsch1994,Siegner1995,Siegner1995a,Siegner1996,Seisyan2016}. Holfeldt et al. measured Fano resonances in biased superlattices where Wannier-Stark excitons coupled to the continuum of higher transitions \cite{Holfeld1998}.
More recently Fano lineshapes in optical excitations coupled to narrow phonon modes have been reported \cite{Yoshino2015}. The reports of Fano asymmetries in metamaterials have been even more prolific \cite{Miroshnichenko2010,Lucky2010}. There is a particular technological interest in these metamaterials. They serve as very high enhancement substrates for SERS and also as efficient nonlinear media. \newline

The theoretical problem of including the coupling to a thermal bath was recognized without an explicit solution by Ugo Fano in 1963, inspired by the problem of pressure broadening \cite{Fano1963}. The motivation is as follows: the system consisting of a discrete and continuum manifolds is coupled to another continuum of modes of the bath that can exchange energy with the system (see Figure \ref{fig:FanoDissipRes}). It is important to stress that there are two continua which are qualitatively different. One corresponds to the system one-particle states, and the other one to excitations of others particles (for example modes of a phonon bath).
Rzazewski and Eberly considered the effect of phase incoherence of the incoming laser at arbitrary strengths of the field and solved exactly the energy resolved population of the continuum using stochastic methods \cite{Rzazewski1983}. In a landmark work, Agarwal and co-workers considered the case of a Fano model coupled to the vacuum modes of light to account for spontaneous emission \cite{Agarwal1982,Agarwal1984}. They provide the exact solution in the case of weak field, and compact expressions for the arbitrary-field strength case (within the rotating wave approximation) in terms of the poles of the resolvent for the continuum populations. The main conclusions unveiled by the expressions is that spontaneous-emission induced decay preserves the Fano minima in both the weak and strong field cases, and the authors examine the consequences on the photoelectron spectra, in particular the effect of electron recycling and the presence of sink states. This is explored further in subsequent work \cite{Agassi1984, Haan1987, Ravi1991}. The role of radiation damping was investigated through the one and two-time correlation function of the electric dipoles by Haus et al. \cite{Haus1983}.

More recent efforts have considered the dissipation in the context of condensed matter instead of ionization. Zhang et al. in a series of papers solved for the absorption of a system with Lindblad dissipator in the strong dissipation regime \cite{Zhang2006,Zhang2011}. They predicted a diminishing asymmetry with increasing field-intensity, which has been verified experimentally and called the nonlinear Fano effect \cite{Kroner2008}. Gallinet and co-workers introduced an analytical continuation of the Fano form and captured the effects of dissipation in plasmonic devices \cite{Gallinet2010}. The solution of scattering by a lossy dielectric has been solved by Tribelsky and Miroshnichenko more recently \cite{Tribelsky2016}. Barnthaller et al. followed a similar treatment in their theory/experiment study of dissipation in waveguides \cite{Baernthaler2010}. Finkelstein-Shapiro et al. calculated the weak-field emission of a Fano model with a Lindblad dissipator and found that the parameters of the lineshape are rescaled by the dissipation \cite{Finkelstein2015}. They then provided the exact solution of the Fano model in the wideband approximation coupled to a Markovian bath \cite{Finkelstein2016-1}.

\begin{figure}[ht]
\centering
\begin{tikzpicture}[scale=0.5]
\draw[thick] (0,0) -- (2cm,0);
\draw[thick] (0,3cm)--(2cm,3cm);
\draw[fill=gray]  (4cm,1cm) rectangle (5cm,5cm);
\draw  (-1cm,-1cm) rectangle (6cm,7cm);
\draw  (9cm,-1cm) rectangle (14cm,7cm);
\draw  (10cm,0cm) rectangle (11cm,5cm);
\draw  (12cm,0cm) rectangle (13cm,5cm);
\node at (2.5,6) {System};
\node at (11.5,6) {Bath};
\node at (3,2) {\Large $\oplus$};
\node at (7.6,2) {\Large $\otimes$};
\end{tikzpicture}
\caption{\label{fig:FanoDissipRes} Energy structure of the Fano model with dissipation. It is important to stress that there are two continua: the one belonging to the system which belongs to the same particle as the dicrete states which are all coupled to a continuum of bosonic modes conforming the bath. The mathematical operations of direct sum and tensor product emphasize this distinction.}
\end{figure}

It is important to recognize that the Fano lineshape can refer to many types of interference: as in the original problem, the interference of quantum mechanical amplitudes in a scattering experiment \cite{Rau2004}, but also the interference of light modes, but even of the interference present in driven coupled classical oscillators \cite{Joe2006,Satpathy2012}. In each of these cases the dissipation is added differently. The interference of quantum mechanical amplitudes is the most challenging case due to the details of the system-bath coupling, restrictions on the complete positivity of the density matrix and situations of non-Markovianity \cite{Breuer2004}. We focus our attention in this article on this case.
It is relevant because
it is still not known how to systematicaly deal with a discrete-continuum Hamiltonian coupled to a Markovian reservoir.
The scattering solution arises from solving the Schrodinger equation in Hilbert space while the dissipative solution arises from solving the Liouville equation in Liouville space, yet experiments pertaining to both cases are equally fit by this expression, lending a strong character of universality to this lineshape.
 \newline

In this article, we aim to provide a clear context for the theoretical problem of Fano interferences in dissipative Liouville space and formalize the origins of its wide applicability mathematically. In part II we review the solution of the scattering Hilbert space problem using Feshbach projection and resolvents. In part III the solution for the dissipative Lindblad dynamics is given using the same methods but in the space of superoperators. The mathematical condition to obtain a Fano profile is made evident and we provide a systematic procedure and recipe to deal with any discrete-continuum Hamiltonian under the wideband approximation. We discuss how to apply the equations to a transport process.

\section{Scattering formalism}
We consider the typical photoionization experiment (Figure \ref{fig:scattering_experiment}).
\begin{figure}
\includegraphics[width=0.4\textwidth]{scattering_experiment.png}
\caption{Scattering experiment: an atomic or molecular beam traverses an interaction region with a laser of variable length and ionizes. The fragmented ionized species are detected at Faradaic plates.}
\label{fig:scattering_experiment}
\end{figure}
The atoms or molecules pass through an interaction region with a laser beam where they become ionized. The charged fragments are then detected capacitevely. The light-matter interaction region $d$ corresponds to an interaction time $T$ which depends upon the speed of the molecular or atomic beam. Detector plates are placed at a distance $D$ from the beam. The Hamiltonian corresponds to:
\begin{align}
&H=H_0+H_V+H_F \\
&H_0=E_{0}\ket{g}\bra{g}+E_e\ket{e}\bra{e}+\int dk E_k\ket{k}\bra{k} \nonumber \\
&H_V=\int dk \big[ V(k)\ket{e}\bra{k}+V(k)^*\ket{k}\bra{e} \big] \nonumber \\
&H_F=F \left[\mu_{e}\cos(\omega_L t)\ket{g}\bra{e}+\mu_{e}^*\cos(\omega_L t)\ket{e}\bra{g}\right] \nonumber \\
&+F \int dk \left[\mu_{c}(k)\cos(\omega_L t)\ket{g}\bra{k}+\mu_{c}^*(k)\cos(\omega_L t)\ket{k}\bra{g}\right],
\label{eq:Hamiltonian}
\end{align}
where $H_0$ is a bare Hamiltonian, $H_V$ is the coupling of the discrete excited state $\ket{e}$ to the continuum set of states $\ket{k}$ and $H_F$ is the interaction with the incident radiation field of amplitude $F$ and angular frequency $\omega_L$, allowing transitions from the ground state $\ket{g}$ to the discrete excited state with transition dipole moment $\mu_e$ and to the continuum of states with transition dipole moment $\mu_c$. Without loss of generality we take $V,\mu_e,\mu_c$ to be real. We solve the dynamics in a rotating frame obtained by applying the unitary transformation $U_L(t) = e^{-i\Omega_L t}$, where $\Omega_L = \omega_L\ket{g}\bra{g}$,  so that in the new frame the Hamiltonian becomes $\hbar\Omega_L + U_LHU_L^{-1}$. Within  the rotating wave approximation (RWA), which consists  in neglecting fast oscillating terms, this Hamiltonian in the rotating frame is time independent. To obtain explicit results, we will make use of the wideband approximation  which consists in neglecting the $k$-dependence for the coupling $V(k)$ and $\mu_c(k)$ in the Hamiltonian~Eq.~\eqref{eq:Hamiltonian} and assuming a linear dispersion relation for the continuum $n=dk/dE$.

