Introduction to Keldysh technique

•

0 likes•216 views

The document introduces the Keldysh technique, which is used to calculate non-equilibrium Green's functions. It discusses equilibrium Green's functions, the Keldysh contour used to calculate non-equilibrium Green's functions, and the application of the Keldysh technique. Key aspects covered include Green's functions on the Keldysh contour, the Larkin representation, identities among Green's functions, equations of motion for Green's functions on the Keldysh contour, and Keldysh Green's functions. The goal is to provide an overview of the Keldysh technique.

Science

Introduction to Keldysh technique
Krzysztof Pomorski
University of Warsaw, Faculty of Physics
kdvpomorski@gmail.com
June 10, 2014
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 1 / 29

Overview
1 Equilibrium Green function
2 Keldysh contour
3 Application of Keldysh technique
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 2 / 29

Equilibrium Green functions
iG(x, t; x , t ) =< φ0|T(ψ(x, t)ψ†
(x , t ))|φ0 > (1)
iG(x, t; x , t ) =
< φ0|S(+∞, −∞)ψ(x, t)ψ†(x , t )|φ0 >
< φ0|S(+∞, −∞)|φ0 >
(2)
S(+∞, −∞) = T exp(−i
+∞
−∞
dt1V (t1)) (3)
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 3 / 29

Keldysh contour
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 4 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 5 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 6 / 29

Green function
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 7 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 8 / 29

Green functions on Keldysh contour
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 9 / 29

Larkin representation
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 10 / 29

Some identities among Green functions
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 11 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 12 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 13 / 29

Green functions equations of motion on Keldysh contour
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 14 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 15 / 29

Keldysh Green functions
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 16 / 29

To be remembered...
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 17 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 18 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 19 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 20 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 21 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 22 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 23 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 24 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 25 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 26 / 29

Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 27 / 29

References
An Introduction to Nonequilibrium Green Functions,
Robert van Leeuwen and Nils Erik Dahlen, 2005
Keldysh technique and nonlinear sigma-model:basic principles and applications,
Alex Kamenev and Alex Levchenko, 2009
An introduction to nonequlibrium many-body theory,
Joseph Maciejko, 2007
Quasiclassical equations of the theory of superconductivity for contiguous metals
and the properties of constricted microcontacts,
A.V.Zaitsev, 1984, Zh. Eksp. Teor. Fiz. 86
Quantum theory of nonequilibrium processes,
P.Danielewicz, 1983
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 28 / 29

The End
Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 29 / 29

The document lists various clothing items and their prices in Bolivares (BSF). It describes a pink dress, blue dress with roses, brown shirt with green and black shorts, and brown flannel trousers with a blue and white shirt. It then provides 12 items and their corresponding prices, including pants for 150 BSF, a jacket for 280 BSF, a blue dress for 320 BSF, pink imported shirts for 190 BSF, sandals for 256 BSF, a monkey toy for 50 BSF, an evening dress for 560 BSF, sports shorts for 56 BSF, tires for 780 BSF, a skirt for 60 BSF, an imported watch for 170 BSF, and pajamas for 80

Preparation and properties of polycrystalline YBa2Cu3o7-x and Fe mixtures

Krzysztof Pomorski

The polycrystalline samples of YBa2Cu3O7-x High-Temperature Superconductor (HTS), also called „YBCO-123”, were prepared by mixing (II) oxide (CuO), carbonate (BaCO3) and yttrium (III) oxide (Y2O3) powders and followed by a heat treatment high temperature (900 °C - 950 °C) flowing oxygen. The polycrystalline samples of YBCO-Fe composites were prepared by grinding the mixture of single phased YBCO-123 and small of iron (1% and 3% wt.), followed over by a heat treatment . The results of structural (SEM, EDS, Raman spectroscopy), magnetic (AC susceptibility and magnetization measurements) and magneto-transport on produced composites will be presented. Scanning electron microscopy (SEM) for YBCO and Fe mixtures showed iron particles homogeneously placed on YBCO grains boundaries. As the concentration of iron particles increased the critical temperature decreased. The magnetization measurements LN temperature revealed transition from diamagnetic to paramagnetic behaviour of YBCO-Fe samples originated from the iron grains.

