text:
Why is Jill Stein leading the recount effort?
She says it has to do with accuracy, not politics
By: Miranda Green
Anybody wishing for a recount in the presidential election found a champion for their cause last week, not in Hillary Clinton, but in Green Party candidate Jill Stein.
Stein received only 1 percent of the national popular vote and came in last among the four major candidates running for president. She also came in last place in Wisconsin, Pennsylvania and Michigan, the three states where she's leading recount efforts. Yet, it was Stein who announced a campaign last Wednesday to raise $7 million to pay for recounts in three swing states, and it was her team that officially filed on Monday for recounts in Wisconsin and Pennsylvania.
The Clinton campaign has been a supportive yet low-profile partner. Other establishment Democrats, including the Obama administration, have been either silent or clearly unsupportive — possibly because supporting a recount could be seen as an admission that election fraud is a real concern. And, of course, Donald Trump himself was not enthusiastic, sending off a flurry of tweets Sunday proclaiming that the only fraudulent votes were those cast for Hillary Clinton, an accusation for which he offered no evidence.
So why then, with such little political support behind her, is Stein the one leading the effort?
This past weekend, Stein told NPR that her motive isn't to benefit Clinton, but rather to provide all parties a chance for clarity.
"It's not just what was the vote count for Democrats and Republicans. It's also a question of what was the vote count for Greens and for Libertarians. We want to know that the votes for Green candidates are getting counted accurately as are the votes for other candidates," she said.
Stein said she is questioning the legitimacy of the vote totals in those states overall — not only the votes cast for Trump. Stein's website emphasizes this point. It states that the recount movement has to do with verifying voting systems that the Green Party views are highly questionable. The website specifically cites online voting machines used in the Michigan, which it states were banned in California because of the possibility of hacking.
"After a divisive and painful presidential race, reported hacks into voter and party databases and individual email accounts are causing many Americans to wonder if our election results are reliable. These concerns need to be investigated before the 2016 presidential election is certified. We deserve elections we can trust," Stein wrote.
But Stein's website also makes another point clear: Questioning the validity and security of the country's current voting system is already an established policy of the Green Party.
A section of Stein's website titled "Why are you really doing this?" states, "The Green Party Platform calls for 'publicly-owned, open source voting equipment and deploy(ing) it across the nation to ensure high national standards, performance, transparency and accountability; use verifiable paper ballots; and institute mandatory automatic random precinct recounts to ensure a high level of accuracy in election results.'"
This is also not the first time that the Green Party has been behind a recount effort. In 2004, the Green Party also pushed a recount in Ohio, questioning the state's decision to disqualify 1,100 ballots. John Kerry had immediately conceded a loss there, but a Green Party-prompted recount found that Bush should be awarded 300 fewer votes. Bush still won the state, and the election.


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Home / 92.5 WBEE / 'This Is Us' star Hannah Zeile opens up about what it's like to work with Mandy Moore
'This Is Us' star Hannah Zeile opens up about what it's like to work with Mandy Moore
By Jacquie Cadorette 98.1 WOGL
Hannah Zeile, who plays teenage Kate Pearson in hit TV show "This Is Us," is opening up about how costar Mandy Moore has inspired her in various ways.
It all started off pretty normally for Zeile, telling WOGL's Glenn Kalina that she worked a food service job in her teenage years to help make a little bit of money before jumping back into acting after a 4-year hiatus.
"I was 18 and working at Chipotle as a cashier. I had done a few things when I was younger, but then I took a complete 4-year break from acting just to go have a high school experience and focus on that," she said.
When she landed a role as teenage Kate on "This Is Us," she had to really dig deep to portray the heavy struggles Kate would face in the show. Luckily, she had a team of people to help her through it.
"I am grateful that the writers and the creators fully reached out to me and wanted to talk through anything I had questions about or talk about how I could portray it because I wanted to do it in a way that was respectful," Zeile shared.
One stand-out cast member in particular is Mandy Moore. Zeile reveals that it's not just Moore's wisdom that puts her in such a high regard, it's the way she carries herself in her day-to-day.
"I think Mandy's one of the most wonderful people in the world, and that if I come to her and have questions, she'll give me advice, but I really appreciate that she just kind of teaches through actions," Zeile said.
"Just watching her and working with her and seeing the way she carries herself has taught me more than her speaking on things with me," she continued.
She concluded, "We have a really nice relationship and a friendship, and she's never wanted to seem like she's talking down to me at all."
Hannah Zeile
Bill Gates is now the owner of the most farmland in the U.S.
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Ever wonder what state matches your personality best? Take this quiz to find out! Consider yourself sophisticated? How about relaxed? Enjoy being in the great outdoors, or socializing with others? There's a state for you!
These questions will help us match you with your perfect state. We'll ask about your favorite activities & what's important to you. We'll also discover what you're looking for from your community. Don't worry; you'll love your new neighbors!
Let's get cozy with your soulmate state! Before you know it, you'll be wearing state shirts, and getting state outline tattoos! Start learning the lingo; it won't be hard since its the language of your heart.


Specatular NEW home by Skuadra Construction in a private gated community in Sharyland ISD! Come enjoy this 4 bedroom 2.5 bath plus a Study with porcelain tile throughout the house, LED lighting, modern fixtures, ceiling fans, plus much much more. House is build with cellular concrete exterior panels and laminate OSB ceilings that helps reduce electricity bill. Open floor plan with a great flow leads you to a gorgeous kitchen with white quartz counter tops. Bedrooms are 12 x 14 feet with a Master walk in closet that is HUGE! Community pool that is being renovated is a few feet away. You have to come see this beauty before it is gone!


Earlier this year, EY held Closing Excellence Seminars in Aarhus and Copenhagen based on their 2018 Nordic Closing Excellence Survey. The survey focused on common characters of high-performers and presented interesting and surprising findings. We've outlined some of these findings and added our own thoughts on the subject as well.
A Risk and Control Matrix brings clarity and overview and is key when managing best-in-class internal controls. A Risk and Control Matrix can provide a valuable overview of internal controls and their relation to key risks in financial processes.
According to the survey, high performers within month-end close often have a Risk and Control Matrix in place, which allows them to manage best-in-class internal controls. This not only brings clarity and overview, it also focuses on areas of risk, and ensures a robust control environment.
Impero is ideal for setting up a risk and control matrix – read more about risk and control here.
Bring your controls to life with Impero: Automate your controls and take full advantage of the many benefits related to automation.
High performers have more trust in their financial reporting.
The survey also suggest that it is possible to speed with the closing process while at the same time increase the quality of the output.
How? Centralisation of the reporting setup is a key driver in optimising the closing process and once activities are centralised, they can be standardised and automated as well. Benefits of centralisation often include efficient roll-out of controls, activities and policies, as well as a strong foundation to develop a more standardised approach that allows for automation. There is also a financial benefit since centralisation offers cost-saving opportunities due to economies of scale.
Impero is great for gathering financial reporting activities in one place. Centralisation, standardisation and automation of processes reduces time spent on the financial closing process and heightens the quality at the same time.
Finally, establishing a shared service center can centralise, standardise and automate your processes, which can generate significant savings and improve the overall quality. With a shared service center, you can gather activities that were once performed in separate locations or divisions in one place, thereby standardising, automating and centralising processes and reduce time spent on these.
Popular services in a shared service center include transaction processing, financial reporting, purchasing and payroll. According to the survey, 79% of high performers within the closing process have a shared service center in place.
Impero is ideal for establishing a shared service center as it enables standardised processes and controls, and it is easy to share control templates throughout the organisation, without spending time on actually sending documentation back and forth.
Organisations can set up reporting dashboards on both company and aggregated level, making it possible to gain a valuable overview of different levels, both in the shared service center and in the retained organisation. Read more about shared service centers and Impero here.


The camera will require a Class 10 MicroSD card, and is capable of using card sizes up to 32gb. How do I erase the MicroSD card while it is in the camera? Press and hold the status button and the video format button for 5 seconds to format the MicroSD memory card.... TmarTn has posted a new video that shows an unboxing of the Call of Duty: Ghosts Prestige Edition Tactical Camera. The camera allows you to strap it on, and record videos in 1080p HD. The camera allows you to strap it on, and record videos in 1080p HD.
The only way a ghost is going to be able to affect what shows up on a camera is for it to actually go inside the camera and alter the film or digital imprint. So it does not look like what you see in the picture, and isn't WHERE you see it in the picture - assuming that the picture has anything to do with a ghost at all. I've never seen anything convincingly not simply a digital or film... Most people are aware of ISO setting on digital cameras. It controls the speed of the shutter on a camera. It measures sensitivity to light. The lower the number the faster the camera shutter letting in less light and the higher the number is, the slower the shutter speed and allows more light in.
In the layer palate, change the transparency of the ghost layer until you get the ghostly effect you want. You may want to add a layer mask to the ghost to hide sections of the ghost, especially if you want them to appear behind objects in your background image.