The solution of the system's dynamics is fully specified by the evolution operator $U(t)$:
\begin{equation}
\Psi(t)=U(t)\Psi(0).
\end{equation}
If the detection plates are far enough from the ionization region so that all the excited atoms have had time to completely ionize, then the ionization probability  is given by \cite{Lambropoulos1981}:
\begin{equation}
P(T)=1-\abs{U_{gg}(T)}^2,
\end{equation}
where $\abs{U_{gg}(T)}^2$ is the probability of finding the system in the ground state at time $T$ assuming it has started in the ground state.
We use the notation  $A_{ij}=\bra{i}A\ket{j}$ for an operator $A$. We have:
\begin{equation}
\label{eq:fourierLaplace}
U_{gg}(t)=-\frac{1}{2\pi i} \int_{\mathbb{R}+i\eta} G_{gg}(z)e^{-izt/\hbar}\mathrm{d} z,
\end{equation}
where $\eta$ is any positive number and $G(z)=(z-H)^{-1}$ is the Hamiltonian resolvent, that can also be written as:
\[
G(z) = -\frac{i}{\hbar} \int_{0}^{+\infty}U(t)e^{izt/\hbar} \mathrm{d} t \text{ for } \Im[z]>0.
\]
 Lambropoulos and Zoller solved for the scattering cross-section under intense fields using the resolvent approach \cite{Lambropoulos1981}. Here we show how the result is obtained using the resolvent approach along with projection operators \cite{Feshbach1962}. We will build on this result in later sections to solve the dissipative case of a Fano system coupled to a thermal bath.
Projection operators allow us to separate the subspace that corresponds to the discrete states from the subspace that corresonds the continuum. These are:
\begin{equation}
P=\ket{g}\bra{g}+\ket{e}\bra{e}; \quad
Q=\int_{-\infty}^{\infty} dk \ket{k}\bra{k}.
\label{eq:PQdef}
\end{equation}
Separating  the Hilbert space in this way allows us to write the the restriction $PG(z)P$ of the exact resolvent $G(z)$ in the discrete subspace as $PG(z)P=(z-H_{\text{eff}})^{-1}$, where $H_{\text{eff}}$ is an effective Hamiltonian acting on the discrete subspace only, but incorporating the effect of the continuum. It is given by $H_{\text{eff}}=PHP+PHQG_0(z)QHP$, where $G_0$ is the resolvent of $H_0$, $G_0(z) = (z-H_0)^{-1}$.
 Because the problem only involves the evolution operator element that evolves the wavefunction from the ground state onto the ground state at a later time, the solution is fully specified in the $P$ subspace (See Appendix~\ref{app:Proj}). \newline

We switch to dimensionless  variables where energies are given in units of $\hbar\gamma = n\pi V^2$, where $n$ is the density of states $n = \frac{\mathrm{d} k}{\mathrm{d} E}$, and times are given in units of $1/\gamma$. In the wide band approximation where $V(k)$ end $\mu_c(k)$ are taken as constants independent of $k$,
the integration over $k$ is explicit and
the effective Hamiltonian in the RWA approximation
introduced in the previous section is:
\begin{equation}
H_{\text{eff}}=\begin{bmatrix}
-i\Omega^2 & \Omega(q-i) \\
\Omega(q-i) & -\epsilon-i
\end{bmatrix},
\label{eq:Heff}
\end{equation}
where $q=\frac{\mu_e}{n\pi \mu_c}$, $\epsilon=(\omega_L-E_e)/\hbar\gamma$, $\Omega=\mu_cF/2V$. The matrix element $G_{gg}(z)$ of the resolvent is given by:
\begin{equation}
G_{gg}(z)=\frac{z+\epsilon+i}{(z-z_1)(z-z_2)},
\end{equation}
where
\begin{equation}
\begin{split}
z_{1,2}&=-\frac{1}{2}(\omega_0\pm\omega), \text{ with }
\omega_0=\left(\epsilon+i(1+\Omega^2)\right) \\
\text{with }  \omega&=\left\{(\epsilon+i)^2 -2\Omega^2\left[1-2q^2 +i(4q + \epsilon)\right] -\Omega^4\right\}^{\frac{1}{2}}.
\end{split}
\end{equation}
We stress that $\omega_0$ and $\omega$ are complex numbers and for $\omega$ both determination of the square root can be used as this choice only affect the conventional labeling of $z_1$ and $z_2$. The inverse Fourier Laplace Eq.~\eqref{eq:fourierLaplace} is immediately obtained and gives:
\begin{align}
U_{gg}(t) &= a_1e^{-iz_1 t} + a_2e^{-iz_2 t}, \\
\text{with } a_1 &= \frac{z_1+\epsilon+i}{z_1-z_2}; \quad a_2 = \frac{z_2+\epsilon+i}{z_2-z_1}. \nonumber
\label{eq:Ugg}
\end{align}
The probability $\abs{U_{gg}(t)}^2$ to remain in the ground state at time $t$, can be written as~:
\begin{equation}
\begin{split}
\abs{U_{gg}(t)}^2 &= e^{-(1+\Omega^2) t}\left(\abs{a_1}^2 e^{\Im[\omega] t } +
\abs{a_2}^2 e^{-\Im[\omega ]t } \right.  \\
&+ \left. 2\Re\left[a_1a_2^* \right] e^{-i\Re[\omega] t} \right) \\
&=\abs{a_1}^2e^{-\Gamma_0 t} + \abs{a_2}^2e^{-\Gamma_2 t}\\
&+2\Re[a_1a_2^*]e^{-i\Re[\omega]t}e^{-\Gamma_1 t}
\end{split}
\end{equation}
\begin{figure}
\includegraphics[width=0.5\textwidth]{scattering.pdf}
\caption{Ionization probability for $q=1$ for three values of the field $\Omega=0.01$ (first row), $\Omega=0.1$ (second row) and $\Omega=5$ (last row). For each field intensity three times are shown. For weak fields ($\Omega=0.01$ first row), during the early times (on the order of $1/n\pi V^2$) the interference pattern is building up. The steady-state rate (middle column, in blue) spans a large time window (the rate $P/T$ does not show a significant change for a time window between $T=10$ and $T=300$). At large times the profile tends towards a Fano-like shape with smaller $q$ parameter although the Fano equation is no longer exact. At intermediate field $\Omega=0.1$, second row, we observe a similar behavior although the time window in which the Fano equation is valid is much smaller. At strong fields $\Omega=5$, last row,  the profile is flat and increases with time until the species have fully fragmented. All time values are given in units of $1/n\pi V^2$.}
\label{fig:scattering}
\end{figure}
To recover the original Fano fragmentation rate, we first have to  consider a  situation where the concept of a rate has a meaning. This is the case if there is a decoupling between the different timescales:
$\Gamma_0 = 1+\Omega^2 -\Im{(\omega)}$, $\Gamma_1 = 1+\Omega^2$  and  $\Gamma_2 = 1+\Omega^2 +\Im{(\omega)}$. This decoupling occurs in the low field limit $\Omega^2 \ll 1$. Indeed
in this limit we have~:
\begin{align*}
\Gamma_0  &= 2\Omega^2\frac{\left(\epsilon + q\right)^2}{1+\epsilon^2} + \mathcal{O}(\Omega^4); \\
\Gamma_2 &=  2+2\Omega^2\left[1 - \frac{\left(\epsilon + q\right)^2}{1+\epsilon^2}\right]+\mathcal{O}(\Omega^4)
\end{align*}
and therefore, in this limit $\Gamma_0 \ll \Gamma_1\simeq \Gamma_2$. Hence, in the range $1/\Gamma_2 \ll t \ll1/\Gamma_0$, $P(t)$ can be written as~:
\[
P(t) = 1-\abs{U_{gg}}^2 \simeq 1-\abs{a_1}^2e^{-\Gamma_0 t}\simeq 1-\abs{a_1}^2\left[1-\Gamma_0t \right].
\]
Furthermore, at the same order of approximation, $\abs{a_1}^2 = 1 - \frac{\Omega^2}{\epsilon^2+1} +\mathcal{O}(\Omega^4)$. Consequently,
\[
P(t) = \frac{\Omega^2}{\epsilon^2+1} +2\Omega^2\frac{(\epsilon +q)^2}{1+\epsilon^2}t +\mathcal{O}(\Omega^4).
\]
The fragmentation rate is therefore given by:
\begin{equation}
\frac{\mathrm{d} P}{\mathrm{d} t} = 2\Omega^2\frac{(\epsilon +q)^2}{1+\epsilon^2} + \mathcal{O}(\Omega^4),
\label{eq:scattRate}
\end{equation}
which is indeed proportional to the Fano profile.
In the experiment described in Figure \ref{fig:scattering_experiment}, a molecular or  atomic beam with constant flux goes through an ionization region of duration $T$. The total number of detected ions is:
\begin{equation}
\begin{split}
N_{\text{ionized}}&=\text{flux}\times P(T) \\
&\approx \text{flux} \times T\frac{dP(t)}{dt}|_{t=0^+} = 2 T\Omega^2\frac{(\epsilon +q)^2}{1+\epsilon^2},
\end{split}
\end{equation}
where the second line is an approximation that gives an exact Fano profile and $t=0+$ means that we consider a sufficiently  small time  such that $t \ll \frac{1}{\Gamma_0}$ which is realized if $t\ll\frac{1}{(1+q^2)\Omega^2}$,
but not too small in the sense that $t\gg 1$ (in units of $\hbar/n\pi V^2$). This is possible for all values of $\epsilon$, only if $\Omega^2(1+q^2)\ll 1$.
It is in this specific sense that  we can say that
for short interaction times but much bigger than $1$, at weak fields, we measure the Fano profile. The need for a short elapsed time for the interference to build-up is not usually recognized, but has been measured experimentally \cite{Kaldun2016}.

Figure \ref{fig:scattering} shows the evolution of the ionization profile at different times (in units of $1/n\pi V^2)$ for an asymmetry parameter of $q=1$ for three values of the field $\Omega=0.01$, $\Omega=0.1$ and $\Omega=5$. For weak fields ($\Omega=0.01$ and $\Omega=0.1$), the Fano profile does not appear right away but builds up during a time $1/n\pi V^2$. This transient corresponding to the sampling time of the continuum by the discrete excited state has been observed experimentally \cite{Kaldun2016}. After this time the Fano expression then develops and is valid for $T \ll 1/\Gamma_0$. At long times, there is a saturation effect where the profile is Fano like with a smaller asymmetry parameter, although we note that this lineshape cannot even approximately be described by a Fano form. This evolution of the profile is absent for strong fields ($\Omega=5$) which shows a flat profile at all times.