QUBIT AGH - Modeling and Implementation of Quantum technologies

Krzysztof Pomorski

Introduction to quantum technologies by QUBIT AGH: Lecture 4

Krzysztof Pomorski

Introduction to quantum technologies by QUBIT AGH: Lecture 3

Krzysztof Pomorski

Introduction to quantum technologies by QUBIT AGH: Lecture 2

Krzysztof Pomorski

Introduction to quantum technologies by QUBIT AGH: Lecture 1

Krzysztof Pomorski

From embodied Artificial Intelligence to Artificial Life

Krzysztof Pomorski

This document discusses the justification of canonical quantization of the Josephson effect and modifications due to large capacitance energy. It presents the commonly used canonical quantization approach and derives the Josephson junction Hamiltonian in second quantization. It also discusses corrections to the Cooper pair box model that arise when the capacitance energy is comparable to the superconducting gap.

Applications of Rapid Single Quantum Flux electronics

Krzysztof Pomorski

Introduction to Full Counting Statistics

Krzysztof Pomorski

Lecture on classical and quantum information

Krzysztof Pomorski

This document provides an overview of a lecture on classical and quantum information theory. It discusses topics such as Maxwell's demon, the laws of thermodynamics, Shannon information theory, quantum measurement, the qubit model, and differences between classical and quantum information theory. The lecture aims to compare classical and quantum information concepts and highlight new properties that emerge from quantum mechanics.

Properties of field induced Josephson junction(s)

Krzysztof Pomorski

Field Induced Josephson Junction (FIJJ) is defined as the physical system made by placement of ferromagnetic strip directly or indirectly [insulator layer in-between] on the top of superconducting strip [3, 4, 7]. The analysis conducted in extended Ginzburg-Landau, Bogoliubov-de Gennes and RCSJ [11] models essentially points that the system is in most case a weak-link Josephson junction [2] and sometimes has features of tunneling Josephson junction [1]. Generalization of Field Induced Josephson junctions leads to the case of network of robust coupled field induced Josephson junctions [4] that interact in inductive way. Also the scheme of superconducting Random Access Memory (RAM) for Rapid Single Flux [8, 9] quantum (RSFQ) computer is drawn [6, 10] using the concept of tunneling Josephson junction [1] and Field Induced Josephson junction [3, 4]. The given presentation is also available by YouTube (https://www.youtube.com/watch?v=uIqXqiwDsSM). Literature [1]. B.D.Josephson, Possible new effects in superconductive tunnelling, PL, Vol.1, No. 251, 1962 [2]. K.Likharev, Josephson junctions Superconducting weak links, RMP, Vol. 51, No. 101, 1979 [3]. K.Pomorski and P.Prokopow, Possible existence of field induced Josephson junctions, PSS B, Vol.249, No.9, 2012 [4]. K.Pomorski, PhD thesis: Physical description of unconventional Josephson junction, Jagiellonian University, 2015 [4]. K.Pomorski, H.Akaike, A.Fujimaki, Towards robust coupled field induced Josephson junctions, arxiv:1607.05013, 2016 [6]. K.Pomorski, H.Akaike, A.Fujimaki, Relaxation method in description of RAM memory cell in RSFQ computer, Procedings of Applied Conference 2016 (in progress) [7]. J.Gelhausen and M.Eschrig, Theory of a weak-link superconductor-ferromagnet Josephson structure, PRB, Vol.94, 2016 [8]. K.K. Likharev, Rapid Single Flux Quantum Logic (http://pavel.physics.sunysb.edu/RSFQ/Research/WhatIs/rsfqre2m.html) [9]. Proceedings of Applied Superconductivity Confence 2016, plenary talk by N.Yoshikawa, Low-energy high-performance computing based on superconducting technology (http://ieeecsc.org/pages/plenary-series-applied-superconductivity-conference-2016-asc-2016#Plenary7) [10]. A.Y.Herr and Q.P.Herr, Josephson magnetic random access memory system and method, International patent nr:8 270 209 B2, 2012 [11]. J.A.Blackburn, M.Cirillo, N.Gronbech-Jensen, A survey of classical and quantum interpretations of experiments on Josephson junctions at very low temperatures, arXiv:1602.05316v1, 2016