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On-Site Commercial Solar Finance
The Irresistible Economic Logic of Commercial Solar
by Rebecca Reed
Dec 1, 2022 1:00:00 PM
Whatever the environmental benefits, building owners aren't going to install rooftop solar energy unless it makes good economic sense. With the cost of solar leveling out, the Inflation Recovery Act's extension of the 30% Federal ITC, and rising utility rates — the economic outcome for business owners has never been better.
Solar Makes Good Business Sense
Now more than ever, solar has become an attractive investment option that allows businesses to turn their roofs into income-generating assets. In this article, we'll discuss the following topics describing the economics behind on-site solar arrays installed by businesses. We'll cover:
How Solar Pays for Itself
How Solar Hedges Against Rising Utility Rates & Inflation
1. How Solar Pays for Itself
Solar arrays are paid for by a combination of Energy Savings, Utility Incentives & Tax Benefits.
A commercial rooftop solar array produces energy that directly powers the building offsetting the total Energy (kWh) that would otherwise need to be purchased by the utility at then current utility rates. A solar array also reduces the instantaneous amount of energy that is required to be provided by the utility (kW), reducing Demand Charges also billed at then current utility rates. Together, when combined with Utility Incentives & Tax Benefits, a solar array is paid for in ~4 years, and all the energy generated year ~4+ is provided for free providing a substantial direct benefit to a business's bottom line.
Utility Incentives
Xcel Energy compensates customers for helping control the Utility's peak demand with a Tariff rider called the Solar PV Demand Credit. This Tariff is monetized in the form of a Demand Credit of $. 07139/kWh for each kWH produced by the solar array between 1 - 7 pm, or 50% of the solar arrays output. The Demand Credit is provided as a credit on your utility bill and is applied against Demand Charges billed by the utility.
All projects between 40-1000kWAC are automatically eligible for the Solar PV Demand Credit.
Companies that install solar are eligible to receive both a 30% Federal Investment Tax Credit as well as Federal and State Depreciation.
The Federal Investment Tax Credit is a dollar-for-dollar one-time tax credit that can be carried forward up to 20 years and can also be used to amend your previous year's taxes. Additionally, 85% of a solar arrays cost is eligible for 100% Federal bonus depreciation in year 1, as well as State 5-year MACRS depreciation.
Together, these tax benefits pay for ~65% of the total cost of the solar project! If your business has a tax bill, instead of writing a check to the government, leverage your tax bill by installing an on-site solar array to produce a significant ROI is an absolute no-brainer.
2. Hedge Against Rising Utility Rates
Energy rates are on the rise due to supply and demand on both the local & global wholesale market, as well as upgrades to the aging grid infrastructure. As utility costs increase with inflation, the value of the energy provided by the solar array increases in kind, providing a natural hedge against the rise in utility expense.
To give some perspective on the recent rise of utility rates, Xcel Energy is raising its commercial rates by approximately 21.2% over the next three years. Minnesota Power increased their rates by 14% starting January 1 of 2022.
There's no indication when electricity prices might stabilize, but locking in your utility rates in the present coupled with immediate and long-term expense savings makes sound business sense.
3. Solar Financing Options
A variety of financing options are available that can make a solar energy system affordable for Minnesota business owners.
When a business puts its available cash to use by purchasing an on-site solar array & monetizes the Utility Incentives and Tax Benefits, a solar array produces ~4 year ROI, ~35% IRR, and 40 year expense savings that compound each year.
Financed Purchase
When a business uses financing to pay for its solar array & monetizes the Utility Incentives and Tax Benefits, a solar array produces positive cashflow every year with an ROI and IRR that are slightly less favorable than a cash purchase.
PACE Purchase
PACE (Property Tax Assessed Financing) is a Federal Program that provides lending for solar arrays using a network of banks that are approved to work with the PACE Program. Instead of making monthly loan payments to the bank, payments are made bi-annually as an assessment added to the property tax bill. PACE loans can be amortized up to 15 years, do not require a personal guarantee, and provide a fantastic avenue for a Business to receive the cash benefits of a solar project without leveraging their own capital or balance sheet.
However you choose to pay for your on-site solar array, the energy generated from it is essentially free once the solar array is paid off. Over the 40-year lifespan of a typical on-site solar array, the sustainable economic benefits are tremendous.
With historically rises in utility costs and our current economic pushing inflation to historic highs, now is the time to lock in these prime solar economics.
Contact iDEAL to learn more and discuss the right option for your business.
As the premier Minneapolis-based commercial solar energy developer, we take a partnership approach to help our customers achieve their environmental initiatives while focusing on what we know best - improving your bottom line.
We are developers, engineers, electricians, finance wizards, and O&M gurus.
Our solar A-Team has installed over 450 commercial systems with over 100+ projects under construction across multiple sectors including commercial for-profit businesses, schools, local governments, and non-profits. By marrying our technical expertise with a combination of tax incentives, utility grants, and multiple financing options, we provide cashflow positive projects from Day 1.
← Solar for Schools: How Minnesota Schools Are Tapping Their Solar Potential
A Case Study: Four Minnesota Manufacturers Who Are Saving Big with Rooftop Solar →
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The Art House is pleased to present Altered, a new exhibition by UK-based artist Tony Heaton. He is a prolific disability rights activist working in sculpture, performance and film. As artist-in-residence throughout March 2019 Heaton used his time in Wakefield to continue his practice in stone carving, as well as experiment with printing techniques in our studio.
Using the direct carving technique, Heaton has created a selection of pieces in Carrara marble, where he completed a residency in Italy in 2018. His works often involve colliding different materials and references or representing familiar motifs or objects in a new context. Through the use of dry humour or playful materials, Heaton is able to provoke and address more serious conversations.
Tony Heaton was in residence between 04 – 29 March 2019 and the exhibition continues until 18 May 2019.


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About Fifa reforms
BEING in a non-professional football set-up should not be an excuse for clubs to neglect players' rights, Namibia Football Players' Union president Sylvester Goraseb said on Tuesday.
As it is, the way Namibian clubs are administered in relation to playing personnel borders on infringement of footballers' human rights, Goraseb intimated during an information sharing session with the press in Windhoek regarding the recent watershed agreement between Fifa and Fifpro.
Last month, Fifa penned a six-year cooperation with Fifpro concerning the governance of professional football worldwide, following Fifpro's initial legal complaint against Fifa to the European Commission in September 2015.
Fifpro will also now be included and engaged on all Fifa decision making bodies, another realisation that Nafpu has been praying for in their long-running battle with the Namibia Premier League and Namibia Football Association.
However, what Nafpu is looking forward to is the establishment of a independent arbitration structure and standard contracts for players which Fifa and Fifpro will work on with football stakeholders.
The reforms will come into effect in March 2018.
With the newly adopted rules, players will now have the right to leave a club in the event of ill-treatment to force them to accept undue amendments to a contract, or in the absence of a salary for two months.
Players may also accrue additional compensation estimated at 3 to 6 months' salary after the departure of a player from a concerned club that fails to pay the salary.
Should a club not comply with Fifa's decision to compensate the players, the club will face an immediate ban on transfers.
"Fifa members who fail to implement these requirements will forfeit their funding from Fifa. These are the kind of consequences that we have been calling for all this time," Kahiriri said.
Whether these radical amendments, designed to solve the issue of poor remuneration for players, are practical in a Namibian context where football structures are negligently malleable remains to be seen.
The scarcity of financial resources and administrative unrest, which resulted in 16 months without competitive domestic football, are other pressing challenges.
"That is why we keep saying to the NFA, NPL and clubs let us sit down and find an amicable solution going forward," said Goraseb.
Fifpro and the Ghana Football Association have reportedly struck a deal for Ghanaian players to receive a fixed minimum wage as part of the pilot of the landmark cooperation agreement.
Through the agreement, Fifa recognises the world players' union as the sole body representing employment interests of players, a development that applies to both bodies' affiliates.
FIFA Mobile Coins is the pocket edition of EA Sports FIFA franchise for Android & iOS devices. As its console version, FIFA Mobile has become the best football simulation game on mobiles, including authentic ultimate team, squad building challenge, seasons, as well as the brand-new exclusive attack mode. FIFA Mobile allows players from all over the world taking part in the football feast, exchange their player card, items, kits in the transfer market. Now you can play FIFA anywhere anytime you want by joining in FIFA Mobile, the best-selling football game in the world.


The US army carried out a drone strike over the weekend against an al-Shabab training camp, about 150 kilometres north of the capital Mogadishu. According to the Pentagon, the strike killed 150. Spokesman Captain Jeff Davis told the strike destroyed a training camp where an "imminent large-scale" attack was being planned: "We know they were going to be departing the camp and they posed an imminent threat to US and African Union forces". Officials told NBC that "the group was conducting "some kind of ceremony" when American drones dropped bombs. The members of al-Shabab, an affiliate of al-Qaeda, were pushed out of Mogadishu by African Union Peacekeeping Forces in 2011. However, the group remained operational as a strong political opponent in Somalia, carrying out frequent attacks aimed at overthrowing the current pro-Western government led by Omar Abdirashid Ali Sharmarke.


text:
\section{Introduction}
\label{sec:intro}
Photoemission spectroscopy\cite{einstein} (PES) is since long
a major tool for gaining information of the electronic
structure of matter.
For instance, angular resolved photoemission spectroscopy (ARPES)
makes it possible to measure the occupied quasiparticle bands,
and photoemission from core levels yields important local
information at the atom being excited. Owing to the usually
rather short mean free path, PES is also well suited for studying surface
states,
adsorbates at surfaces, etc.

Photoelectron spectra are usually interpreted
in terms of the one-electron spectral function $A(\epsilon)$ corresponding
to a sudden removal of an electron. In emission from solids,
however, the photoelectron is created at a certain distance from
the surface and may undergo losses on its way out.
In the sixties, Berglund and Spicer\cite{spicer} proposed a
semi-empirical model involving primary
excitation, transport to the surface, and transmission through the
surfaces as three separate steps. Clearly a three-step description
can at best be an approximation. An important step forward was taken
by Schaich and Ashcroft\cite{schaich} and by Mahan\cite{mahan},
who formulated the problem as a one-step quantum-mechanical
process and presented model results for independent electrons.
The Schaich-Ashcroft response formulation was soon generalized to
account for interaction by Caroli \textit{et al.}\cite{caroli}
who applied the formalism to phonon effects.
Among important early works I would also like to mention the
studies of plasmon losses by Langreth and collaborators
\cite{lang, chang-lang1, chang-lang2, lang2}. In particular,
they explain why the satellites are greatly modified and
suppressed also when the excitation energy is quite high,
and why the satellites are so weak in, say, x-ray emission.

In strict one-electron theory, the photoelectrons cannot undergo
losses by scattering against other electrons, phonons, and impurities.
As a consequence, the entire solid will contribute to the photocurrent
which is then limited by the penetration depth of the electromagnetic
radiation. In reality, the current is limited by the escape depth
of the photoelectrons, in practice usually just a few atomic layers.
Thus the mean free path must somehow enter the theory, and
in the mid-seventies ways to remedy this shortcoming were developed
by Feibelman and Eastman\cite{feibelman}, Pendry\cite{pendry},
and Liebsch\cite{liebsch,liebsch2}.
In essence, the no-loss photocurrent is to be calculated in a one-step
but independent-electron way with one important exception: The
photoelectron is assumed to move in the non-Hermitian
optical potential, the (advanced) self-energy $\Sigma_a$.
The photoelectron
orbitals then get damped inside the sample, and the yield becomes
limited by the photoelectron escape depth as it should. Today there
exists several computer codes based on these ideas which take
the underlying bandstructure into account in a realistic way.

The crucial
point of introducing damped photoelectron orbitals was first
obtained by Langreth\cite{lang2} in the case of impurity scattering,
and by Caroli \textit{et al.}\cite{caroli} in the case
when the escape depth is limited by phonons. In the mid-eighties,
by Almbladh\cite{alm85} and Bardyszewski and Hedin
\cite{hedin85} considered the problem of interacting electrons using two
seemingly rather different techniques, one based
on many-body perturbation theory and one based on scattering theory.
These works largely justify the above one-electron-like methods for
the no-loss photocurrent but they also predict corrections, which, for instance,
modify the optical matrix elements.