To conclude this section we would like to stress that the explanation for the asymmetric profile originally given by Fano is valid for  very specific experimental conditions, namely scattering with weak field and observations at intermediate times, which were well adapted to the experimental setup available at that time. In this type of scattering experiment, the  incident flux of particles is constant. However, the Beutler-Fano formula has been used in a plethora of experimental contexts where these specific conditions are not fulfilled.  One of our objective in this article is to understand if and why the Beutler-Fano formula works in these variety of context.
Surprisingly, as we show in the next section, taking into account dissipative processes broadens the conditions under which Beutler-Fano profiles can be observed, justifies its choice as a phenomenological fit and explains its overwhelming success.

\section{Dissipative formalism}
Let consider a steady-state monochromatic irradiation that  impinges upon the system, as in the original Fano scattering case, but now we suppose that the   "fragmented" species (such as an electron in a continuum or in a conduction band) are restored to the ground state by dissipative processes induced by an environment. For instance, in gas phase  this environment can be collisions with others particles or  vacuum field fluctuation inducing spontaneous emission. In condensed phase, the environment may be constituted by phonons or by the Coulomb interaction of the photogenerated electron-hole pair.
In any case, the environment is here considered  as a Markovian bath at zero temperature. In such case, the evolution of the system state, represented by the density operator $\rho(t)$, fullfils a Liouville equation:
\begin{equation}
\frac{\mathrm{d} \rho}{\mathrm{d} t} = L(\rho)=-\frac{i}{\hbar}[H,\rho]+L^D(\rho),
\end{equation}
 where the generator of the dissipative evolution has the  Lindblad form,  $L^D=\sum_i \Gamma_i\big(  D_i\rho D_i^{\dagger}-\frac{1}{2}\{D_i^{\dagger}D_i,\rho \}\big)$ where $D_i$ are Krauss operators \cite{Lindblad1976,Gorini1976}.
We will repeatedly use the isomorphism from the column form to the tensorial product~\cite{Havel2003}
given by $L\tilde{\rho}R\rightarrow \bar{R} \otimes L \rho$, where $\rho$ is the
column form of $\tilde{\rho}$ through the correspondance:
$\tilde{\rho} = \sum_{ij} \rho_{ij}\ket{i}\bra{j} \rightarrow \rho =
\sum_{ij} \rho_{ij} \kket{ij}$, where $\kket{ij} \equiv \ket{i}\otimes\ket{j}$. We start by considering that the dissipation induces population relaxation from  the continuum states  to the ground state, and from the discrete excited state to the ground state, only (see Fig.~\ref{fig:FanoDissip}).

\begin{figure}[ht]
\centering
\begin{tikzpicture}[scale=0.7]
\draw[thick] (0,0) -- (4cm,0) node[right]{$\ket{g}$};
\draw[thick] (0,3cm)--(4cm,3cm) node[right]{$\ket{e}$};
\draw[fill=gray]  (6cm,1cm) rectangle (7cm,5cm) node[right]{$\ket{k}$} ;
\draw[->,thick] (2cm,0) --(2cm,2.9cm) node[midway, right] {$\mu_{e}$};
\draw [->,thick] (2.5cm,0cm)--(6.25cm,3.25cm)
node[midway, above] {$\mu_{k}$};
\draw[<->,thick] (3cm,3.1cm) to[out=45,in=135] node [sloped, above] {$V(k)$} (6.5cm,3.1cm);
\draw [->,thick,decorate,decoration=snake] (6.25cm,2.75cm)--(3cm,0)
node[midway,sloped ,below,] {$\Gamma_c$};
\draw [->,thick,decorate,decoration=snake] (1cm,2.9cm)--(1cm,0) node[midway,left] {$\Gamma_e$};
\end{tikzpicture}
\caption{\label{fig:FanoDissip} Energy levels and transitions of a Fano-type model with dissipation. Hamiltonian coupling are indicated by straight arrows, dissipative processes by twisted arrows. Population relaxations from continuum states, at a rate $\Gamma_c$, and from the discrete excited state, at a rate $\Gamma_e$ to the ground state are only considered.}
\end{figure}

The explicit expression of $L$ has a Hamiltonian part $H$ that is given by Eq.~\eqref{eq:Hamiltonian},
and a dissipative part $L^D = L^D_{\text{pop}}+L^D_{\text{pure}}$.
Where $L^D_{\text{pop}}$ describe the relaxation of excited state populations.
Pure dephasing, in other words additional decay of coherence, is described by
$L^D_{\text{pure}}$.
\begin{align}
L^D_{\text{pop}}&=\int dk \Gamma(k) \Big\{ A(k,g)\otimes A(k,g)  \nonumber \\
& - \frac{1}{2}\left[1\otimes A^{\dagger}(k, g)A(k,g) +
  A^{\dagger}(k,g)A(k,g)\otimes 1\right]\Big\}   \nonumber \\
&+\Gamma_e \Big\{ A(e,g)\otimes A(e,g)  \nonumber \\
& - \frac{1}{2}\left[1\otimes A^{\dagger}(e, g)A(e,g) +
  A^{\dagger}(e,g)A(e,g)\otimes 1\right]\Big\},
\label{eq:dissipation_k}
\end{align}
\begin{eqnarray}
&L^D_{\text{pure}} =-\gamma_{eg}\big[\ket{e}\bra{e}\otimes\ket{g}\bra{g}+\ket{g}\bra{g}\otimes\ket{e}\bra{e}\big] \nonumber\\
&-\int dk\gamma_{kg}\big[\ket{k}\bra{k}\otimes\ket{g}\bra{g}+\ket{g}\bra{g}\otimes\ket{k}\bra{k}\big] \nonumber \\
&-\int
dk\gamma_{ke}\big[\ket{k}\bra{k}\otimes\ket{e}\bra{e}+\ket{e}\bra{e}\otimes\ket{k}\bra{k}\big],
\label{eq:pureD}
\end{eqnarray}
$A(i,j)=\ket{j}\bra{i}$ are the
jump operators and $\Gamma(k)$ is the population relaxation rate from
state $\ket{k}$ to $\ket{g}$ as is $\Gamma_e$ for the $\ket{e}$ population. $\gamma_{ij}$ is the pure dephasing rate for the $ij$ coherence.
As in the scattering case, we apply the RWA approximation, which gives a time-independent Liouvilian operator $L$ in the rotating frame, obtained through the unitary transformation
$L=e^{i\underline{\Omega}_Lt}\mathcal{L}(t)e^{-i\underline{\Omega}_Lt}$. Where $\mathcal{L}(t)$ is the original time-dependent  Liouville operator and $\underline{\Omega}_L$ is a diagonal matrix whose
elements are equal to  $\pm \omega_L$ for excited(ground)-ground(excited) coherences, and zero elsewhere.
That is
$\underline{\Omega}_L=\omega_L\left(\kket{eg}\bbra{eg} +\int \mathrm{d} k \kket{kg}\bbra{kg}\right)
- \omega_L\left(\kket{ge}\bbra{ge}  +\int \mathrm{d} k \kket{gk}\bbra{gk}\right)$.
The observable originally addressed by Fano is
 the total population in the continuum set of states under steady-state conditions and  we will focus in this observable.
The absorption cross-section $\Im(\rho_{eg}+\int dk \rho_{kg})$ can just as easily be calculated as both it and the total population are obtained from a knowledge of the steady-state density matrix.
\subsection{Feshbach projectors, resolvent and effective Liouvillian}
Our objective is to compute the steady state $\frac{\mathrm{d} \rho}{\mathrm{d} t} = 0$, which is the kernel of $L$, that is the solution of $L(\rho) = 0$.
In analogy to the scattering case, we define partition superoperators \cite{Finkelstein2016-1}:
\begin{equation}
\mathcal{P}=P\otimes P;\quad%
\mathcal{Q}=P\otimes Q + Q\otimes P + Q\otimes Q.
\label{eq:partitions}
\end{equation}
where $P$ and $Q$ have been defined in Eq.~\eqref{eq:PQdef}.
It can be shown that the complete kernel of $L$ can be obtained in two steps (see Appendix~\ref{app:Proj}).
\begin{equation}
\begin{split}
L_{\text{eff}}\mathcal{P}\rho&=0 \\
\mathcal{Q}\rho&=\mathcal{Q}\mathcal{G}_0(0)\mathcal{Q}\mathcal{V}\mathcal{P}\rho
\end{split}
\label{eq:kernel}
\end{equation}
where the effective Liouvillian is \cite{Finkelstein2016-1}:
\begin{equation}
\begin{split}
L_{\text{eff}}&\equiv \mathcal{P}L_0\mathcal{P}+\mathcal{P}\mathcal{V}\mathcal{Q}\mathcal{G}_0(0)\mathcal{Q}\mathcal{V}\mathcal{P}\equiv \mathcal{P}L_0\mathcal{P}+\mathcal{W}
\end{split}
\label{eq:Partition-Liouvillian}
\end{equation}
where $L_0=\mathcal{P}L\mathcal{P}+\mathcal{Q}L\mathcal{Q}$ is the block-diagonal Liouvillian of the whole system, $\mathcal{G}_0(z)=(z-L_0)^{-1}$ is its resolvent and $\mathcal{V} = L-L_0$. The operator $\mathcal{W}=\mathcal{P}\mathcal{V}\mathcal{Q}\mathcal{G}_0\mathcal{Q}\mathcal{V}\mathcal{P}$ captures the effect of the continuum on the two-level system. The projection $\mathcal{P}\rho$ of the exact steady-state density matrix in the 4 dimensional subspace spanned by the discrete sates and their associated coherences, is obtained through the kernel of the effective Liouvillian which is a $4\times 4$ matrix. This is a considerable simplification as it can be easily done numerically or symbolically by the appropriate software.
In a second step, the population in the continuum set of states - the observable of interest - is obtained  from
Eq.~\eqref{eq:kernel} as \cite{Finkelstein2016-1}:
\begin{equation}
\begin{split}
\int dk \rho_{kk}&=tr(\mathcal{Q} \rho)=\sum_{\{ij\}} C_{\{ij\}} (\mathcal{P} \rho_0)_{\{ij\}},
\end{split}
\label{eq:Ci}
\end{equation}
where $C_{\{ij\}}=\int dk \bbra{kk} \mathcal{Q}\mathcal{G}\mathcal{Q}\mathcal{Q}L\mathcal{P}\kket{ij}$ with $\kket{ij}=\kket{gg},\kket{eg},\kket{ge},\kket{ee}$ and  $\mathcal{Q}\mathcal{G}\mathcal{Q}=(\mathcal{Q}(\underline{\Omega}_L-L)\mathcal{Q})^{-1}$. In this way, we have expressed the total population of the continuum as a linear combination of the elements of the density matrix in the subspace spanned by the discrete states only, with coefficients $C_{ij}$. Equations \eqref{eq:kernel} and \eqref{eq:Ci} give a method for calculating  the population in the continuum set of states. In general this is an involved calculation that does not always result in a closed form solution. We will show the conditions necessary for equation \eqref{eq:Ci} to conclude in a Fano profile, and will illustrate a simple method of evaluation of the effective operators in \eqref{eq:kernel} that highlights the connection between the scattering problem and the dissipative one.  \newline