Main ideas behind Artificial Life

Krzysztof Pomorski

BIRDS DIVERSITY OF SOOTEA BISWANATH ASSAM.ppt.pptx

goluk9330

Ahota Beel, nestled in Sootea Biswanath Assam , is celebrated for its extraordinary diversity of bird species. This wetland sanctuary supports a myriad of avian residents and migrants alike. Visitors can admire the elegant flights of migratory species such as the Northern Pintail and Eurasian Wigeon, alongside resident birds including the Asian Openbill and Pheasant-tailed Jacana. With its tranquil scenery and varied habitats, Ahota Beel offers a perfect haven for birdwatchers to appreciate and study the vibrant birdlife that thrives in this natural refuge.

Farming systems analysis: what have we learnt?.pptx

Frédéric Baudron

Randomised Optimisation Algorithms in DAPHNE

University of Maribor

JAMES WEBB STUDY THE MASSIVE BLACK HOLE SEEDS

Sérgio Sacani

The pathway(s) to seeding the massive black holes (MBHs) that exist at the heart of galaxies in the present and distant Universe remains an unsolved problem. Here we categorise, describe and quantitatively discuss the formation pathways of both light and heavy seeds. We emphasise that the most recent computational models suggest that rather than a bimodal-like mass spectrum between light and heavy seeds with light at one end and heavy at the other that instead a continuum exists. Light seeds being more ubiquitous and the heavier seeds becoming less and less abundant due the rarer environmental conditions required for their formation. We therefore examine the different mechanisms that give rise to different seed mass spectrums. We show how and why the mechanisms that produce the heaviest seeds are also among the rarest events in the Universe and are hence extremely unlikely to be the seeds for the vast majority of the MBH population. We quantify, within the limits of the current large uncertainties in the seeding processes, the expected number densities of the seed mass spectrum. We argue that light seeds must be at least 103 to 105 times more numerous than heavy seeds to explain the MBH population as a whole. Based on our current understanding of the seed population this makes heavy seeds (Mseed > 103 M⊙) a significantly more likely pathway given that heavy seeds have an abundance pattern than is close to and likely in excess of 10−4 compared to light seeds. Finally, we examine the current state-of-the-art in numerical calculations and recent observations and plot a path forward for near-future advances in both domains.

Evidence of Jet Activity from the Secondary Black Hole in the OJ 287 Binary S...

Sérgio Sacani

Wereport the study of a huge optical intraday flare on 2021 November 12 at 2 a.m. UT in the blazar OJ287. In the binary black hole model, it is associated with an impact of the secondary black hole on the accretion disk of the primary. Our multifrequency observing campaign was set up to search for such a signature of the impact based on a prediction made 8 yr earlier. The first I-band results of the flare have already been reported by Kishore et al. (2024). Here we combine these data with our monitoring in the R-band. There is a big change in the R–I spectral index by 1.0 ±0.1 between the normal background and the flare, suggesting a new component of radiation. The polarization variation during the rise of the flare suggests the same. The limits on the source size place it most reasonably in the jet of the secondary BH. We then ask why we have not seen this phenomenon before. We show that OJ287 was never before observed with sufficient sensitivity on the night when the flare should have happened according to the binary model. We also study the probability that this flare is just an oversized example of intraday variability using the Krakow data set of intense monitoring between 2015 and 2023. We find that the occurrence of a flare of this size and rapidity is unlikely. In machine-readable Tables 1 and 2, we give the full orbit-linked historical light curve of OJ287 as well as the dense monitoring sample of Krakow.