There are several excellent recent
reviews of solid-state photoemission \cite{schattkebook,hufner,kevan}.
In this paper, I would
like to concentrate on how the techniques of non-equilibrium
Green's functions can be used both for obtaining approximations
suitable for calculations in real materials as well as for obtaining
general results like the structure of the quasiparticle no-loss part
of a photoelectron spectrum.

\section{Basic theory}
\label{basic}
I begin by a brief account of the quantum-mechanical
description of the steady photoelectron current. As mentioned above,
methods based on scattering theory\cite{adawi,mahan,hedin85}, and methods
based on quadratic response formalism and many-body perturbation theory\cite{schaich,caroli,
hermeking,lang,lang2,alm85}. I begin by one-particle theory in
order to illustrate the various limiting procedures, and generalize
then to interacting systems.

\subsection{Independent particles}
\label{sec:oneparticle}
Let us first consider independent electrons.
The photoemission process can be considered as an inelastic scattering process
with a photon in the initial state and an asymptotically free electron
in the final state. In order to strengthen the analogy with scattering,
let us take the system to occupy an finite volume $v$ enclosed
in a quantization box of volume $V$. Because the photoelectron enters
in the final rather than the initial state, its wavefunctions will obey ingoing
wave boundary conditions\cite{gell-mann,adawi}. To first order in the radiative
coupling we obtain
\begin{equation}
\label{eq:i0scatt}
J_p = 2 \pi \sum_n^{occ} | \langle \chi_p^- | \Delta | n \rangle |^2
\delta(\epsilon_p - \omega - \epsilon_n) .
\end{equation}
Here, $J_p$ is the momentum-decomposed photocurrent,
$\Delta$ the coupling to the radiation field (\textit{cf}. Eq. (\ref{eq:dH})),
$\omega$ the photon energy,
and $\epsilon_\nu$ one-electron energies. Atomic (Hartree) units are used.

The photoelectron spectrum probes the occupied part of the one-electron
spectrum. For independent electrons, the spectral function can be written
\begin{equation}
A(\epsilon) = \sum_n | \phi_n \rangle \delta(\epsilon - \epsilon_n)
\langle \phi_n |
\end{equation}
in terms of eigen-orbitals $\phi_n$. In terms of the spectral function,
we have
\begin{equation}
J_p = 2 \pi \langle \chi_p^-  | \Delta A(\epsilon_p - \omega) \Delta^\dag |
\chi_p^-  \rangle
\end{equation}
for photoelectron energies below threshold $\mu + \omega$. Here $\mu$ is
the Fermi level relative to the vacuum level.

In order to compare with the response formulation of Schaich and Ashcroft,
let us introduce orbitals $\phi_{\tilde{p}}$ which are plane waves
well outside the sample and which vanish inside, and let $c_{\tilde{p}}$
be the associated destruction operator.
We assume that the external field has been slowly switched on
in the remote past, (modulated by $e^{\eta t }$), and take the average
$2 \eta \langle c_{\tilde{p}}^+ c_{\tilde{p}} \rangle$ as a measure
of the steady momentum-decomposed photocurrent. The details how the plane
waves are truncated inside and near the sample will not influence
the final results.
We have
\begin{equation}
\label{eq:kt}
K(t) = H + \left [ \delta H e^{-i\omega t }   + \delta H^\dag e^{i\omega t }
\right ] e^{\eta t} ,
\end{equation}
where $H$ describes the system in the absence of external fields, and where
\begin{equation}
\label{eq:dH}
\delta H = - \int {\mathbf{j}}({\mathbf{r}}) \cdot {\mathbf{A}}({\mathbf{r}}) =
\sum_{kl} c_k^+ c_l \Delta_{kl}
\end{equation}
gives the coupling to the radiation field.
We use a radiation gauge such that the scalar potential $\delta \Phi$ vanishes.
(The diamagnetic
coupling then gives no contribution to leading order, see Ref \cite{schaich}.)
We assume that the system has been subject to the field for $t<0$,
and define the photocurrent by
\begin{equation}
J_p   = \lim_{\eta \rightarrow 0^+}
2 \eta \langle c^+_{\tilde{p}} c_{\tilde{p}} \rangle .
\end{equation}
As in scattering theory the infinite volume limit should be taken before
the limit $\eta \rightarrow 0$ ,
i.e., $\eta$ should be considered large compared to the
level spacing due to the quantisation box V.
Following Liebsch\cite{liebsch}, we develop each initial-state
orbital $n$ in time to obtain
\begin{equation}
\phi_{n,\eta}(t=0) =   \left [
1  + G^r(\epsilon_n + \omega  + i \eta) \Delta
+ G^r(\epsilon_n - \omega  + i \eta) \Delta^\dag \right ] \phi_n ,
\end{equation}
where $G^{r/a}(\epsilon)  = 1 / (\epsilon - h \pm i \delta) $ are the
retarded/advanced one-electron Green's functions, and $h_{kl}$
the one-electron Hamiltonian matrix of the unperturbed
system.  We next form the expectation value
$\langle c^+_{\tilde{p}} c_{\tilde{p}} \rangle $
and sum over
occupied states initial states to obtain
\begin{eqnarray}
\label{eq:jp1}
J_p  &=& \lim 2 \eta \sum_n^{occ}
| \langle \tilde{p} |
G^r(\epsilon_n + \omega  + i \eta) \Delta | n \rangle |^2 \\
&=& \lim_{\eta \leftarrow 0}
2 \eta \int_{- \infty}^0 dt \int_{- \infty}^0 dt^\prime
\; i \; \langle \tilde{p} | G^r(-t^\prime) \Delta G^<(t^\prime - t)
\Delta^\dag G^a(t) | \tilde{p} \rangle \;
e^{i \omega (t - t^\prime)} \; e^{\eta (t + t^\prime)} .
\label{eq:jp2}
\end{eqnarray}
Here,
$G^<$ is the usual lesser function,
$\langle k | G^< (t)| l \rangle = i \langle N | c_k^+(0) c_l(t) | N \rangle$,
and $| N \rangle$ the $N$-electron ground state.
In order to obtain Eqs. (\ref{eq:jp1}, \ref{eq:jp2}) we have used the fact
that electrons in initial states $n$ are confined to the solid,
and we have dropped the negative-frequency term
which is easily seen not to contribute to the photocurrent in
the limit $\eta \rightarrow 0^+$.
In this limit one can further replace the truncated orbital
$\phi_{\tilde{p}}$ with a plane wave $\phi_p$  (see \textit{e.g} Ref.
\cite{alm85}).  Eq. (\ref{eq:jp2}) is then equivalent to the Schaich-Ashcroft
independent-electron result.

In order to see the equivalence between the scattering and response
formulations, we express $G^{r/a}$ in terms of the Green's function
$G^{r/a}_0$ for free space and the scattering matrix $T^{r/a}$,
\begin{equation}
G^{r/a}(\epsilon) = G^{r/a}_0(\epsilon) + G^{r/a}_0(\epsilon)
T^{r/a}(\epsilon) G^{r/a}_0(\epsilon) .
\end{equation}
As remarked above, we can replace the truncated plane wave $\phi_{\tilde{p}}$
with $\phi_p$ in the limit $V \rightarrow \infty$, $\eta \rightarrow 0^+$.
In this limit we have
\begin{eqnarray}
\langle n | 1 &+& \Delta G^a(\epsilon_n + \omega - i \eta) | \tilde{p} \rangle
=
\langle n | \Delta G^a(\epsilon_n + \omega - i \eta) | \tilde{p} \rangle
\nonumber \\
&=& \frac{1}{\epsilon_n + \omega - \epsilon_p - i \eta}
\langle n | \Delta [ 1 + G^a_0(\epsilon_p - i \eta) T^a(\epsilon_p - i \eta) ]
| p \rangle \nonumber
\end{eqnarray}
and the wave operator $1 + G^a_0 T^a$ transforms $\phi_p$
into  $\chi^-_p$. In this way,
\begin{displaymath}
| \langle \tilde{p} | G^r(\epsilon_n + \omega  + i \eta) \Delta |
n \rangle |^2
\rightarrow \frac{2\eta \langle \chi^-_p | \Delta | n \rangle|^2}
{(\epsilon_n + \omega - \epsilon_p)^2 + \eta^2}
\rightarrow 2 \pi | \langle \chi^-_p | \Delta | n \rangle|^2
\delta((\epsilon_n + \omega - \epsilon_p) ,
\end{displaymath}
which establishes the equivalence between the response and the
scattering approaches for independent electrons.

The geometry with a finite but possibly macroscopic
sample is convenient for performing the somewhat
subtle limits above, but in actual calculations one
usually let the sample grow until it fills a half-space.
The final-state orbitals $\chi^-_p$ are then replaced by
their two-dimensional (2D) analogues, \textit{i.e.}, time-reversed
states for scattering against the surface of the
sample. These states are usually referred to as time-reversed
LEED states because similar 2D scattering enters in the problem of low
energy electron diffraction (LEED).

As stressed in the Introduction, strict one-particle theory
is unphysical and leads to a yield limited by the radiation
penetration depth rather than the photoelectron escape depth.
If the propagators in Eq. (\ref{eq:jp2}) are replaced by their
interacting counterparts, the final-state orbitals get damped
inside the sample and the photocurrent limited by the escape
depth as it should.