\subsection{Conditions for a Beutler-Fano profile}
The Beutler-Fano lineshape characterizes the dependence of the continuum states population as a function of irradiation frequency, which appears in the model as the dimensionless parameter $\epsilon=(\omega_L-E_e)/\hbar\gamma$. To understand the origin of the Fano form we must understand the $\epsilon$-dependence of the population in the continuum. We note that the Beutler-Fano profile needs not to be exactly expressed as a function of $\epsilon$ but can be given as a function of an effective $\epsilon_{\text{eff}}$ that has been shifted and rescaled with respect to $\epsilon$, $\epsilon_{\text{eff}}= \frac{\epsilon+\Delta}{\sigma}$ (see appendix~\ref{app:FanoPolynome}). This will give the same functional lineshape.
It can be shown that a ratio of polynomials of order 2 in $\epsilon$ is equivalent to writing it as a Beutler-Fano lineshape plus a Lorentzian function, or alternatively as a Fano profile with a complex asymmetry parameter $\underbar{q} = q +iq_\text{i}$ (see Appendix~\ref{app:FanoPolynome}):
\begin{align}
f(\epsilon,q)&=\frac{\abs{\epsilon_{\text{eff}}+ \underbar{q}}^2}{\epsilon_{\text{eff}}^{2}+1}
=\frac{(q+\epsilon_{\text{eff}})^2}{\epsilon_{\text{eff}}^{2}+1} +  \frac{q_{\text{i}}^2}{\epsilon_{\text{eff}}^{2}+1} \nonumber \\
&=\frac{a_0 + a_1\epsilon + a_2\epsilon^2}{b_0 + b_1\epsilon + b_2\epsilon^2},
\end{align}
Therefore, to prove that the profile is of  Beutler-Fano type  is equivalent to prove that the observable is the ratio of two polynomials of order 2 in $\epsilon$. \newline

The effective Liouvillian is calculated by means of exact resummation of perturbative expansions as was carried out in Refs. \cite{Finkelstein2015} and \cite{Finkelstein2016-1}.
The result for the model that considers dissipation from the continuum states $\ket{k}$ and from the  discrete excited state $\ket{e}$ to the ground state $\ket{g}$ with dissipation rates $\Gamma_c$ and $\Gamma_e$ is:
\begin{equation}
L_{\text{eff}}=\left[\begin{matrix}
0 & K\Omega & K^*\Omega & 2\Gamma_e+2 \\
-K^*\Omega & A & 0 & -K\Omega \\
-K\Omega & 0 & A^* & -K^*\Omega \\
0 & -K\Omega & -K^*\Omega & -2
\end{matrix}\right]
\end{equation}
in units of $n\pi V^2$, where $K=1+iq$, $A=-\Gamma_e -\Omega^{2} - i \epsilon - \gamma_{eg} - 1$ and $\Omega=F\mu_c/2V$, $\gamma_{eg}$ is the dephasing rate of the two levels system (TLS) and all other parameters have been previously defined. We note that  the system is impervious to the pure dephasing processes between the continuum and the TLS in the wideband approximation, as . In preparation to tackling more general cases, we will  do two key steps:
\begin{enumerate}
\item \textit{Separate the effective Liouvillian in two parts: a scattering contribution and a generalized quantum jump operator} \\
\item \textit{Reduce the solution of the kernel of the $4\times 4$ $L_{\text{eff}}$ matrix to a linear equation of $3\times 3$ matrices using the conditions for relaxing maps (i.e. having a unique steady-state) \cite{Davies1970,Spohn1977} }
\end{enumerate}

For the first step we write:
\begin{equation}
L_{\text{eff}}=-i(1 \otimes H_{\text{eff}}-\bar{H}_{\text{eff}}\otimes 1)+\tilde{L}
\end{equation}
where we can recognize $H_{\text{eff}}$ as the effective Hamiltonian of the scattering problem Eq. \eqref{eq:Heff} and $\tilde{L}$ is a generalized quantum jump operator that ensures the conservation of the trace of the density matrix \cite{Plenio1998,Breuer2004,Gardiner1992,
Piilo2008}.
The quantum jump approach was originally introduced in the modelling of fluorescence decay. In our case $\tilde{L}$ not only restores population to the ground state from populations in the excited state, but also from ground-excited coherences as can be seen from the elements in the upper row of $\tilde{L}$. The total population in the continuum (Eq. \eqref{eq:Ci}) as a function of the populations of the disrete partition is fully specified by a column vector $\mathbf{C}$ containing the coefficients $C_i$ and an appropriate normalization $\int dk \rho_{kk}+\rho_{gg}+\rho_{ee}=1$. These three elements, $H_{\text{eff}}$, $\tilde{L}$, and $\mathbf{C}$ fully specify the solution:
\begin{equation}
\begin{split}
H_{\text{eff}}&=\begin{bmatrix}
-i\Omega^2 & (q-i)\Omega \\
(q-i)\Omega & -\epsilon-i \\
\end{bmatrix} \\
\tilde{L}&=\begin{bmatrix}
2\Omega^2 & 2\Omega & 2\Omega & 2 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{bmatrix}, \; \mathbf{C}=\begin{bmatrix}
2\Omega^2 \\ \Omega \\ \Omega \\ 1
\end{bmatrix}
\end{split}
\end{equation}

The second step involves calculating the kernel of $L_{\text{eff}}$ by transforming the problem to a linear equation $M v=b$. We can do this because the Lindblad form of a two-level system is written in the basis of Pauli matrices, so it fulfills the condition that the generators are self-adjoint and that only the identity commutes with them \cite{Spohn1977}. As a consequence there is a unique steady-state, one of the elements of the density matrix is determined by the normalization condition and the problem reduces to the linear equation of dimension $3 \times 3$. We use $\rho'$ to denote the unnormalized density matrix. Then:
\begin{equation}
\begin{split}
M&=\left[\begin{matrix}
0 & Q\Omega & Q^*\Omega \\
-Q^*\Omega & A & 0 \\
-Q\Omega & 0 & A^* \\
\end{matrix}\right];\;
v=\begin{bmatrix}
\rho_{gg}' \\
\rho_{ge}' \\
\rho_{eg}'
\end{bmatrix};\;
b= \begin{bmatrix}
-2\Gamma_e-2 \\
Q\Omega \\
Q^*\Omega
\end{bmatrix}
\end{split}
\label{eq:Cramer}
\end{equation}
Cramer's formula tells us that:
\begin{equation}
\begin{bmatrix}
\rho'_{gg} \\
\rho'_{eg} \\
\rho'_{ge} \\
\rho'_{ee}
\end{bmatrix}=\frac{1}{\text{det}(M)}\begin{bmatrix}
\text{det}(M_1) \\
\text{det}(M_2) \\
\text{det}(M_3) \\
\text{det}(M)
\end{bmatrix}
\end{equation}
where $\text{det}(M_i)$ is the determinant obtained from the matrix $M$ by replacing the $i$-th column by the  vector $b$. We can neglect the overall prefactor $\frac{1}{\text{det}(M)}$ since it will cancel during the normalization. We look at each element of the density matrix.
\begin{enumerate}
\item  The structure of the effective Liouvillian is such that the various elements $\text{det}(M_i)$ are polynomials in $\epsilon$ of order 0, 1 and 2 (see Equation \eqref{eq:Cramer}).
\item The population of the continuum is a linear combination of the density matrix in the $\mathcal{P}$ subspace with $\epsilon$-independent coefficients, so that along with the normalization condition $\rho_{gg}+\rho_{ee}+\int dk \rho_{kk}=1$ we arrive at the end result.
\end{enumerate}

The previous steps prove that
\begin{equation}
\int dk \rho_{kk}=\frac{\sum_{n=0}^2 a_n\epsilon^n}{\sum_{n=0}^2 b_n\epsilon^n}
\end{equation}
which by a judicious normalization of the variables can be brought back to a general Beutler-Fano profile (see Appendix~\ref{app:FanoPolynome}). The dependence on the square of $\epsilon$ arises from the determinant of $M_1$ that involves the product of the coherences. This is a direct consequence of the wideband approximation and can be traced back to the fact that $L_{\text{eff}}-L_0$ does not depend on $\epsilon$ (the same reasons lead to $\epsilon$-independent $C_i$ coefficients). After analyzing the possible generalizations of the dissipation channels we will revisit the structure of Eq. \eqref{eq:Cramer}. \newline

The condition that allows us to express the kernel problem as a linear equation is very general and stems from the assumption of a steady-state of dimension 1. This condition can be broken whenever the relaxation mechanism is towards a manifold of states that do not have dissipation within them and is not typical of most physical systems. In this case, we must solve for the kernel directly.