Introduction_Ch_01_Biotech Biotechnology course .pptx

QusayMaghayerh

gastroretentive drug delivery system-PPT.pptx

Shekar Boddu

Microbiology of Central Nervous System INFECTIONS.pdf

sammy700571

IMPORTANCE OF ALGAE AND ITS BENIFITS.pptx

OmAle5

Gadgets for management of stored product pests_Dr.UPR.pdf

PirithiRaju

Insectsplayamajorroleinthedeteriorationoffoodgrainscausingbothquantitativeandqualitativelosses Wellprovedthatnogranariescanbefilledwithgrainswithoutinsectsastheharvestedproducecontainegg(or)larvae(or)pupae(or)adultinsectinthembecauseoffieldcarryoverinfestationwhichcannotbeavoidedindevelopingcountrieslikeIndia Simpletechnologiesfortimelydetectionofinsectsinthestoredproduceandtherebyplantimelycontrolmeasures

Authoring a personal GPT for your research and practice: How we created the Q...

Leonel Morgado

Thematic analysis in qualitative research is a time-consuming and systematic task, typically done using teams. Team members must ground their activities on common understandings of the major concepts underlying the thematic analysis, and define criteria for its development. However, conceptual misunderstandings, equivocations, and lack of adherence to criteria are challenges to the quality and speed of this process. Given the distributed and uncertain nature of this process, we wondered if the tasks in thematic analysis could be supported by readily available artificial intelligence chatbots. Our early efforts point to potential benefits: not just saving time in the coding process but better adherence to criteria and grounding, by increasing triangulation between humans and artificial intelligence. This tutorial will provide a description and demonstration of the process we followed, as two academic researchers, to develop a custom ChatGPT to assist with qualitative coding in the thematic data analysis process of immersive learning accounts in a survey of the academic literature: QUAL-E Immersive Learning Thematic Analysis Helper. In the hands-on time, participants will try out QUAL-E and develop their ideas for their own qualitative coding ChatGPT. Participants that have the paid ChatGPT Plus subscription can create a draft of their assistants. The organizers will provide course materials and slide deck that participants will be able to utilize to continue development of their custom GPT. The paid subscription to ChatGPT Plus is not required to participate in this workshop, just for trying out personal GPTs during it.

快速办理(UAM毕业证书)马德里自治大学毕业证学位证一模一样

hozt8xgk

学校原件一模一样【微信：741003700 】《(UAM毕业证书)马德里自治大学毕业证学位证》【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。本公司拥有海外各大学样板无数，能完美还原。 1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700 【主营项目】一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！二.真实使馆公证(即留学回国人员证明,不成功不收费) 三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度) 如果您处于以下几种情况： ◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】 ◇面对父母的压力，希望尽快拿到； ◇不清楚认证流程以及材料该如何准备； ◇回国时间很长，忘记办理； ◇回国马上就要找工作，办给用人单位看； ◇企事业单位必须要求办理的 ◇需要报考公务员、购买免税车、落转户口 ◇申请留学生创业基金留信网认证的作用: 1:该专业认证可证明留学生真实身份 2:同时对留学生所学专业登记给予评定 3:国家专业人才认证中心颁发入库证书 4:这个认证书并且可以归档倒地方 5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息 6:个人职称评审加20分 7:个人信誉贷款加10分 8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才

Male reproduction physiology by Suyash Garg .pptx

suyashempire

fermented food science of sauerkraut.pptx

ananya23nair

Methods of grain storage Structures in India.pdf

PirithiRaju

•Post-harvestlossesaccountforabout10%oftotalfoodgrainsduetounscientificstorage,insects,rodents,micro-organismsetc., •Totalfoodgrainproductioninindiais311milliontonnesandstorageis145mt.InIndia,annualstoragelosseshavebeenestimated14mtworthofRs.7,000croreinwhichinsectsaloneaccountfornearlyRs.1,300crores. •InIndiaoutofthetotalproduction,about30%ismarketablesurplus •Remaining70%isretainedandstoredbyfarmersforconsumption,seed,feed.Hence,growerneedstoragefacilitytoholdaportionofproducetosellwhenthemarketingpriceisfavourable •TradersandCo-operativesatmarketcentresneedstoragestructurestoholdgrainswhenthetransportfacilityisinadequate