\subsection{Interacting electrons}
\label{interacting}
We expand $\langle c_{\tilde{p}}^+  c_{\tilde{p}} \rangle$
directly in orders of the perturbation.
The linear response vanishes identically because all electrons
are confined to the sample in the ground state,
$\tilde{c}^+_p \tilde{c}_p | N \rangle = 0$. In the radiation
gauge, the diamagnetic coupling involving ${\mathbf{A}}^2$ gives no
contribution. The remaining contributions can be written
\begin{equation}
\label{eq:jpi1}
J_p(\epsilon)  = \lim_{\eta \rightarrow 0^+}
2 \eta \int_{- \infty}^0 dt \int_{- \infty}^0 dt^\prime
e^{i \omega (t - t^\prime)} \; e^{\eta (t + t^\prime)}
\langle N | \delta H^\dag(t) \hat{N}_p(0) \delta H(t^\prime)
| N \rangle .
\end{equation}
Eq. (\ref{eq:jpi1}) involves a three-particle path-ordered
Green's function
\begin{equation}
\label{eq:Rp}
R_p(t, t^\prime) =
\sum_{klmn}
\Delta^*_{k,n}\Delta_{l,m}
\langle N | c^+_k(t) c_n(t) c^+_{\tilde{p}}(0)c_{\tilde{p}}(0)
c^+_l(t^\prime) c_m(t^\prime) | N \rangle ,
\end{equation}
which may be evaluated by standard Keldysh technique\cite{keldysh}.
To lowest order, all unconnected contractions vanish because
\begin{equation}
G^<(t) | \tilde{p} \rangle = 0, \; \langle \tilde{p} | G^< (t) = 0
\label{eq:constraint}
\end{equation}
both with and without interaction.
By the same argument, there is only one non-vanishing connected
contraction (see Fig. \ref{pe0}), which gives
\begin{eqnarray}
R^{(0)}_p(t, t^\prime) &=&
i \langle \tilde{p} | G^>_0(-t^\prime) \Delta G^<_0(t-t^\prime)
\Delta^\dag G^>_0(t) | \tilde{p} \rangle \nonumber \\
&=&
i \langle \tilde{p} | G^r_0(-t^\prime) \Delta G^<_0(t-t^\prime)
\Delta^\dag G^a_0(t) | \tilde{p} \rangle
\label{eq:jp0k}
\end{eqnarray}
when $t, \; t^\prime < 0$.
Eq. (\ref{eq:jp0k}) gives back
the previous independent-electron result in Eq. (\ref{eq:jp2}).

\begin{figure}[htbp]
\begin{center}
\includegraphics*[scale=0.6]{pics/pe0.eps}
\caption{The lowest-order non-vanishing diagram for the
photoemission process}
\label{pe0}
\end{center}
\end{figure}

In the present problem, the correlation
$R_p(t, t^\prime)$ in Eq. (\ref{eq:Rp}) is a ground-state
correlation which simplifies the book-keeping of Keldysh diagrams.
The Keldysh propagators refer to the contour in Fig. (\ref{contour})
which means
that we assume that the interacting ground state can be generated
by switching on the interaction adiabatically in the remote past,
\begin{equation}
R_p(t, t^\prime) =
\langle N, 0 | S^\dag(\infty) \delta H^\dag(t) c^+_{\tilde{p}} S(\infty)
 S^\dag(\infty) c_{\tilde{p}} \delta H(t^\prime) S(\infty)
| N,0 \rangle .
\end{equation}
Thus $t = t_-$, $t^\prime = t^\prime_+$, and $c^+_{\tilde{p}} c_{\tilde{p}}$
is straddling the two branches of the Keldysh contour in Fig. (\ref{contour}).
(The indices $\pm$ refer to the positive and negative time-ordered parts,
respectively.)
The propagators joining points $\mu,\; \nu$ of the different
time-ordered parts are
\begin{displaymath}
G(t_\mu, t_\nu) =
\begin{array}{l}
G^c(t - t^\prime),\;\; \mu,\;\nu = + \\
G^{\tilde{c}}(t - t^\prime),\;\; \mu,\;\nu = - \\
G^<(t - t^\prime),\;\; \mu = +, \;\nu = - \\
G^>(t - t^\prime),\;\; \mu = -, \;\nu = + \;,
\end{array}
\end{displaymath}
where $G^{c}$, $G^{\tilde{c}}$ are propagators with positive
and negative time-ordering, respectively, and $G^{\lessgtr}$ the usual
lesser/greater functions. At zero temperature we have
\begin{equation}
a^\lessgtr(\epsilon) b^\gtrless(\epsilon) = 0
\end{equation}
for any Fermi propagators $a$ and $b$. Further, with the above assumption
of adiabatic switching, the expansion of a time-ordered propagator
will only involve propagators with the same time ordering.

\begin{figure}[htbp]
\begin{center}
\includegraphics*[scale=0.6]{pics/contour.eps}
\caption{Keldysh contour at $T=0$}
\label{contour}
\end{center}
\end{figure}

The contribution from a  general diagram
can be reduced to a form analogous to the one-electron Golden Rule
form in Eq. (\ref{eq:i0scatt}).
In the expansion in full Green's functions, any diagram
ends with a pair of electron lines joined to the
vertex $N_p$ representing the analyser (Fig. \ref{p_gen}). This means that
the correlation $R_p$ in Eq. (\ref{eq:Rp}) is of
the general form
\begin{equation}
R_p(t, t^\prime) = - \int \; dx \; d\tau \int \; dx' \; d\tau'
\langle \tilde{p} | G^c(-\tau') | x' \rangle
\langle x' | I(t, t'; \tau , \tau') | x \rangle
\langle x | G^{\tilde{c}}(\tau) | \tilde{p} \rangle ,
\end{equation}
where $I$,
the remain when the exit fermion lines have been removed,
is invariant under a simultaneous translation of
all four times and can be written
\begin{equation}
I(t, t'; \tau , \tau') =
\int \frac{d\nu d\nu' d\nu''}{(2 \pi)^3}
I(\nu, \nu'; \nu'',\nu' + \nu'' - \nu) \;
e^{-i\nu t + i \nu' t'} e^{i \nu'' \tau - (\nu + \nu' - \nu'')\tau'} .
\end{equation}
We notice
that $G^c$ and $-G^{\tilde{c}}$ can be replaced by retarded and advanced
propagators, respectively, since $\tilde{p}$ projects out the particle
part. The action of $G^{r/a}$ on the orbitals $\tilde{p}$ and the limit
$\eta \rightarrow 0$ can now be done analytically in much the same
way as for independent particle, which gives
\begin{equation}
\label{eq:JpI}
J_p = \langle \chi^-_p | I(\omega, \omega; \epsilon_p, \epsilon_p)
| \chi^-_p \rangle.
\end{equation}
Here $\chi^-_p$ is an one-electron time-reversed LEED orbital solved in
the potential $V_C + \Sigma^a(\epsilon_p)$. ($V_C$ is the total
Coulomb potential from the nuclei and the equilibrium electron density.)
The self-energy $\Sigma^a(\epsilon)$
is non-Hermitian with a finite imaginary part inside the sample.
This makes $\chi^-_p$ decaying inside the sample with a decay length determined
by energy losses. Thus all parts of the spectrum including the no-loss
part is now limited by the escape depth of the photoelectrons.

\begin{figure}[htbp]
\begin{center}
\includegraphics*[scale=0.6]{pics/p_gen.eps}
\caption{Reduction of a general photoemission diagram}
\label{p_gen}
\end{center}
\end{figure}

In the case of optical responses and transport, the ideas of
self-consistent approximations put forward by Kadanoff and
Baym\cite{kadbaym1, kadbaym2, baym} has been extremely
successful. It is the present author's opinion that this level
in not possible to achieve in the case of photoemission. In particular,
the Bethe-Salpeter equation which emerges as a result of selfconsistency
will include interaction lines of all orders. If we open up such
a diagram corresponding to a given approximation
to the self-energy, infinitely many photoemission
diagrams will result. For sp-bonded solids, the
most important conserving approximation is
the self-consistent screened exchange approximation\cite{baym,hedin65}, usually
referred to as the $GW$ approximation.
Fortunately, the fulfilment of macroscopic
conservation laws are less crucial for useful approximations
to photoelectron spectra. In photoemission, only a small fraction of
the emitted photoelectrons are actually measured. The majority
of photoelectrons which make up the overall background is usually
of no interest at all; instead the interest is focused on the spectral shapes
in a limited energy window. Often, processes of different
orders will contribute at different energies. Losses to plasmons
is here a typical example. What is important is to have approximations
which can explain the observed spectral profiles and
which fulfil basic requirements
such as positiveness.

\subsection{Low-order diagrams}
Let us expand the basic 3-particle correlation $R_p$
in orders of the screened interaction
$W(\omega)=v \epsilon^{-1}(\omega)$.
The non-vanishing first-order diagrams are shown in Fig. (\ref{pe1}).
As was the case for independent electrons, the condition in
Eq. (\ref{eq:constraint}) limits the number of non-vanishing contractions.
Vertices belonging to the forward (backward) time-ordered parts are
are labelled + (-), respectively.
The diagrams (a-c) involve
only self-energy insertions and should be omitted if we expand
in the full Green's function.
The remaining first-order diagrams fall into two classes,
namely those with interaction line joining point in the same
leg (d and e) and those with the interaction line joining
points in different legs (f, g, and h).
Consider first diagram f. It is well known that this diagram
describes an extrinsic loss, but to illustrate the
technique we give some details of the analysis.
The interaction line here represents the boson-like correlation
\begin{equation}
 W_> ({\mathbf{r}} t ,{\mathbf{r}}' t') = -i\langle N|\delta V_H ({\mathbf{r}} t) \delta V_H ( {\mathbf{r}}' t')
 | N \rangle
 = -i \int_0^\infty \; d \omega^\prime B({\mathbf{r}}, {\mathbf{r}}^\prime, \omega^\prime )
 e^{-i \omega^\prime ( t - t^\prime)},
\end{equation}
where the spectral function $B$ is given by the dynamical structure
factor $S({\mathbf{r}},{\mathbf{r}}',\omega)$ convoluted with two Coulomb interactions
($v$), $B(\omega)=v*S(\omega)*v$. The fermion line from t' to t represents
$G^<$.
and the remaining lines time-ordered or anti-time-ordered functions
$G^{c/\tilde{c}}$. After reduction according to Eq. (\ref{eq:JpI}) we obtain
\begin{equation}
\label{eq:loss_f}
J_p^{(f)} = 2 \pi \int_{-\infty}^0 d\epsilon \; \int_0^\infty \; d\omega^\prime
\delta(\epsilon + \omega - \omega^\prime - \epsilon_p)
\langle \chi_p^- | \underbrace{G^c(\epsilon + \omega) \Delta A(\epsilon)
\Delta^\dag G^{c\dag}
(\epsilon + \omega)}_{B(\omega^\prime)} | \chi_p^- \rangle
\end{equation}
where we have used an underbrace to indicate
how the spatial coordinates in $B(\omega)$ should be connected to the
electron propagators. Here and in the following we use the identity
$G^{\tilde{c}}(\epsilon) = - G^{c \dag}(\epsilon)$ in order to express
final results in spectral or lesser functions and functions with
positive time-ordering.