It is also important to clarify the nature of the steady-state in particular in connection to photoelectron spectroscopy experiments in the presence of radiative damping \cite{Agarwal1984}. With pure Hamiltonian evolution, the asymptotic limit of the population will be entirely in the continuum. In the dissipative case where the generator of dynamics is a Lindblad operator there will always be a true steady-state which consists of a fraction of electrons in the ground state (which can be negligible if the dissipation rate is much smaller than the Rabi frequency). A more realistic description can be obtained by introducing a sink state which acts as a detector. Alternatively, if the atoms are continuously pumped into the system it can be seen as a transport experiment, a problem solved in the next section.

\subsection{Non-equilibrium stationary transport.}
Beutler-Fano profiles has also been predicted and observed in electronic transport \cite{Huang2015,Baernthaler2010,Xiao2016} where a confined electronic quantum system (atom, molecule, quantum dot, circuit) is connected to electrodes.
As noted in Refs~\cite{Nitzan2002,Weiss2006} the knowledge of the equilibrium stationary state $\rho$, obtained in the previous section through Eq.~\eqref{eq:Partition-Liouvillian} and Eq.~\eqref{eq:Ci} can also be used to describe the following non-equilibrium stationary electronic transport situation.
Take the same system as above but where population from the continuum state to the ground state, at rate $\Gamma_c$,  is now replaced by a current $J$ flowing across the system,  with $J =\int dk \Gamma_c \rho_{kk}$ (see figure~\ref{fig:transportFano}).
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.6]
\draw[thick] (-4,0) -- (0cm,0) node[right]{$\ket{g}$};
\draw[thick] (0,3cm)--(4cm,3cm) node[right]{$\ket{e}$};
\draw[fill=gray]  (6cm,1cm) rectangle (7cm,5cm) node[right]{$\ket{k}$} ;
\draw[->,thick] (-2cm,0) --(2cm,2.9cm) node[midway, right] {$\mu_{e}$};
\draw [->,thick] (-1.5cm,0cm)--(6.25cm,3.25cm)
node[midway, above] {$\mu_{k}$};
\draw[<->,thick] (3cm,3.1cm) to[out=45,in=135] node [sloped, above] {$V(k)$} (6.5cm,3.1cm);
\draw [->,thick,decorate,decoration=snake] (1cm,2.9cm)--(-3cm,0) node[midway,left] {$\Gamma_e$};
\draw[->,line width=1.5] (7.1cm,2.5) -- (8cm,2.5);
\draw[line width=1.5] (8cm,2.5) -- (9cm,2.5);
\draw[line width=1.5] (9cm,2.5) -- (9cm,-1cm);
\draw[->,line width=1.5] (9cm,-1cm) -- (2cm,-1cm) node[pos=0.5,anchor=south]{$J =\int dk \Gamma_c \rho_{kk}=r\rho_{gg}$};
\draw[line width=1.5] (2cm,-1cm) -- (-5cm,-1cm);
\draw[line width=1.5] (-5cm,-1cm) -- (-5cm,0cm);
\draw[->,line width=1.5] (-5cm,0cm) -- (-4.1cm,0cm);
\end{tikzpicture}
\caption{\label{fig:transportFano} Energy levels and transitions of a Fano-type model with dissipation for the electronic transport set-up. Hamiltonian coupling are indicated by straight arrows, dissipative processes by curly arrows. Population relaxations  from the discrete excited state, at a rate $\Gamma_e$ to the ground is considered. The population relaxation from the continuum set of states is now replaced by as a stationary current $J$ flowing across the systems.}
\end{figure}
The master equation describing this transport set-up can be written as:
\begin{equation}
\dot{\rho}=L_{\text{t}}\rho+J,
\label{eq:FanoTransport}
\end{equation}
where $L_{\text{t}}=L-\int dk \Gamma(k) A(k,g)\otimes A(k,g)$ is the same Liouvillian as the original $L$ (see Eq.~\eqref{eq:dissipation_k}), except that it does not include the  population relaxation from the continuum set of states back to the ground state.
It was shown that the stationary solution of Eq.~\eqref{eq:FanoTransport} is the same as the equilibrium stationary solution $L\rho=0$, if the current $J$ is exactly taken as $J =\int dk \Gamma(k) \rho_{kk}$ \cite{Nitzan2002,Weiss2006}. This was carried out in the context of electron transport through a molecular bridge.
Moreover,  because the current is stationary, it can also be written as $J = r\rho_{gg}$ where the transfer rate $r$ is from the ground state to any of the continuum states. This transfer rate can therefore be expressed as:
\begin{equation}
r = \frac{\int dk \Gamma(k) \rho_{kk}}{\rho_{gg}}.
\label{eq:Transport}
\end{equation}
The transfer rate $r$ is an intrinsic characteristic of the system coupled to the laser field.
It is independent of $\Gamma(k)$ which is a constant noted $\Gamma_c$ in the wide band approximation. The constant $\Gamma_c$ only sets the time scale to reach the stationary regime.
The transfer rate $r$ gives the probability per unit of time for an electron to  jump from the ground state to one of the continuum states.
We have shown in Ref.~\cite{Finkelstein2016-1} that $r$ as a function of $\epsilon$ can also be written as the sum of a Beutler-Fano profile and a Lorentzian function. Furthermore, in the limit of low field, with $\Omega\ll 1$ and setting $\Gamma_e = 0$ (that is ignoring any dissipative process) we exactly recover the scattering rate
given by Eq.~\eqref{eq:scattRate}~:
\[
r(\epsilon;\Gamma_e=0) = \frac{\mathrm{d} P}{\mathrm{d} t} + \mathcal{O}(\Omega^4)= 2\Omega^2\frac{(\epsilon +q)^2}{1+\epsilon^2} +
\mathcal{O}(\Omega^4).
\]
Consequently, we can affirm  that this transport set-up constitutes a well defined generalization of the original Fano scattering formalism, adapted to include dissipative processes and intense incident laser field.

We have explicitly proved that in a very general way a Beutler-Fano profile is observed even for intense incident fields and when dissipative processes are included. Doing so, we have also developed a method to obtain the stationary state for a dissipative system with continuum spectrum, which relies on obtaining an effective Liouville operator in the discrete states subspace, through partitioning and resummation of Dyson equations.
In the next section, we will use this method to tackle the more general problems of multiple discrete levels coupled to multiple continua with arbitrary Markovian dissipative channels. In theses cases, we expect to observe a departure from the strict Beutler-Fano profile.

The model presented in the last section is an example of a discrete-continuum Hamiltonian with Markovian dissipation channels, but both the Hamiltonian structure and Markovian channels can be generalized. We start by reviewing the possible additional dissipation channels and then move on to consider an arbitrary discrete-continuum Hamiltonian.

\subsection{Generalizing the dissipation: incoherent hopping and finite temperature effects}
  A first extension is to include  an incoherent decay at a rate $\Gamma_{ce}$ from the continuum states to the discrete excited state in addition to the decay to the ground state at a rate $\Gamma_{cg}$.
The effective Liouvillian can be obtained following the same technique as before.
For ease of readability, in this section and what follows the explicit form of the effective Liouvillians will be listed in the Appendix~\ref{app:FormOperators}. In this case $L_{\text{eff}}-L_0$ is also $\epsilon$-independent and the system relaxes to the ground state (due to $e-g$ population decay), so that we may say that the final profile will be in Fano form as well. We can follow a similar line of reasoning as for the preceding section with the use of Cramer's rule. Here the general $M$ matrix is:
\begin{equation}
\begin{split}
M&=\left[\begin{matrix}
K & C & C^* \\
B^* & A & 0 \\
B & 0 & A^* \\
\end{matrix}\right]
\end{split}
\end{equation}
where $K=2\Omega^2(\beta-1)$, with $\beta=\frac{\Gamma_{cg}}{\Gamma_{cg}+\Gamma_{ec}}$; and  $B=-\Omega(1+iq)$,  $C=\Omega(\beta-1+iq)$. The same order of $\epsilon$ dependences indeed lead to a Fano profile plus a Lorentzian. \newline

Finite temperature effects, or incoherent terms that will take population from the discrete states and transfer it to the continuum partition are also physically important. Let's consider the rate from ground state to the continuum $\Gamma_{g\to k}$. The total injection into the continuum $\int dk \Gamma_{g\to k}$ diverges in the wideband approximation. It is a problem that only exists when the accepting states are not finite. This is resolved because physically the continuum does not extend to infinity. This means that incoherent pathways into the continuum cannot be included within the wideband approximation and go beyond the ambitions of this work. Extending beyond the wideband approximation in Liouville space is considerably more complicated than in the Hilbert space and will be presented in the future. \newline

Once having established the possible most general relaxation channels, we move on to generalize the solution of Fano interference in Hamiltonians of arbitrary complexity, meaning multiple discrete levels and multiple continua where the wideband approximation is still valid.

\subsection{Multiple discrete-continuum Hamiltonian with Markovian dissipation channels}

In his seminal 1961 article \cite{Fano1961}, these multi-levels multi-continua structures were addressed but in  the weak-field Hamiltonian scattering approach of Section I., but to our knowledge, no general solution have been published to date in Liouville space.
As we will see, while their solution does not conform to the Beutler-Fano profile they can be worked out by the effective Liouvillian approach explained in this article.
The method of solution is similar as to what has been presented before and we provide a recipe to calculate the continuum population in the most general case.