23PH301 - Optics - Optical Lenses.pptx

RDhivya6

Recently uploaded

BIRDS DIVERSITY OF SOOTEA BISWANATH ASSAM.ppt.pptx

goluk9330

Farming systems analysis: what have we learnt?.pptx

Frédéric Baudron

Randomised Optimisation Algorithms in DAPHNE

University of Maribor

JAMES WEBB STUDY THE MASSIVE BLACK HOLE SEEDS

Sérgio Sacani

Evidence of Jet Activity from the Secondary Black Hole in the OJ 287 Binary S...

Sérgio Sacani

Introduction_Ch_01_Biotech Biotechnology course .pptx

QusayMaghayerh

gastroretentive drug delivery system-PPT.pptx

Shekar Boddu

Microbiology of Central Nervous System INFECTIONS.pdf

sammy700571

IMPORTANCE OF ALGAE AND ITS BENIFITS.pptx

OmAle5

Gadgets for management of stored product pests_Dr.UPR.pdf

PirithiRaju

Authoring a personal GPT for your research and practice: How we created the Q...

Leonel Morgado

快速办理(UAM毕业证书)马德里自治大学毕业证学位证一模一样

hozt8xgk

Male reproduction physiology by Suyash Garg .pptx

suyashempire

fermented food science of sauerkraut.pptx

ananya23nair

Methods of grain storage Structures in India.pdf

PirithiRaju

23PH301 - Optics - Optical Lenses.pptx

RDhivya6

Pests of Storage_Identification_Dr.UPR.pdf

PirithiRaju

11.1 Role of physical biological in deterioration of grains.pdf

PirithiRaju

MICROBIAL INTERACTION PPT/ MICROBIAL INTERACTION AND THEIR TYPES // PLANT MIC...

ABHISHEK SONI NIMT INSTITUTE OF MEDICAL AND PARAMEDCIAL SCIENCES , GOVT PG COLLEGE NOIDA

Microbial interaction Microorganisms interacts with each other and can be physically associated with another organisms in a variety of ways. One organism can be located on the surface of another organism as an ectobiont or located within another organism as endobiont. Microbial interaction may be positive such as mutualism, proto-cooperation, commensalism or may be negative such as parasitism, predation or competition Types of microbial interaction Positive interaction: mutualism, proto-cooperation, commensalism Negative interaction: Ammensalism (antagonism), parasitism, predation, competition I. Mutualism: It is defined as the relationship in which each organism in interaction gets benefits from association. It is an obligatory relationship in which mutualist and host are metabolically dependent on each other. Mutualistic relationship is very specific where one member of association cannot be replaced by another species. Mutualism require close physical contact between interacting organisms. Relationship of mutualism allows organisms to exist in habitat that could not occupied by either species alone. Mutualistic relationship between organisms allows them to act as a single organism. Examples of mutualism: i. Lichens: Lichens are excellent example of mutualism. They are the association of specific fungi and certain genus of algae. In lichen, fungal partner is called mycobiont and algal partner is called II. Syntrophism: It is an association in which the growth of one organism either depends on or improved by the substrate provided by another organism. In syntrophism both organism in association gets benefits. Compound A Utilized by population 1 Compound B Utilized by population 2 Compound C utilized by both Population 1+2 Products In this theoretical example of syntrophism, population 1 is able to utilize and metabolize compound A, forming compound B but cannot metabolize beyond compound B without co-operation of population 2. Population 2is unable to utilize compound A but it can metabolize compound B forming compound C. Then both population 1 and 2 are able to carry out metabolic reaction which leads to formation of end product that neither population could produce alone. Examples of syntrophism: i. Methanogenic ecosystem in sludge digester Methane produced by methanogenic bacteria depends upon interspecies hydrogen transfer by other fermentative bacteria. Anaerobic fermentative bacteria generate CO2 and H2 utilizing carbohydrates which is then utilized by methanogenic bacteria (Methanobacter) to produce methane. ii. Lactobacillus arobinosus and Enterococcus faecalis: In the minimal media, Lactobacillus arobinosus and Enterococcus faecalis are able to grow together but not alone. The synergistic relationship between E. faecalis and L. arobinosus occurs in which E. faecalis require folic acid