The obvious physical interpretation of Eq. (\ref{eq:loss_f}) is that it describes
primary photo-excitation from an initial occupied level ($\epsilon$) to a
level of energy $\epsilon + \omega$. The photoelectron then suffers an
energy loss by exciting a plasmon or electron-hole pair of energy
$\omega^\prime$ and hits the detector with an energy
$\epsilon + \omega - \omega^\prime$. Consider next
the diagrams g and h in Fig. 3. Using a similar technique as above
we obtain
\begin{equation}
\label{eq:loss_gh}
J_p^{(g)} + J_p^{(h)} = 4 \pi \Re \int_{-\infty}^0 d\epsilon \; \int_0^\infty \; d\omega^\prime
\delta(\epsilon + \omega - \omega^\prime - \epsilon_p)
\langle \chi_p^- | \underbrace{G^c(\epsilon + \omega)
\Delta A(\epsilon)}_{B(\omega^\prime)}
G^{c \dag}(\epsilon - \omega') \Delta^\dag | \chi_p^- \rangle
\end{equation}
describing
loss processes where interference between the potential from the hole
left behind and the outgoing photoelectron
interfere\cite{chang-lang1,chang-lang2,lang2}. The `intrinsic'
losses, finally, are describe by the satellite structure of the hole
spectral function A. The diagrams f-h plus the first-order
satellite in $A$ ($c$)
give the first-order contribution to the first plasmon satellite as
obtained by Inglesfield\cite{ingles83} in the case of photoemission from core
levels.

\begin{figure}
\begin{center}
\includegraphics*[scale=0.7]{pics/pe1.eps}
\caption{First-order diagrams for the photoemission process}
\label{pe1}
\end{center}
\end{figure}

We now turn to the first-order diagrams (d) and (e) with no interaction
lines joining the (+) and (-) parts.
In this case the interaction lines represent time-ordered correlations,
\begin{equation}
\label{eq:noloss_dh}
J_p^{(d)}  = 2 \pi \int_{-\infty}^0 d\epsilon \; \int_0^\infty \; d\omega^\prime
\delta(\epsilon + \omega - \epsilon_p)
\langle \chi_p^- | \Lambda^{(1)}(\epsilon + \omega, \epsilon)
A(\epsilon) \Delta^\dag | \chi_p^- \rangle
\end{equation}
where
\begin{equation}
\langle n | \Lambda^{(1)}(\epsilon,\epsilon') | m \rangle =
i \int \; \frac{d \omega'}{2 \pi}
\langle n | \underbrace{G^c(\epsilon - \omega') \Delta G^c(\epsilon' - \omega')}_{
W^c(\omega')} | m \rangle
\end{equation}
is a first-order correction to the usual (time-ordered) vertex
function.  The diagram (e) gives the complex conjugate $[J_p^{(d)}]^*$.
The appearance of $\delta(\epsilon + \omega - \epsilon_p)$ in Eq. (\ref{eq:noloss_dh})
shows that they contributes to the no-loss current.

The remaining two diagrams ($k$) and ($l$), finally, describe a screening
of the photon field in the solid\cite{feibelman}. The screening will
modify the electromagnetic field by local-field effects which are
lattice-periodic deep inside the solid but more complicated near the surface.
Most photoemission calculations to date do not take these effects into account.
Effects of such screening has been considered by Liebsch\cite{liebsch3},
Schattke\cite{schattke1, schattke2}, and by others.
In the following
discussion they will be considered included in the optical vertex $\Lambda$.

With independent-electron propagators, the photoelectron orbital is approximated
to zeroth order in the interaction and is undamped inside the solid.
If we regard the diagrams skeletons and use full Green's functions (diagram ($c$)
should then be omitted), the photoelectron orbital gets damped inside as it should.

\subsection{Treatment based on scattering theory}
Scattering theory furnishes an equivalent description of the photoemission
process and has been the basis for several interesting new
results\cite{hedin98,hedin99}. The obvious generalisation of the
one-electron result is to replace the one-electron scattering
orbital $ | \chi^-_p \rangle $ by its many-body counterpart
$| f \rangle \equiv | \chi^-_p,s^- \rangle \equiv | N-1, s, p, - \rangle$
of energy $E_f = \epsilon_p + E_s(N-1)$ with an asymptotically
free electron $p$ and a $N-1$-electron system left behind in some
excited state $s$,
\begin{equation}
\label{eq:jp_gold}
J_p = 2 \pi \sum_s | \langle f | \delta H | N \rangle |^2
\delta ( E_i - E_f ))
\end{equation}
The equivalence with the response formulation can be demonstrated with
a variety of methods. One way is to consider the limiting behaviour of
the amplitude
\begin{displaymath}
\langle N - 1, s | c_p\delta H \frac{1}{E_i - H + i \eta}  | N \rangle
\end{displaymath}
inherent in the response formulation and verify that it tends to
\begin{displaymath}
\frac{1}{E_i - E_f + i \eta} \langle f | \delta H | N \rangle
\end{displaymath}
when $\eta \rightarrow 0$. There are some subtleties involved because
the photoelectron is identical the electrons in the sample.
For a discussion, see \textit{e.g.} Ref. \cite{alm85}.

A drawback with the above treatment is that every possible final many-body state
has to be treated explicitly, a clearly impossible task in a `full' treatment.
In practice, however, one has so far only been able to account for losses
to low orders. In sp-bonded materials, for example, the important
excitations are boson-like and consist of plasmons and particle-hole pairs. The
plasmons carry the major oscillator strength. Going back to Fig. (\ref{pe1}),
diagrams ($c$) and ($f-h$) all have a real boson in the final state. By summing
over possible intermediate virtual states with some subspace, the propagators
become renormalised and one obtains an approximation to the first boson loss
satellite with damping properly included. The idea to work in subspaces
is the essence of the Hedin-Bardyszewski approach\cite{hedin85}. To make
the problem more clear-cut, Hedin following an idea of McMullen
\textit{et al.}\cite{birger}
considered the photoelectron as distinguishable from other electrons
in the sample, the `blue-electron model'.

The very existence of the Golden-Rule expression in Eq. (\ref{eq:jp_gold})
suggests that also the results from response theory can be put in a similar
form. This is indeed the case, and a technique how it may be achieved will
be discussed at the end of this paper.

\section{No-loss current}
\label{no_loss}
Photoemission spectra typically consist of a quasi particle-like
peak and various losses at lower kinetic energy. A mathematically
precise definition of a no-loss part can only be given in the
uninteresting case where the sample ends up in the $N-1$-particle
ground state. If we are willing to accept a certain fuzziness,
we can define a "no-loss" part with about the same precision
as quasi particles below the Fermi level. In practice there is
usually no difficulty to identify, say, core-electron quasi particles,
or valence-electron quasi particles well below the Fermi energy
so long as their lifetime broadening is small on the energy scale
of interest.

Our foregoing analysis suggest that interaction lines which join
the positive and negative time-ordered parts of a diagram
correspond to energy losses in the final state. There must always
be at least one $G^<$ line joining the two optical vertices in
a diagram, \textit{i.e}, there is always an excitation where an
electron has been removed. In first order, the diagrams ($c$, $f-h$)
in Fig. (\ref{pe1})
contribute to additional losses involving particle-hole
pairs or plasmons because they involve $W^>$.
In an interaction-picture representation for 3-current correlation $R_p$
we have
\begin{equation}
 R_p (t,t') = \langle 0 | T^\dag \left [ S(-\infty, \infty) \delta H(t)
 c (0) \right ] T \left [ S(-\infty, \infty) c (0)\delta H(t) \right ]
 |0\rangle .
\end{equation}
We insert a complete set of final $N-1$-electron states between the
forward- and backward time-ordered parts and expand. The $N-1$ electron
ground state corresponds to ejecting an electron from the Fermi surface
adiabatically. If the sample has well-defined quasi particles it is
natural to filter out all final states with energies a couple of lifetime
widths away for the quasi-particle energy. This corresponds essentially
to excluding interaction and electron lines which cross the two
time-ordering parts. If we sum all diagrams of this kind, we obtain
\begin{equation}
\label{eq:noloss}
J_p =
2 \pi \; \int_{-\infty}^\mu \delta(\epsilon_p - \epsilon - \omega)
\langle \chi_p^- | \Lambda(\epsilon + \omega, \epsilon)
A(\epsilon) \Lambda^\dag(\epsilon + \omega, \epsilon) |  \chi_p^- \rangle
\; d\epsilon
\end{equation}
(see Fig (\ref{noloss})). Here, $\Lambda(\epsilon, \epsilon^\prime)$ is the screened,
time-ordered vector-coupling vertex.
In order to obtain only the no-loss part the integration with
respect to $\epsilon$ should be confined to the quasi particle part of $A(\epsilon)$.
How this should be done cannot be specified exactly, as a consequence of the fact
that the sample is generally left in an unstable excited state.
The impreciseness  is of the order of the lifetime width of the hole left behind.
Experimental angular-resolved spectra show that the quasi-particle
concept is useful also for states far below the Fermi energy and that
spectra of real systems can be considered composed of a no-loss part
that reflects the quasi-particle bandstructure, and a loss part that
reflects the dynamical response of the system.

The vertex correction is clearly related to the problem of how the optical
matrix elements should be calculated. In the dipole approximation,
the velocity ($\Delta_{kl} \sim \langle k | {\mathbf{A}} \cdot {\mathbf{p}} | l \rangle$),
length ($\Delta_{kl} \sim \langle k | {\mathbf{E}} \cdot {\mathbf{r}} | l \rangle$),
and acceleration ($\Delta_{kl} \sim \langle k | A \cdot \nabla w({\mathbf{r}}) | l \rangle$)
formulas are equivalent. For independent particles the equivalence
readily follows by commuting the one-electron Hamiltonian with the momentum,
and $w$ is then the effective one-electron lattice potential.
When the independent-electron
propagators are replaced by their interacting counterparts, however, the
equivalence is lost. There is also a question how the effective potential
$w$ should be chosen. This problem resolved by the present author
in the mid-eighties\cite{alm86}.
The replacement of the bare
optical matrix element by the dressed vertex $\Lambda_{v/L/a}$ restores
the equivalence almost completely\cite{alm86}. The remaining discrepancy
is of order of the lifetime width of the hole left behind and is clearly
related to the fuzziness of quasi particles away from the Fermi surface.
This again shows that Eq. (\ref{eq:noloss}) furnishes a good description
in systems with well-defined quasi particles. The acceleration
matrix elements involve $\epsilon^{-1}(\omega) {\mathbf{A}} \cdot \nabla w_{nuc}({\mathbf{r}})$
(a polarisation where are nuclei have been shifted a distance ${\mathbf{A}}$.
The last result was first obtained by Hermeking\cite{hermeking}.

\begin{figure}[htbp]
\begin{center}
\includegraphics*[scale=0.7]{pics/noloss.eps}
\caption{The no-loss part of the photocurrent}
\label{noloss}
\end{center}
\end{figure}

\section{Energy Losses}
\label{sec_losses}

We shall here mainly be concerned with plasmon losses in sp-bonded materials.
As is well known
plasmon losses can be produced either "intrinsically" in connection with the
primary photo-excitation, or "extrinsically" by the escaping photoelectron on
its way out.  At lower kinetic energies the two modes
of plasmon excitation interfere, leading to a suppression of the
satellite
strength. This interference has in the past been described using
semi-classical models where the photoelectron is assumed to follow a classical
trajectory and where the photoelectron and the hole left behind are represented
by external potentials\cite{mahan73,gadzuk75,longe,tougaard}.
In the case of core-electron photoemission,
Hedin \textit{et al.}\cite{hedin98,hedin2003} have
shown that a fully quantum-mechanical description of the leading
satellites agrees quite well with  a semi-classical description for excitation
energies a couple of plasmon energies above threshold. It also shows that
interference between intrinsic and extrinsic plasmon production persists
up to the keV range, thereby confirming the earlier works by
Chang and Langreth\cite{chang-lang1, chang-lang2}. However, there are
to our knowledge no similar studies for photoemission from valence states.