We obtain the solution by first calculating the effective Liouvillian in the discrete state subspace. We consider an $N$-levels system coupled to $M$ separate continua.  The continuum $a$ will relax to the discrete level $b$ with a rate $\Gamma^{(a)}_{b}$. We have:
\begin{equation}
\begin{split}
H_0&=\sum_{i=1}^N E_i \ket{i}\bra{i} + \sum_{\substack{i,j=1 \\ i\neq j}}^N \mu_{ij} \ket{i}\bra{j} \\
H_{\text{eff}}-H_0&=-i\sum_{a=1}^M\sum_{i,j=1}^{N}n^{(a)}\pi V_{i}^{(a)}V_{j}^{(a)}\ket{i}\bra{j} \\
L_D&=\sum_k \Gamma_k\big(  D_k\rho D_k^{\dagger}-\frac{1}{2}\{D_k^{\dagger}D_k,\rho \}\big)\\
\tilde{L}&=\sum_{a=1}^{M}\sum_{i,j=1}^{N}\sum_{b=1}^{N}\frac{2\Gamma_{b}^{(a)}}{\sum_{l=1}^{N}\Gamma_{l}^{(a)}}
n^{(a)} \pi V_{i}^{(a)}V_{j}^{(a)}\kket{bb}\bbra{ij} \\
C^{(a)}_{\{ij\}}&= \sum_{i,j=1}^{N} \frac{n^{(a)}2\pi V_{i}^{(a)}V_{j}^{(a)}}{\sum_{l=1}^{N}\Gamma_{l}^{(a)}}  \\
& \sum_{a=1}^{M} \int dk_a \rho_{k_ak_a} + \sum_{b=1}^{N} \rho_{bb} = 1
\end{split}
\label{eq:recipe}
\end{equation}
where $V_i^{(a)}$ is the coupling (including radiative coupling) between level $i$ and the continuum $(a)$ and
$\Gamma_b^{(a)}$ is the relaxation rate from the continuum $a$ to the discrete state $b$. $L_D$ is the dissipation within the discrete manifold and here $D_i$ are the Krauss operators corresponding to the discrete manifold only. The transformation into the dimensionless constants appearing throughout this article is straightforwardly obtained by normalizing by the effective width of choice $\gamma=n\pi V^2$ (where the chosen coupling $V$ varies depending on the Hamiltonian structure).
This is one of the main results of this article and a landmark result in the Fano literature. It is the generalization of the Fano problem to any discrete-continuum Hamitlonian in a Markovian environment at zero temperature within the wideband approximation. Figure \ref{fig:multiple_continua} shows the population in the continuum of a general Fano system consisting of three discrete levels ($0$, $1$, and $2$) and two continua $A$ and $B$ along with the characteristic asymmetric lineshapes.

\begin{figure}[ht]
\centering$
\begin{array}{cc}
\begin{tikzpicture}[scale=0.7]
\draw[thick] (0,0) node[left]{$\ket{0}$} -- (4cm,0);
\draw[thick] (0,3cm) node[left]{$\ket{1}$} --(4cm,3cm);
\draw[thick] (0,4cm) node[left]{$\ket{2}$} --(4cm,4cm);
\draw[fill=gray]  (4.5cm,1cm) rectangle (5.5cm,6cm) node[right]{$\ket{A}$} ;
\draw[fill=gray]  (-2cm,1cm) rectangle (-1cm,6cm) node[right]{$\ket{B}$} ;
\end{tikzpicture} \\ \includegraphics[width=0.5\textwidth]{general-Fano-example.pdf}
\end{array}$
\caption{\label{fig:multiple_continua} Populations in a general Fano system consisting of three discrete levels ($0$, $1$, and $2$) and two continua $A$ and $B$. The parameters and couplings are $E_1=10$, $E_2=20$, $\mu_{01}=0.3$, $\mu_{02}=0.4$, $V_{12}=0$, $\Gamma_{31}=0.05$, $\Gamma_{21}=0.04$, $V_{1}^{(A)}=0.05$, $V_{2}^{(A)}=0.1$, $V_{3}^{(A)}=0.2$, $V_{1}^{(B)}=0.1$, $V_{2}^{(B)}=0.3$, $V_{3}^{(B)}=0.02$, $\Gamma^{(A)} =0.5$, $\Gamma^{(B)}=0.7$. $\mu_{ij}$ is the transition dipole moment between states $i$ and $j$, $V_{ij}$ the electronic coupling and $\Gamma$ the relaxation rates.}
\end{figure}

We summarize the difference between the approach followed in this article and in particular the one followed in the papers by Agarwal and co-workers \cite{Agarwal1984}. A fundamental difference stems from the construction of the dissipation superoperator which is tied to the radiation field in the case of Agarwal et al. and is purely phenomenological in the case presented. Both suffer from the local approximation which requires a reinterpretation of the value of the dissipation rates as the values of the Hamiltonian couplings are varied. The apporaches to a solution also differ. In \cite{Agarwal1984}, the solution is obtained by an elegant density factorization matrix that gives the time-evolution of the populations. In this case (and our other works \cite{Finkelstein2016-1}), we use Feshbach projection methods that solve directly for the steady-state by working in the superoperator space. The advantage is that the extension to any number of arbitrary continua and discrete states is straightforward, both populations and coherences are simultaneously solved. The dynamics is also obtaineable from this approach and will be addressed in subsequent work. A disadvantage worth noting is that deviations of the wideband approximation (for example an energy dependent dissipation rate) can only be solved perturbatively while in \cite{Agarwal1984} some energy dependences can be solved exactly.

\section{Conclusion}

The celebrated Fano profile describes a phenomenological dependence on the irradiation wavelength that is common to many theories. Often times the apparent simplicity of this form makes it easy to forget the host of phenomena that unfolds as the field becomes more intense. This behavior is strongly dependent on the experimental system and configuration of the experiment, and dictates the fundamentally important decision to use Hilbert space or Liouville space descriptions. The results are quite different. The Liouville space solution is solved via an effective superoperator method that reduces the problem of taking the kernel of an infinite matrix to taking the kernel of a $4 \times 4$ matrix. We have analyzed this structure in detail and shown the mathematical arguments to obtain a Fano profile. We have also generalized the approach to any discrete-continuum Hamiltonian coupled to a Markovian bath under the wideband approximation. Population in the continua of these systems can be now straightforwardly obtained (see Figure \ref{fig:multiple_continua}).

\section{Acknowledgements}

D.F.S. thanks a Marie-Sklodowska-Curie Individual Fellowship. We thank O. Atabek and V. Mujica for fruitful discussion.

\clearpage

redpajama_set_name: RedPajamaArXiv


text:
Q: Connecting to a server and running a file with a GUI using bash on Windows and Xming I'm running the Linux subsystem for Windows and Xming.
I am attempting to connect via ssh to a remote server and run a GUI program in Xming.
After initiating Xming, I run the following commands:
$ export DISPLAY=:0.0
$ ssh -X user@address
$ ./gui.sh

And I get the following error:
Unable to initialize GTK: could not open display

Exporting the display after I ssh returns the same error.
I have tried using ssh -Y as well.
Is this just a limitation of bash on Windows, or am I missing something?

redpajama_set_name: RedPajamaStackExchange


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text:
Атанас Димитров Белчев е български учител и революционер, малешевски войвода на Вътрешната македоно-одринска революционна организация.

Биография

Белчев е роден през 1872 или 1875 година в малешевското село Русиново, тогава в Османската империя. Получава средно образование и в продължение на много години учителства в Малешевско. Влиза във ВМОРО.

В 1897 година Белчев участва в създаването на оръжейната работилница на организацията в кюстендилското село Сабляр. В 1903 година участва в Илинденско-Преображенското въстание с четата на Христо Чернопеев.

След въстанието в 1906 година Белчев става ръководител на Малешевска революционна околия.

На 29 октомври 1910 година четата на войводата Белчев се сражава с първата дружина на летящия античетнически отряд (авджи табур). Сражението завършва без победител.

Загива в Мраморно море по време на Балканската война през 1912 година като доброволец в Македоно-одринското опълчение.

Вижте също
 Иван Белчев

Бележки

Български революционери от Македония
Дейци на ВМОРО
Хора от община Берово
Български просветни дейци от Македония
Загинали през Балканските войни
Македоно-одрински опълченци

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The photo was made by Canon EOS 600d camera with shoot mode EF50mm f/1.8 II - 50.0mm · ƒ/1.8 · 1/250s · ISO 400, gives a image excellent quality. It was archived in the category "Health/Medical", largest resolution is 5184×3456 pixels, you can download it to JPG format. We were tagged: Yoga, Spinal Twist, Yoga Posture, Health, Exercise.