LEARNING TO LIVE WITH LAWS OF MOTION .pptx

yourprojectpartner05

Recently uploaded (20)

BIRDS DIVERSITY OF SOOTEA BISWANATH ASSAM.ppt.pptx

Farming systems analysis: what have we learnt?.pptx

Randomised Optimisation Algorithms in DAPHNE

JAMES WEBB STUDY THE MASSIVE BLACK HOLE SEEDS

Evidence of Jet Activity from the Secondary Black Hole in the OJ 287 Binary S...

Introduction_Ch_01_Biotech Biotechnology course .pptx

gastroretentive drug delivery system-PPT.pptx

Microbiology of Central Nervous System INFECTIONS.pdf

IMPORTANCE OF ALGAE AND ITS BENIFITS.pptx

Gadgets for management of stored product pests_Dr.UPR.pdf

Authoring a personal GPT for your research and practice: How we created the Q...

快速办理(UAM毕业证书)马德里自治大学毕业证学位证一模一样

Male reproduction physiology by Suyash Garg .pptx

fermented food science of sauerkraut.pptx

Methods of grain storage Structures in India.pdf

23PH301 - Optics - Optical Lenses.pptx

Pests of Storage_Identification_Dr.UPR.pdf

11.1 Role of physical biological in deterioration of grains.pdf

MICROBIAL INTERACTION PPT/ MICROBIAL INTERACTION AND THEIR TYPES // PLANT MIC...

LEARNING TO LIVE WITH LAWS OF MOTION .pptx

Introduction to Keldysh technique

1. Introduction to Keldysh technique Krzysztof Pomorski University of Warsaw, Faculty of Physics kdvpomorski@gmail.com June 10, 2014 Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 1 / 29

2. Overview 1 Equilibrium Green function 2 Keldysh contour 3 Application of Keldysh technique Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 2 / 29

4. Keldysh contour Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 4 / 29

5. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 5 / 29

6. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 6 / 29

7. Green function Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 7 / 29

8. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 8 / 29

9. Green functions on Keldysh contour Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 9 / 29

10. Larkin representation Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 10 / 29

11. Some identities among Green functions Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 11 / 29

12. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 12 / 29

13. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 13 / 29

14. Green functions equations of motion on Keldysh contour Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 14 / 29

15. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 15 / 29

16. Keldysh Green functions Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 16 / 29

17. To be remembered... Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 17 / 29

18. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 18 / 29

19. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 19 / 29

20. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 20 / 29

21. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 21 / 29

22. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 22 / 29

23. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 23 / 29

24. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 24 / 29

25. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 25 / 29

26. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 26 / 29

27. Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 27 / 29

28. References An Introduction to Nonequilibrium Green Functions, Robert van Leeuwen and Nils Erik Dahlen, 2005 Keldysh technique and nonlinear sigma-model:basic principles and applications, Alex Kamenev and Alex Levchenko, 2009 An introduction to nonequlibrium many-body theory, Joseph Maciejko, 2007 Quasiclassical equations of the theory of superconductivity for contiguous metals and the properties of constricted microcontacts, A.V.Zaitsev, 1984, Zh. Eksp. Teor. Fiz. 86 Quantum theory of nonequilibrium processes, P.Danielewicz, 1983 Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 28 / 29

29. The End Krzysztof Pomorski (FUW) Keldysh technique June 10, 2014 29 / 29

Introduction to Keldysh technique

Recommended

Recommended

More Related Content

More from Krzysztof Pomorski

More from Krzysztof Pomorski (6)

Recently uploaded

Recently uploaded (20)

Introduction to Keldysh technique