As will be discussed below, a straight-forward expansion in orders of the screened
interaction $W$ will not in general guarantee positive spectral densities.
I will here outline a different summation order in  which the partial sums
have a golden-rule-like form involving transition amplitudes $\tau_{fi}$.
Thus, each partial sum has the
generic form
\begin{equation}
I(\omega) = \sum_f |\tau_{fi}|^2 \delta(E_i + \omega - I_f),
\label{eq:GR}
\end{equation}
where $i, f$ label real excitations in the initial and final states,
respectively.  The transition amplitudes can be related to cut Keldysh diagram.
By performing an expansion of the amplitudes to a given order, each partial sum
gives a positive result.
The procedure amounts to splitting complete Keldysh
diagrams in pieces and to sum them a particular order such that every
partial sum is positive. If carried out of infinite order, `all' complete
diagrams are summed. I will outline the procedure with the low-order plasmon
losses in photoemission as an example, and give some new model
results for valence photoemission from a simple-metal surface.

\subsection{Lowest-order contributions}
\label{sec:loss1}

Let us begin with the lowest-order contributions where no real
losses have occurred. Up to first order in $W$,
the zeroth-order diagram in Fig. \ref{pe0}
and diagrams (d) and (e) in Fig. \ref{pe1} contribute
and will involve the combination
\begin{displaymath}
\langle \chi_p^- | \Delta A(\epsilon) \Delta^\dag | \chi_p^- \rangle +
2 \Re \langle \chi_p^- | \Lambda^{(1)}(\epsilon + \omega, \epsilon)
\Delta A(\epsilon) \Delta^\dag | \chi_p^- \rangle .
\end{displaymath}
The obvious missing piece in the above approximation is the term
$\langle \chi_p^- | \Lambda^{(1)} A(\epsilon) \Lambda^{(1)\dag} | \chi_p^- \rangle$.
If this term is added, a manifestly positive result is obtained,
\begin{displaymath}
\langle \chi_p^- | [ \Delta + \Lambda^{(1)}]
A(\epsilon) [\Delta + \Lambda^{(1)}]^\dag | \chi_p^- \rangle
\end{displaymath}
in which the transition amplitudes rather than the spectral intensity
has been truncated to a given order.

Contributions with no real excitations in the final state are somewhat
artificial and will give no contribution when particle-hole
excitations are included in the screened interaction. The mechanism
is essentially the same as in the Langreth theorem\cite{lang3}.
In the case of the simpler $G^<$ function we have
\begin{equation}
G^<(\epsilon) = [1 + G^r (\epsilon) \Sigma^r(\epsilon)] G_0^< (\epsilon)
[1 + \Sigma^a(\epsilon) G^a(\epsilon)] + G^r (\epsilon)
\Sigma^<(\epsilon) G^a(\epsilon) .
\label{eq:langtheo}
\end{equation}
If there are no real excitations in a particular spectral region,
$\Sigma^<$ vanishes, and the first term in Eq. (\ref{eq:langtheo})
gives the entire contribution. As soon as real excitations occur,
the first term tends to zero in the infinite-volume limit and the
entire contribution comes from the second term. What actually occurs
is that previously sharp single-particle-like excitations become
broadened. By the same mechanism, contributions with no real
excitations in the final state except a perfectly sharp quasi particle
will not contribute to the photoemission current when broadening by
particle-hole pairs is included.

We next proceed to the first-order
diagrams $(c)$ and $(f-h)$ in Fig (\ref{pe1}) which contribute to
a one-boson loss.
These four diagrams nicely combine into a complete
square of intrinsic and extrinsic satellite amplitudes.
We make use of the fact that the spectral functions $B(\omega)$
and $A(\epsilon)$ are Hermitian and positive-definite.
They can thus be diagonalised,
\begin{eqnarray}
\label{eq:diagB}
\langle {\mathbf{r}} | B(\omega) | {\mathbf{r}}' \rangle &=& \sum_\mu b_\mu^2(\omega)
v_\mu(\omega, {\mathbf{r}}) v_\mu^*(\omega, {\mathbf{r}}') , \\
\label{eq:diagA}
\langle {\mathbf{r}} | A(\epsilon) | {\mathbf{r}}' \rangle &=& \sum_n a_n^2(\epsilon)
u_n(\epsilon, {\mathbf{r}}) u_n^*(\epsilon, {\mathbf{r}}') .
\end{eqnarray}

The ``intrinsic' part $(c)$ can be written
\begin{equation}
\label{eq:loss_c}
J_p^{(c)} = 2 \pi
\langle \chi_p^- |
 \Delta A^<(\epsilon_p - \omega) \Delta^\dag
| \chi_p^- \rangle ,
\end{equation}
where $A^< = G^c \Gamma^< G^{c \dag}$ and $\Gamma^< = - i \Sigma^< / 2 \pi$.
In the $GW$ approximation\cite{hedin65}, we have
\begin{eqnarray}
\lefteqn{\langle {\mathbf{r}} | \Gamma^<(\epsilon_p - \omega) | {\mathbf{r}}'
\rangle =}\nonumber \\
& & \sum_{n\mu} \int d \omega ' a^2_n (\epsilon_p + \omega ' - \omega) b^2_\mu
( \omega')
u_n(\epsilon_p + \omega ' - \omega, {\mathbf{r}}) u_n^*(\epsilon_p + \omega ' - \omega, {\mathbf{r}}')
 v_\mu(\omega', {\mathbf{r}} ) v_\mu^*(\omega', {\mathbf{r}} )\nonumber \; .
\end{eqnarray}
We insert this in Eq. (\ref{eq:loss_f}) to obtain
\begin{equation}
J_p^{(c)} = 2 \pi \sum_{n\mu} \int_0^\infty d \omega'  |
M_{1,1,a}^{n\mu}(\omega') |^2
a_n^2(\epsilon_p + \omega' - \omega) b_\mu^2(\omega') \; ,
\end{equation}
where
\begin{equation}
\label{eq:M1}
M_{1,1,a}^{n\mu} = \langle \chi_p^- | \Delta G^c(\epsilon_p - \omega)
| v_\mu^*(\omega') u_n(\epsilon_p + \omega' - \omega) \rangle \; .
\end{equation}
We next turn to the purely extrinsic part ($f$). Again we rewrite
$A^<$ and $B(\omega)$ in a diagonalising basis to obtain
\begin{equation}
J_p^{(f)} = 2 \pi \sum_{n\mu} \int_0^\infty d \omega'  | M_{1,1,b}^{n\mu}
(\omega') |^2
a_n^2(\epsilon_p + \omega' - \omega) b_\mu^2(\omega') ,
\end{equation}
where in this case
\begin{equation}
\label{eq:M2}
M_{1,1,b}^{n\mu} =
\langle \chi_p^- v_\mu(\omega') | G^c(\epsilon_p + \omega')
\Delta | u_n(\epsilon_p + \omega' - \omega) \rangle .
\end{equation}
The two interference terms $(g-h)$, finally, can be expressed
in a similar way but with matrix elements $M_{1,1,a}^* M_{1,1,b}$.
The total contribution can then be written
\begin{equation}
J_p^{(1,1)} = 2 \pi \sum_{n\mu} \int_0^\infty d \omega'
\left | M_{1,1}^{n\mu}(\omega') \right |^2
a_n^2(\epsilon_p + \omega' - \omega) b_m^2(\omega') \; ,
\end{equation}
where
\begin{equation}
M_{1,1} = M_{1,1,a} + M_{1,1,b} \;.
\end{equation}
The approximation of keeping only the renormalised diagrams
($c, f-h$) has a close correspondence to the $GW$ approximation
and may be termed a `$GW$ approximation for photoemission'.

In the simplest non-selfconsistent $G_0W$
approximation, the spectral function in $G^<$ should be approximated by its
independent-particle equivalent in $\Sigma^\lessgtr$. (For different levels
of selfconsistency, see Ref. \cite{holm_barth98}.) In this
approximation,
$a_m^2(\epsilon)$ is replaced by $\delta(\epsilon - \epsilon_m)$ in the
above expressions, and remaining propagators by their $G_0W$ equivalents.
One can also in principle
do partial selfconsistency with respect to $G$, which in this
context amounts to calculate $A(\epsilon)$ selfconsistently
from Eq. (\ref{eq:diagA}), the resulting $\Sigma^\lessgtr$, and the
Langreth theorem, Eq. (\ref{eq:langtheo}).