Hackspace Capital (HAC) is a cryptocurrency token and operates on the Ethereum platform. Hackspace Capital has a current supply of 1,000,000,000 HAC with 323,468,764 HAC in circulation. The last known price of Hackspace Capital is 0.000923 USD and is up 0.00% over the last 24 hours. More information can be found at https://hackspace.capital/.


text:
Bath Rugby Digest: Harry trolled, Leroy still loves Bath, golf day, kitman nabs trophy
We take an alternative look at what's been happening in and around the club...
An alternative look at the world of Bath Rugby
The start of the Aviva Premiership is fast approaching, Bath Rugby are in the middle of their pre-season fixtures, but there's still been plenty going on off the field too.
Here's the latest edition of the Bath Rugby Digest...
Harry gets trolled
Harry Davies was not a happy bunny after having a try disallowed against the Ospreys.
He didn't spot Jay Baker in pursuit as he ran the ball in behind the posts, was tackled and referee Dan Thomas deemed the winger to have been held up.
If video replays and a TMO were in operation, the outcome may have been different.
Unfortunately for Harry, he wasn't getting any sympathy from his team-mates...
Bath Rugby re-sign tighthead prop Anthony Perenise from Bristol Rugby
Questionable techniques
It was the players' golf day at Cumberwell Park recently and it's fair to say there are a huge variety of techniques and standards amongst the squad.
Some of the worst swings have mysteriously disappeared from social media, but here's a taste of the day...
Bath Rugby Digest: JJ's doppelganger, Bowden back, Thomas runs, big hand for Flats
Leroy still has a soft spot...
Fans' favourite Leroy Houston clearly still has a soft spot for Bath.
The number eight came back last autumn as injury cover before returning to Queensland Reds.
He is about to embark on a Top14 campaign with Bordeaux-Begles, but if his Twitter profile is anything to go by, one club above all still holds a place in his heart...
Leroy Houston still has a Bath Rugby background on his Twitter profile
Rocco with the regiment
As most people know, as well as being a professional rugby player Semesa Rokoduguni is still a serving soldier with the Royal Scots Dragoon Guards.
He met up with his regiment in Scotland recently...
Bath Rugby Digest: Bench press PB, axe throwing, Harry Potter fandom, Vegas baby
Middy gets the goods
Courtesy of beating Ospreys - who also have Canterbury as their kit manufacturer - Bath Rugby won their first trophy of the season in the form of the Canterbury Cup.
There was no drinking champagne out of it on the way back over the Severn Bridge, however.
Kitman Steve Middleton and performance analyst Matthew Watkins had the honour of bringing the silverware home.
Mixed news on the injury front...
Our weekly injury updates are back up and running (pardon the pun).
Unfortunately from a Bath point of view, Dave Attwood's long-term knee issue is still unresolved.
Here's the latest on the lock's struggles, as well as the fitness of Sam Underhill, Nathan Catt, Freddie Burns and Tom Homer.
(Clockwise from left) Freddie Burns, Nathan Catt, Sam Underhill and Dave Attwood
TransportThe 7 best taxi services in BathShort and long distance, taxis, minibuses and airport transfers
Bath NewsBath Christmas Market will not be extended until 2020 - Visit Bath chief executive tells whyThe city's tourism board wanted to run the event for 25 days but has settled for an 18-day market for the next three years


A. "Water for the city" educational component launched!
A. Renewal of the UNESCO Chair on ESD in the Mediterranean!
C. MEdIES seminars on education about marine litter and water: Registrations open until 28/4!
The Programme "Water for the city" coordinated by GWP-Med is taking place in Alexandroupoli, Greece is in cooperation with the Municipality and the Municipal Service for Water Supply and Sanitation for Alexandroupoli. The programme aims to enhance the city water supply (by a technical work for increasing the capacity of the city's water reservoir) and to promote sustainable water management at city level, through awareness raising of students and teachers, as well as of local stakeholders and citizens.
(4) The capacity building of the local teachers (approx. 400 teachers).
To this end, MEdIES initiated the cooperation with the ESD Officers of Primary and Secondary Educational Directory of Evros in order to co-organise: (a) The first round of the school visits (to reach ~ 600 students in the first week of April) (b) the first seminar for teachers (scheduled for April 3, 2017).
Prof Scoullos, MEdIES Coordinator and GAP PN1 Co-Chair, actively participated in all sessions of the GAP Review Forum and UNESCO Week for "Peace and Sustainable Development: the Role of Education" that took place from 6 to 10 March 2017 in Ottawa, Canada. The events aimed to examine pedagogical approaches and teaching practices to achieve the Sustainable Development Goals (SDGs) through ESD and Global Citizenship Education (GCED). From 6 to 8 March the "Review Forum for the GAP" particularly aimed to review the progress so far in the implementation of the projects/initiatives under the GAP.
MEdIES/MIO and the UNESCO Chair on ESD in the Mediterranean were involved in the seminar about "The lost rivers' deltas of Attica" that was organised by the Centre of Environmental Education of Elefsina (Attica) and the ESD Officers of the Educational Directorates and took place on 18 March 2017. The seminar particularly focused on the ecosystem and biodiversity of Kifissos and Ilissos rivers deltas in Attica, an important delta within the urban environment, and included theoretical presentations as well as field work. 60 educators and 22 experts participated.
The Hellenic Ministry of Education defined a thematic week for the secondary schools in Greece dedicated to, among others, food, diet and their sustainable aspects. In this thematic axis the MEdIES material on Mediterranean food was included in the Ministry's official list of proposed educational material to be used by teachers and schools.
In close collaboration with GWP-Med and the new Water Conservation Awareness Center of Malta, MEdIES is working on the development of two interactive games to be played, by visitors of the Centre via touch screens. Both games are especially designed for players of 7-10 yrs age. The first game on the "Water Cycle" shall be launched in the Inauguration Ceremony of the Centre, on 21 April 2017, while, the second game "water in forts" is expected to be completed by July. Within this project, two more e- games will be developed by the GWP-Med team (target age 10-14 yrs).
The UNESCO Chair on Sustainable Development Management and Education in the Mediterranean, established in 2012 at the National and Kapodistrian University of Athens (NKUA), was renewed by the UNITWIN/UNESCO Chairs Programme for a period of 4 years: 2017- 2021. MEdIES is closely linked with the Chair and, particularly, in capacity building activities on ESD.
Registrations remain open until 28 April 2017.


text:
Q: PrimeFaces 5.1 not being included properly I'm trying to leverage PrimeFaces 5.1 in my JSF application.  The app is deployed as an EAR file, with 1 WAR module and multiple EJB modules.  The entire thing is built using Maven, and deployed on Wildfly 8.1.
I've included the PrimeFaces dependency in my root-level pom.xml like this:
<dependency>
                <groupId>org.primefaces</groupId>
                <artifactId>primefaces</artifactId>
                <version>${version.primefaces}</version>
            </dependency>

...and in my WAR pom.xml, I've declared it as a dependency like this:
<dependency>
            <groupId>org.primefaces</groupId>
            <artifactId>primefaces</artifactId>
        </dependency>

When I build the EAR using Maven, I can see that the primefaces-5.1.jar file is included, as expected, under my WAR module in /WEB-INF/lib.  That much seems to be working.
My JSF page has a simple <p:messages /> tag in it, with a JSF FacesMessage set via an action class.  However, when I visit the page itself I do not see the <p:messages /> component rendered.  Instead, if I view the source I actually see "<p:messages ... />".  That is, I see the JSF source for that tag, rather than the rendered component.
I am declaring PrimeFaces in my JSF file like this...
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml"
    xmlns:h="http://java.sun.com/jsf/html"
    xmlns:ui="http://java.sun.com/jsf/facelets"
    xmlns:f="http://java.sun.com/jsf/core"
    xmlns:p="http://primefaces.org/ui">
<h:head>
...

...and when I view the source of the rendered JSF page, I see the text "<html xmlns:p="http://primefaces.org/ui">".
It seems to me that the PrimeFaces rendered is not being initialized or called properly.  I've followed the directions on the PrimeFaces site that indicate how to get started with the library, but either my project structure is wrong or I am missing a step.
Any idea why my PrimeFaces JSF library is not being included and used properly?
EDIT:  My web.xml declaration of the Faces Servlet looks like this:
<web-app xmlns="http://java.sun.com/xml/ns/javaee" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
    xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd"
    version="3.0">
    <servlet>
        <servlet-name>Faces Servlet</servlet-name>
        <servlet-class>javax.faces.webapp.FacesServlet</servlet-class>
        <load-on-startup>1</load-on-startup>
    </servlet>

    <servlet-mapping>
        <servlet-name>Faces Servlet</servlet-name>
        <url-pattern>*.xhtml</url-pattern>
    </servlet-mapping>

    <servlet-mapping>
        <servlet-name>Faces Servlet</servlet-name>
        <url-pattern>/javax.faces.resource/*</url-pattern>
    </servlet-mapping>
...

A: Turns out this was an issue in how Eclipse was deploying my project's EAR file to the app server.  The WAR project wasn't set to include the Maven dependencies in the deployment assembly.  Once I made that change it deployed as expected and Primefaces worked without issue.


Barbell cycling for this workout- it's important to stay relaxed on the deadlifts because it's light but easy to lose control of your form. Break up the hang power cleans in to manageable sets. The grip will be tested here. The weight for the barbell should depend upon your skill level of squat cleans. If you did this weight fresh, you could cycle at least 5 or more reps.
6 burpee box jumps 24/20"