The matrix elements $M_{1,1,a}$ and $M_{1,1,b}$ can be represented graphically
at cut diagrams with only + vertices and one dangling interaction line
$W^>$ as in Fig. \ref{fig_m1}.
When joined with the corresponding lower
half, the four diagrams (c), (f-h) will emerge.

\begin{figure}[htbp]
\begin{center}
\includegraphics*[scale=0.65]{pics/m1.eps}
\caption{Transition amplitudes to first order as cut Keldysh diagrams }
\label{fig_m1}
\end{center}
\end{figure}

\subsection{Structure of higher-order contributions}
\label{sec_loss2}

Already the above $GW$-like approximation gives at least a qualitative
description of how the leading plasmon satellite is modified by interference.
However, although $GW$ theory is usually quite accurate for quasi particle
positions it gives a somewhat poor representation of the satellite shape.
In the spectral function $A(\epsilon)$ there is only one satellite
which is too broad and with a mean energy too far away from the quasi particle.
By adding the first vertex diagram and self-consistency diagrams one improves
the satellite in the case of core electrons, and model studies indicate
that also the valence electron spectrum is improved. A corresponding
approximation for photoemission will involve at least two screened interactions.

\begin{figure}[htbp]
\begin{center}
\includegraphics*[scale=0.65]{pics/m2.eps}
\caption{Transition amplitudes contributing to the second plasmon satellite }
\label{fig_m2}
\end{center}
\end{figure}

\begin{figure}[htbp]
\begin{center}
\includegraphics*[scale=0.65]{pics/m1b.eps}
\caption{Transition amplitudes modifying the first plasmon satellite }
\label{fig_m1b}
\end{center}
\end{figure}

Starting with second order theory, a large number of diagrams occurs
which most probably gives very small contributions. The screening
of the photons can now in principle interfere with the excitations
shaken up by the photoelectron. If such contributions are neglected,
the coupling to the photon field enters solely in form of a time-ordered
screened optical vertex $\Lambda$ as in Eq. (\ref{eq:noloss}).
Except possibly very close to threshold, the important processes are those
where photoelectron, once created, remains until it is detected. In terms
of diagrams this corresponds to adding screened interaction lines to the
basic independent-electron triangle in Fig. \ref{pe0}. The leading-order
amplitudes which contribute to the second plasmon satellite are illustrated
in Fig. \ref{fig_m2}. The dangling interaction lines can be combined in two
different ways when complete photoemission diagrams are formed. As a
result, the amplitudes in Fig. \ref{fig_m2} produce 18 complete diagrams.
The contribution from these 18 diagrams can be written
\begin{eqnarray}
J_p^{(2,2)} &=& 2 \pi \sum_{n\mu\nu} \int_0^\infty d \omega_1 d \omega_2
\left | \sum_{l =  a, b, c} M_{2,2,l}^{n\mu \nu} +
M_{2,2,l}^{n\nu \mu} \right |^2
\nonumber \\
&\times&
a_n^2(\epsilon_p + \omega_1 + \omega_2 - \omega)
b_\mu^2(\omega_1)b_\nu^2(\omega_2) ,
\end{eqnarray}
where
\begin{eqnarray}
M_{2,2,a}^{n\mu \nu} &=& \langle  \chi_p^- | \Delta G^c(\epsilon_p - \omega)
v_\mu(\omega_1) G^c(\epsilon_p + \omega_1 - \omega) |
v_\nu(\omega_2) u_n(\epsilon_p + \omega_1 + \omega_2 - \omega) \rangle
\nonumber \\
M_{2,2,b}^{n\mu \nu} &=& \langle  \chi_p^- v_\mu(\omega_1) | G^c(\epsilon_p + \omega_1) \Delta
G^c(\epsilon_p + \omega_1 - \omega) |
v_\nu(\omega_2) u_n(\epsilon_p + \omega_1 + \omega_2 - \omega) \rangle
\\
M_{2,2,c}^{n\mu \nu} &=& \langle  \chi_p^- v_\mu(\omega_1) | G^c(\epsilon_p + \omega_1)
v_\nu(\omega_2) G^c(\epsilon_p + \omega_1 + \omega_2) \Delta |
v_\nu(\omega_2) u_n(\epsilon_p + \omega_1 + \omega_2 - \omega) \rangle
\nonumber
\end{eqnarray}

In addition, there are amplitudes which modify the
shape of the first plasmon satellite containing one dangling interaction
line (Fig. \ref{fig_m1b}).
The latter amplitudes are to be added to
the first-order amplitudes which are the squared and summed. The diagrams
which result from pairing off with the amplitudes $M_{1,1}$ in Fig. \ref{fig_m1}
are of second order in $W$. In this way 24 complete Keldysh diagrams are
obtained, and they give a contribution of the form
\begin{eqnarray}
J_p^{(1,2a)} &=& 4 \pi \Re \sum_{n\mu} \int_0^\infty d \omega_1
 \left [ M_{1,1}^{n\mu} \right ]^*
M_{1,2}^{n\mu} \;
a_n^2(\epsilon_p + \omega_1 - \omega)
b_\mu^2(\omega_1) \; ,
\label{eq:j12a}
\end{eqnarray}
where $M_{1,2}$ is the sum of the six amplitudes $M_{1,2,l}$ in Fig.
\ref{fig_m1b}.
The sum
$J_p^{(1,1)} + J_p^{(1,2a)}$
and thereby the complete second-order current
$J_p^{(1,1)} + J_p^{(1,2a)} + J_p^{(2,2)}$
is not positive-definite. If we add the diagrams where the second-order
amplitudes to the first boson satellite are paired against
themselves a manifestly positive
contribution to the first boson satellite is obtained,
\begin{eqnarray}
J_p^{(1,2)} &=& 2 \pi \sum_{n\mu} \int_0^\infty d \omega_1
\left | M_{1,1}^{n\mu} + M_{1,2}^{n\mu} \right |^2
a_n^2(\epsilon_p + \omega_1 - \omega)
b_\mu^2(\omega_1) .
\label{eq:j12}
\end{eqnarray}
The sum $J_p^{(1,2)} + J_p^{(2,2)}$ includes all second-order and part of
the third-order contributions to the photoelectron current.

The above procedure can evidently be extended to any order. The basic idea
is to sum transition amplitudes to a given order, and then form all diagrams
containing these amplitudes by pairing as above. For a given order $n$
the current is the sum $J^{(1,n)}_p + J^{(2,n)}_p + \cdots + J^{(n,n)}_p$
corresponding to $1, 2, \ldots, n$ boson losses. Each partial current
$J^{(r,n)}_p$ will involve amplitudes with $r$ dangling and
up to $n-r$ time-ordered interaction lines. The partial current
$J^{(r,n)}_p$ is obtained by pairing these amplitudes in all
possible ways. The partial current will include all diagrams
up to order $n$, and part of the contribution of order between
$n$ and $2n-r$ and it will be manifestly positive.
If one could continue indefinitely, eventually all diagrams
will be included. The method of expanding transition amplitudes rather than spectral
densities is also applicable for obtaining approximations
to the one-electron spectral function and to the dynamical structure
factor.

\subsection{Model calculations of plasmon and electron-hole losses}

I here describe model calculations in the simplest non-trivial
approximation in which we keep the four
diagrams $(c)$ and $(f-h)$ in Fig (\ref{pe1}).

In the expressions for matrix elements, $G^c$ one can usually
approximate it by $G^r$ in Eq. (\ref{eq:M2}) and by a $G^a$
in Eq. (\ref{eq:M1}).
In our model calculations we have further approximated $G^{r/a}$ by
$1/(h_0 \pm i \Gamma)$
with a damping from the on-shell value of $\Im \Sigma$. The matrix
elements can then be evaluated by propagating the orbitals in space
under influence of a non-Hermitian Hamiltonian which greatly
simplifies the calculations. The system was approximated by a
a semi-infinite jellium perturbed by a weak lattice
pseudo potential. (Without a lattice potential only surface
photoemission can occur because of momentum conservation.)
The dielectric function and thus $B(\omega)$ was approximated
by a semi-analytical result by Bechstedt
\textit{et al.}\cite{bechstedt}.

\begin{figure}[htbp]
\begin{center}
\includegraphics*[angle=270,scale=0.35]{pl7_5.ps}
\caption{Photocurrent as function of photoelectron energy in Ry.
The zero level corresponds to the bottom of the valence band.
The spectrum is excited 7.5 Ry above threshold, and the photoelectron
mean free path is approximated by a constant corresponding to
$\Gamma_p = 0.3$ Ry.}
\label{pl7.5}
\end{center}
\end{figure}

In Fig. (\ref{pl7.5}) we show results for plasmon losses
with an excitation energy 7.5 Ry above threshold. These
and the following results correspond to aluminium, and
the lattice ${\mathbf{G}}$ vector, which acts as momentum source, has a parallel
component of 0.7 a.u. and a component of 2.6 a.u. perpendicular
to the surface.
The extrinsic losses dominate, and the total loss is
somewhat smaller than the sum of the extrinsic and intrinsic
ones. However, we have observed that interference
depend on the direction of the photocurrent even at 7.5 Ry. The two
loss mechanisms are therefore not completely decoupled
even at \~ 100 eV. In Fig. (\ref{pla4.5}) we have lowered
the excitation energy to 4.5 Ry. In this case the interference
is much stronger, and the extrinsic and intrinsic parts
interfere destructively.

\begin{figure}[htbp]
\begin{center}
\includegraphics*[angle=270,scale=0.35]{pl4_5.ps}
\caption{Photocurrent excited 4.5 Ry above threshold. $\Gamma_p = 0.3$ Ry.
Notations as in Fig. \ref{pl7.5}}
\label{pla4.5}
\end{center}
\end{figure}

Finally one may ask how the quasi particle line shape is modified
by the transport and interference effects. In our calculations
we have obtained almost negligible effects.
As an example, I show
the quasi particle region at an excitation energy of 2.5 Ry
(Fig. (\ref{peh2.5})).
The broadening that is seen without
any particle-hole effects comes from the
finite mean free path which smears the momentum selection
rules normal to the surface.

\begin{figure}[htbp]
\begin{center}
\includegraphics*[angle=270,scale=0.35]{eh_2.5.ps}
\caption{Broadening of the quasi particle peak at normal emission.
$\omega_i = 2.5$ Ry.
For notations see Fig. \ref{pl7.5}}
\label{peh2.5}
\end{center}
\end{figure}

As remarked above, the first-order $GW$ theory gives a rather crude
representation of the shape of the plasmon satellites.
The description will be improved by going to second order in transition
amplitudes as described in Sec. \ref{sec_loss2}.
This higher-order approximation is still simple enough to
allow for numerical evaluations.
Within the approximations used above for the first-order results
the second-order amplitudes can again be obtained by
propagating one-electron orbitals which makes the calculation manageable.
As the excitation energy is further increased, more and more plasmon satellites
will result in experimental spectra. At sufficiently high energies,
the energy losses can be described by semi-classical approaches in which
the photoelectron is considered as a classical particle which moves
along a certain trajectory\cite{ah83,hedin2003} or by an integral equation
which approximates the losses at high energies\cite{chang-lang2}. We expect
that explicit quantum-mechanical calculations up to second order in $W$ will
cover the energy window up to the limit where these simpler methods are applicable.
Extensions to second order along the lines given here are on the way
and will be presented elsewhere.

\section{Concluding remarks}

In this paper I have discussed how
techniques from non-equilibrium Green's function theory may be used
to develop useful approximations as well as for establishing
general results such as the structure of the no-loss quasi particle
part of the spectrum. Although I have discussed energy losses in
some detail in the second part, I would like to emphasis that it
is the no-loss quasi particle part that is usually of primary
interest in experimental studies. The current computational schemes
in which the photoelectron moves in a non-Hermitian optical potential
is essentially correct. The necessary ingredients are here sufficiently
accurate approximations for the self-energy including its imaginary
part. It may be necessary to account for its non-locality at least
in some approximate way. The proper evaluation of matrix elements
the screened optical field is another area where improvements
may be necessary. Especially in spectral regions where the photoelectron
self-energy is rapidly varying it may also be necessary to account
for the vertex corrections discussed in Sec. \ref{no_loss}.

In order to treat energy losses below the main quasi-particle peak,
a regrouping of diagrams in many-body perturbation theory has been proposed.
In each order the partial sums have a Golden-Rule-like form which guarantees positive
spectral intensities.  This way of regrouping may be useful
also in other problems involving spectral intensities. One such
problem is how to improve the one-electron spectral function
beyond $GW$ theory.

Some new model results for valence-electron
photoemission have been presented, and more realistic results are on the way.
The model results confirm the
expectations that interference effects modify the shape and
strength of plasmon satellites also quite far away from the
excitation threshold, whereas the quasi-particle part is little modified.
Based on our ongoing work we intend to compare fully quantum-mechanical
results to semi-classical descriptions
of the photoelectron transport away from threshold.

\section*{Acknowledgements}
It is a pleasure to thank the organisers and especially Michael Bonitz
for an excellent workshop.
The present work was supported by the EU's 6th Framework Programme through
the NANOQUANTA Network of Excellence (NMP4-CT-2004-500198).
\section*{References}

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


Takehiro Ito, Erik D. Demaine, Nicholas J. A. Harvey, Christos H. Papadimitriou, Martha Sideri, Ryuhei Uehara, and Yushi Uno, "On the Complexity of Reconfiguration Problems", in Proceedings of the 19th Annual International Symposium on Algorithms and Computation (ISAAC 2008), Gold Coast, Australia, December 15–17, 2008, pages 28–39.
Reconfiguration problems arise when we wish to find a step-by-step transformation between two feasible solutions of a problem such that all intermediate results are also feasible. We demonstrate that a host of reconfiguration problems derived from NP-complete problems are PSPACE-complete, while some are also NP-hard to approximate. In contrast, several reconfiguration versions of problems in P are solvable in polynomial time.
The paper is available in PostScript (1134k) and PDF (176k).


A Cape Girardeau woman is dead this morning following a crash in Bollinger County.
The wreck happened Tuesday on Route KK near 2:30.
54-year-old Nancy Herren was driving eastbound when she ran off the road several times.
Herren hit an embankment and overturned.


What would you do if you were told that your quality of life could be improved by following three concrete steps? Several years ago I was involved in a study looking at the impact of positive psychology techniques on improving quality of life in cancer patients. Since being involved in this trial, I have been fascinated by the ability of such relatively 'simple' techniques in improving people's quality of life, mood and overall well-being.
Positive Psychology is a relatively new field of psychology which studies the positive side of human functioning and performance. Instead of focusing on psychological problems, positive psychologists try to understand what makes people thrive and flourish. Positive psychologists are interested in aspects like character strengths or traits, positive social relationships, positive experiences and other factors which contribute to positive functioning. This growing field of research has also led to many techniques and interventions that aim to improve all aspects of positive functioning, such as mood, health and even work performance.
1. The gratitude journal. This is one of my favourite Positive Psychology techniques, and perhaps one of the easiest one to adopt as part of your daily routine. Every night before going to bed write down at least three things you are grateful for. This simple daily habit helps you reflect on all the things that you are grateful for (therefore training your brain to think more positively) and can do wonders for your mood as well as your sleep.
3. Practice mindfulness. The concept of mindfulness has stemmed from Eastern traditions and is about learning to focus our minds on the present moment. The idea behind mindfulness is to acknowledge each sensation, thought, and emotion without analyzing or judging it in any way. Mindfulness-based techniques take a lot of practice, but they can do wonders for decreasing stress. Try to find moments every day where you can practice mindfulness, whether it is when you are eating breakfast or taking the bus to work. Practicing mindfulness on a daily basis can decrease stress, increase positive emotions, and improve overall well-being.
Positive psychology interventions are cropping up everywhere. They are being used in schools, in health-care, and also in organizations. Organizations are starting to realize that attributes that are linked to good performance, good leadership, and success (attributes such as optimism and resilience) can in fact be learned. For example, even if you think you are not a natural optimist, you can in fact train your brain to start thinking more positively.
If you would like to know more about Positive Psychology, contact us to learn how Positive Psychology techniques can be applied to your organization.
Great question. Flow is something which is really hard to control, and cannot be forced. Studies have shown that certain types of people tend to experience flow more frequently (e.g. people who rate high in personality characteristics such as persistence and curiosity). There are however certain things that you can do to help enable flow. These things include having clear goals of what you are trying to achieve in your task and being confident you have the skills needed to complete the task. So in other words, it will be easier to achieve flow if you have a good 'fit' between the difficulty of the task and your own skills and level of confidence in achieving that task.
To follow up on Eva's comment & question, I think that getting into the flow mind-set is most challenging, especially in a work environment where you have so many stimuli around you.


At around 8:30PM on Friday, September 23rd, a man was found hanging in McGolrick Park, dead from an apparent suicide. The victim, most likely homeless and a public inebriate, was found half sitting on the bench from which he probably jumped, with a rope tied around his neck on one end and to a fence on the other. This marked at least the third death of a homeless person in a neighborhood park this year and the second suicide – another victim succumbed to the elements. The tragedy strengthened the calls of many Greenpointers to establish a shelter in the neighborhood to deal with its unique homeless population.
Advocates for Greenpoint's homeless agree with Levin and Lentol, arguing that the proposed McGuinness shelter will bring in an overload of homeless from throughout the five boroughs, offering only temporary shelter. Meanwhile, there is no outreach planned for local homeless, such as those in McCarren and McGolrick Park as well as other public spaces.
I hope the poor yuppies and hipsters didn't have to witness this.
This is such a hip neighborhood now.


text:
Dixon Fatal Car Accident on Batavia Road, January 16
Home > Catastrophic Injury > Dixon Fatal Car Accident on Batavia Road, January 16
At Least 1 Killed in Dixon Car and Train Crash on Batavia Road
DIXON (January 16, 2018) – One person was killed in a collision involving a train on Batavia Road Tuesday afternoon, according to San Francisco Gate.
At approximately 2:59 p.m. a Capitol Corridor Amtrak train crashed into a car near the 7118 block of Batavia Road. It was not immediately clear why the vehicle was on the train tracks at the time of the incident.
The California Highway Patrol dispatch indicated that the collision resulted in one fatality. The name of the deceased has not been yet released pending notification of next of kin.
At this time, additional details on the tragic crash were not disclosed. Investigators are still determining how and why the incident happened.
If your loved one has been involved in an accident involving a train, and you are unsure of what steps to take, we urge you to contact Johnson Attorneys Group. You may speak with our experienced wrongful death lawyers at 800-235-6801 for a free case consultation.
batavia road
Capitol Corridor Amtrak train
Dixon car accident
Dixon fatal crash
dixon train accident


Here is a sample of 4815. It consists of lines made up of the first 13 books.
~ indicates where a book ends short of 48 pages.
Some quotes/excerpts have been slightly altered.
Liverpool based poet and editor. I have had four pamphlets of poetry published, most recently After Stikklestad (Knives, Forks and Spoons Press, 2010). Penned in the Margins published my first collection, Steak & Stations, in 2010.
Adam Marek One of the best writers in Britain.
Comma Press Great Manchester based publisher of fiction and poetry.
Pened in the Margins My publisher so I'm biased but probably the best independent publisher in the UK.


text:
Why You Can't Pay Attention and How to Think Deeply Again with Johann Hari
Have you noticed that your ability to pay attention is collapsing? Did you know that in the US teenagers can focus on one task for only sixty-five seconds at a time and office workers average only three minutes?
Like so many of us Johann Hari was finding that constantly switching from device to device and tab to tab...
Why Your Happiness Matters with Ericka Souter
Parenting is hard. But being a parent doesn't mean you have to stifle your most basic wants and needs. It doesn't mean it has to consume you to the degree of self-sacrifice and martyrdom and you definitely don't need to lose yourself to be a good parent.
Ericka Souter, author of How to Have a Baby and a Life on...
How to Ask for What You Need in a Relationship
Dr. Yvette Erasmus, a returning guest from last year's Ep. 262: When Your Needs Are Not Met on how to build and enjoy deeply connected, fulfilling and life-affirming relationships.
SOME KEY POINTS
What to do when you are growing and changing and your partner isn't
Do you feel like you have grown apart to...
How Mother Loss Shapes Who We Become
Warning: This episode contains mature themes and sensitive topics.
While I think the conversation is deep, important and rich, it could be triggering for some. Please use your best judgment and assess whether you are in the right state of mind to be exposed to such content at this point in time.
Hope Edelman and Dr....


text:
Q: Problem FBConnect (IPHONE), code not run on didLoad Three days ago this code worked...:(
The label will not update to show the loaded facebook username.
//Interface .h
IBOutlet UILabel *namefb;
...
@property(nonatomic, retain)UILabel *namefb;

//Implementation .m

- (void)request:(FBRequest*)request didLoad:(id)result {

        NSArray* users = result;

    NSDictionary* user = [users objectAtIndex:0];

    NSString* name = [user objectForKey:@"name"];

       namefb.text=[NSString stringWithFormat:@"Log-in: %@", name];//not update
}

(I have also connected the label in IB and imported all fbconnect delegates )
When I run it in debug, the variable name is right, but namefb.text does not get updated..
Any ideas?
sorry for my english..:)

A: Your code assumes three things:

*

*The result object is of type NSArray.

*The NSArray has at least one object, which is an NSDictionary.

*That object has a key "name" that has an NSString object associated with it.
Test each of these three things, perhaps by using some NSLog() statements, and you should see where the problem is.

A: Make sure you connected namefb to a UILabel object in Interface Builder. Simply making that variable an outlet won't cause an object to appear there out of thin air—you need to create the object (in IB) and plug it into the outlet (in IB).
Until it's connected to an object, the variable will hold nil, and a message to nil does nothing.

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