text:
Updated On: Feb 10, 2014
This week's member and steward tip posted today
Jan. 2, 2014 | Your website administrator was off during the holidays, so postings commenced today. Be sure to check back for a new helpful tip every Monday.
Teamsters urged to boycott Yuengling beer
Jan. 6, 2014 | The IBT General Executive Board recently voted to support a Teamsters Union boycott of Yuengling beer over the owner's push for anti-union laws. The owner of D.G. Yuengling & Sons, Inc., based in Pottsville, Pa., publicly stated that Pennsylvania should become a "right-to-work" for less state. Click here for Yuengling beer products to boycott, and substitutes that Teamster members either produce or deliver.
Tell Congress to renew unemployment insurance now
Jan. 7, 2014 | More than 1.3 million unemployed Americans were cut off December 28, 2013, from the federal Emergency Unemployment Compensation (EUC) program, a vital lifeline of support needed for them and their families to survive while they continue to look for work in our lagging economy. An additional 72,000 jobseekers will lose their benefits each week until the program is restored. Congress should restore this vital lifeline to those who will slip into deeper poverty without these benefits. A bipartisan 3-month reauthorization of unemployment benefits is the first order of business for the Senate this week. It's the right thing for our economy, as consumer spending will drop and more jobs will be lost as a result if the benefits aren't renewed. Please call your members of Congress today at 877-267-2485 and tell them the renew unemployment insurance now.
Massive trade bill filed in Congress; you can help stop it
Jan. 10, 2014 | Legislation was filed yesterday to make it easier to pass job-killing trade deals like NAFTA…Here's what you can do: Click on this link and send an email to your representatives in Congress. Do it now. We cannot allow Congress to give a rubber stamp to the TPP and other bad trade deals by allowing Fast Track to pass. (Read the full post at teamsternation.org.)
Teamsters honor legacy, celebrate contributions of Martin Luther King, Jr.
Jan. 20, 2014 | Teamsters across the country are honoring the legacy of civil rights and labor leader Martin Luther King, Jr. today. King devoted his life to securing rights for minorities and eliminating segregation in society. He believed that the path to economic freedom and social justice were one and the same and strongly supported the labor movement…Under the leadership of General President James R. Hoffa, the Teamsters donated more than $25,000 to King in 1961 and sent supplies to marchers and other civil rights workers camped out in Selma and Montgomery, Alabama, and other locations along the Freedom Ride routes. King was supporting union sanitation workers in Memphis on the day he was assassinated. Learn more at teamster.org.
Union growth should serve as signal to elected officials
Jan. 27, 2014 | The union movement is growing. In the last year, thousands of workers took to the streets to protest low pay and their lack of ability to organize. They have stood up to the nation's largest retailers saying they demand respect in the workplace. And new U.S. Labor Department numbers released Friday back that up. Continue reading at teamster.org.
Applications are available for The James R. Hoffa 2014-2015 Scholarship
Jan. 28, 2014 | The Union offers scholarships through the James R. Hoffa Memorial Scholarship Fund for high school seniors. The Fund is established solely to provide scholarships to the child or financially dependent grandchild of a member of the Teamsters. The application deadline is March 31, 2014. Click here to download the application and academic record form. Additional information here.
Teamsters to take part in tomorrow's Day of Action against Fast Track
Jan. 30, 2014 | Tomorrow, Jan. 31st, people across North American will be taking part in an Inter-Continental Day of Action against Fast Track and the Trans-Pacific Partnership (TPP). The TPP is another bad trade deal that could become the law of the land without any debate or amendments if Fast Track legislation is allowed to pass. We can't let that happen! Please be sure to call your Representative and Senators tomorrow at 1-888-979-9806 and tell them to vote NO on Fast Track. And if you're able to, please join one of the many events that are being planned nationwide for tomorrow. A listing can be found here. For more information, go to Fast Track is the Wrong Track for Teamsters.


When all you have is a man in a rubber suit, every problem looks like a building waiting to be crushed.
That was the situation faced by the makers of Toho's 1962 sci-fi epic Gorath. They had a perfectly serviceable variant of When Worlds Collide about a rogue star poised to smash the Earth. They had spaceships and tidal waves, not to mention a lunatic scheme to shove the entire planet out of harm's way by installing enormous rockets at the South Pole. But was that enough to put butts in the seats?
And that is why, 67 minutes into an 88-minute movie, the heat from the rocket engines released a prehistoric walrus from the Antarctic ice. Because the utter annihilation of the human race needed a kicker. At least a huge marine mammal buried at the South Pole makes a bit more sense than certain mountain-dwelling octopi I could name.
With only twenty more minutes to save the world, Maguma really didn't have much of a chance to spread his flippers. In the original Japanese release, he was butchered from the air by a laser-equipped aircraft. In the American edit, he was removed from the film entirely.


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Kansas City Chiefs | 2019-20 Season Highlights ᴴᴰ
By admin | March 8, 2020 | 50
Music Outro: Travis Scott – Highest In The Room
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#NFL #KansasCityChiefs #NFLHighlights #ProBowl #NFL100 #Highlights #AFCWest #SuperBowl54 #PatrickMahomes #MVP
Posted in Chiefs
Braylon Castilleja on March 8, 2020 at 10:34 pm
13:34 everyone's like oh you're still here
Froggy World on March 8, 2020 at 10:35 pm
Chiefs 2020 Champs on March 8, 2020 at 10:35 pm
I'm still enjoying this win🏆💯💯💯 We CHAMPS‼
Brandon Lewis on March 8, 2020 at 10:39 pm
We are the legion of zoom 💨💨💨💨
Matthew Marshall on March 8, 2020 at 10:40 pm
Honestly the whole season could be a highlight
Jakoby Rimmer on March 8, 2020 at 10:44 pm
i like how rogers dident throw it away
Telltale Twotones on March 8, 2020 at 10:44 pm
You left out one of the best highlights: when Arrowhead management put up a sign in the Texans playoff game saying they'd run out of fireworks because the Chiefs had scored too many touchdowns.
4K Slime on March 8, 2020 at 10:45 pm
The best moment of my life was when I went to arrowhead and I had a blast tail gating and watching Alex smith dominate and Justin hustin sacking Philip rivers in week 17 in 2017 I love this team and was going crazy when I saw they Patrick mahomes lead this to to a Super Bowl and one
Derek Mathews on March 8, 2020 at 10:45 pm
Love the offensive, defensive highlights and special teams too.
roddyrich yt13 on March 8, 2020 at 10:47 pm
Lets be honest the chiefs are over power and receivers are too fast
Grant Clement on March 8, 2020 at 10:47 pm
best season ever!!!!!!
tyler feldman on March 8, 2020 at 10:48 pm
IT'S BEEN SO LONG, SO MANY YEAR OF KANSAS CITY BEING THE LAUGHING STOCK OF THE LEAGUE AHHHHHHHH
jjmah7 on March 8, 2020 at 10:49 pm
I watched this entire thing with a huge smile on my face. Go Chiefs!!! What a season!
Callie Cox on March 8, 2020 at 10:49 pm
I LOVE THE CHIEFS
Christopher L Williams on March 8, 2020 at 10:50 pm
The Kingdom will Reign Forever
D.C. Christian on March 8, 2020 at 10:51 pm
Did anyone hear that the chiefs won the super bowl?
Nissan370Z on March 8, 2020 at 10:51 pm
Champions!
Lebogang Legodi on March 8, 2020 at 10:53 pm
7:15 Woooohh Tyreek Speedster Hill coming through
BYRON WESTBROOK on March 8, 2020 at 10:56 pm
Love how frank clark just jumps on lamar jacksons back
Paul Wilson on March 8, 2020 at 10:57 pm
I think it is fitting that the defense made that last real play of the game since it was the defense that cost us the chance last year at getting to the super bowl. show just how improved they are under Spags.
Anthony Hernandez on March 8, 2020 at 10:57 pm
15:35 DAMN BOI!!
Jay Els on March 8, 2020 at 11:00 pm
Great scheme. Speed kills.
Carl Brennen on March 8, 2020 at 11:07 pm
I have been a Chief fan since 1969. From The Bahamas but went to Grinnell College in Iowa '72. Waiting for this Superbowl since last appearance in 1970. Deward Darling Wide Receiver from The Bahamas playred for the Chiefs and now Corner Back Rashad Fenton #27 mother is a Bahamian. HAIL TO THE CHIEF.
Christopher Cupp on March 8, 2020 at 11:08 pm
The Chiefs overcame adversity all year to bring home the LOMBARDI!! This team is much more than just Pat Mahomes. They won the Super Bowl as a TEAM!!
ChezCubing on March 8, 2020 at 11:08 pm
7:17 the speed of tyreek hill
Mark Aaronson on March 8, 2020 at 11:09 pm
I'm about 90% certain that Mahomes and the chiefs intentionally put themselves in losing situations to purposely play from behind and win. I'm sure their game plan is "look like shit, throw the game, say sike"
Jorge Eduardo Herrera Ortega on March 8, 2020 at 11:10 pm
I m a big mexican fan of KC, and I was so glad when Andy Reid recive the Lombardi, I love you CHIEFS……
Ian White on March 8, 2020 at 11:14 pm
this video makes me happy
Dave Beale on March 8, 2020 at 11:14 pm
Why are they showing the highlights from the Colts game that they lost…and i thought Mahomes was supposed to be injured(or whatever excuse for losing that game?) but didn't look like it from the way he was running around, even better than Brady would have on his best day…!?!
Jean Henry on March 8, 2020 at 11:14 pm
Sucks! Hill is great ,best in nfl
NightHawk Gaming on March 8, 2020 at 11:14 pm
Way to go #ChiefsKingdom let's do what what we did this season and carry to next season
Eva Perkins on March 8, 2020 at 11:16 pm
Patrick is the best thing for his team.he sees the best in his players.patrick is always pa
frank mccollum on March 8, 2020 at 11:17 pm
Chiefs, Everyone of you players, Offense and Defense.. Plz, Plzplz stay with the Chiefs, everyone of you had the most Magical season, went to the Super Bowl and Won that thing.. You all are So Amazing!! Please stay with the KC Chiefs. Its very much like magic when you all are on the field.. KC would Love another Super Bowl, maybe 10 more, You guys are totally the greatest team.. Lets get another one. 20-21..!
GambinoRilone23 on March 8, 2020 at 11:22 pm
That's impressive, but did you know 15 minutes can save you 15% or more on car insurance?
Nathan Playz Roblox on March 8, 2020 at 11:23 pm
God dang Damien Williams is insane
Ivan Blank on March 8, 2020 at 11:25 pm
I love watching the silly little celebrations after they score a touchdown in a badass way…
Weston Kenemore on March 8, 2020 at 11:26 pm
Mark Baugher on March 8, 2020 at 11:30 pm
This is the best highlight video I've seen!
Don't think the game is over if your winning against the chiefs
Bjorn Yesterday on March 8, 2020 at 11:31 pm
Love 1:40. Mahomes turns blocker asap
IIIo2 on March 8, 2020 at 11:33 pm
Their season started in florida and ended in florida