Theory of electron transport in semiconductors: a pathway from elementary physics to nonequilibrium green functions
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Berlin [u.a.]
Springer
2010
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Schriftenreihe: | Springer series in solid-state sciences
165 |
Schlagworte: | |
Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
Beschreibung: | Literaturangaben |
Beschreibung: | XXVI, 588 S. Ill., graph. Darst. 24 cm |
ISBN: | 9783642105852 |
Internformat
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245 | 1 | 0 | |a Theory of electron transport in semiconductors |b a pathway from elementary physics to nonequilibrium green functions |c Carlo Jacoboni |
264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
300 | |a XXVI, 588 S. |b Ill., graph. Darst. |c 24 cm | ||
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490 | 1 | |a Springer series in solid-state sciences |v 165 | |
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Datensatz im Suchindex
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adam_text |
CONTENTS PART I BASIC CONCEPTS IN SEMICONDUCTOR PHYSICS 1 SURVEY OF
CLASSICAL PHYSICS 3 1.1 NEWTON DYNAMICS 3 1.2 WORK AND ENERGY 4 1.3
HAMILTONIAN FORMULATION OF DYNAMICS 6 1.4 CANONICAL TRANSFORMATIONS 7
1.5 SMALL OSCILLATIONS 8 1.6 MAXWELL EQUATIONS 10 1.7 ELECTROMAGNETIC
POTENTIALS AND GAUGE TRANSFORMATIONS 11 1.8 HAMILTONIAN OF A CHARGED
PARTICLE IN AN ELECTROMAGNETIC FIELD 13 2 FUNDAMENTALS OF QUANTUM
MECHANICS 15 2.1 THE FIRST POSTULATES 16 2.2 EQUATIONS OF MOTION 18
2.2.1 PICTURES AND REPRESENTATIONS 18 2.2.2 EVOLUTION OPERATOR AND ITS
EQUATION OF MOTION 19 2.2.3 EQUATION OF MOTION IN SCHROEDINGER AND
HEISENBERG PICTURES 20 2.2.4 INTERACTION PICTURE 20 2.3 HEISENBERG
UNCERTAINTY RELATIONS 21 2.4 HOW TO DEAL WITH A GENERAL
QUANTUM-MECHANICAL PROBLEM IN A SYSTEM WITH A CONSTANT HAMILTONIAN 22
2.5 THE {Q} REPRESENTATION: WAVE MECHANICS 23 2.6 IDENTICAL PARTICLES
AND PAULI EXCLUSION PRINCIPLE 25 3 FUNDAMENTALS OF STATISTICAL PHYSICS
27 3.1 INTRODUCTION 27 3.2 LIOUVILLE THEOREM 28 3.3 THE FUNDAMENTAL
HYPOTHESES OF STATISTICAL MECHANICS 30 3.4 MAIN DEFINITIONS AND RESULTS
OF STATISTICAL MECHANICS 31 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1000032175 DIGITALISIERT DURCH X CONTENTS 3.5 THERMAL
BATH 34 3.6 THE THREE FUNDAMENTAL STATISTICAL ENSEMBLES 34 3.6.1
MICROCANONICAL ENSEMBLE 35 3.6.2 CANONICAL ENSEMBLE 35 3.6.3 GRAND
CANONICAL ENSEMBLE 36 3.7 EQUILIBRIUM PARTICLE DISTRIBUTIONS IN IDEAL
GASES 37 3.7.1 CLASSICAL GAS: MAXWELL-BOLTZMANN DISTRIBUTION 38 3.7.2
BOSE DISTRIBUTIONS 38 3.7.3 FERMI DISTRIBUTION 39 3.7.4 CLASSICAL LIMIT
39 4 CRYSTAL STRUCTURES 41 4.1 CRYSTALS 41 4.2 LATTICES 42 4.3 CRYSTAL
BONDING 46 4.4 RECIPROCAL LATTICE 47 5 PHONONS 49 5.1 THE VIBRATING
STRING 50 5.2 THE SIMPLEST LINEAR CHAIN 52 5.3 MONATOMIC LINEAR CHAIN
WITH MULTIPLE COUPLING 55 5.4 DIATOMIC LINEAR CHAIN 56 5.5
THREE-DIMENSIONAL LATTICE VIBRATIONS 59 5.6 NORMAL COORDINATES AND
QUANTIZATION - PHONONS 63 5.7 PHONON MOMENTUM AND CRYSTAL MOMENTUM 66
5.8 EXPERIMENTAL DETERMINATION OF PHONON DISPERSIONS 66 6 BLOCH STATES
AND BAND THEORY 69 6.1 BLOCH THEOREM 69 6.2 DENSITY OF STATES 72 6.3
TIGHT-BINDING APPROACH 73 6.4 BAND-STRUCTURE CALCULATIONS 74 6.4.1 LCAO
METHOD 75 6.4.2 FC P METHOD 76 6.4.3 PSEUDOPOTENTIAL METHOD 76 6.5 BAND
STRUCTURES OF MOST IMPORTANT SEMICONDUCTORS 80 6.6 EFFECTIVE-MASS
APPROXIMATION 80 6.7 BLOCH WAVEPACKETS 81 6.7. CONTENTS XI 7.3.2
ACCELERATED QUANTUM ELECTRONS IN FREE SPACE 89 7.3.3 ACCELERATED BLOCH
STATES 90 7.4 ENVELOPE FUNCTION FOR STEADY STATES 91 7.5 EFFECTIVE-MASS
THEOREM FOR A WAVEPACKET IN SLOW-VARYING ELECTRIC AND MAGNETIC FIELDS 95
7.6 TIME-DEPENDENT ENVELOPE FUNCTION 98 7.7 SEMICLASSICAL DYNAMICS 99
SEMICONDUCTORS 103 8.1 FREE DYNAMICS OF BLOCH ELECTRONS 103 8.2 A FULLY
OCCUPIED BAND CANNOT CARRY CURRENT 104 8.3 HOLES 105 8.4 INSULATORS,
CONDUCTORS, SEMICONDUCTORS 106 8.5 INTRINSIC AND DOPED SEMICONDUCTORS
108 8.5.1 DONORS AND ACCEPTORS 108 8.5.2 N-DOPED AND P-DOPED
SEMICONDUCTORS 110 8.6 CHARGE-CARRIER STATISTICS 110 8.6.1 METALS ILL
8.6.2 SEMICONDUCTORS 114 8.7 GENERAL MODELS OF BANDS FOR CUBIC
SEMICONDUCTORS 117 8.7.1 DIFFERENT TYPES OF EFFECTIVE MASSES 120 8.7.2
HERRING-VOGT TRANSFORMATION 122 8.7.3 NONPARABOLICITY 123 PART II
SEMICLASSICAL TRANSPORT IN BULK SEMICONDUCTORS 9 ELECTRONIC INTERACTIONS
127 9.1 CLASSIFICATION 127 9.2 FUNDAMENTALS OF SCATTERING -
CRYSTAL-MOMENTUM CONSERVATION 129 9.3 ELECTRON-PHONON SCATTERING RATES -
DEFORMATION POTENTIAL . 132 9.3.1 ELECTRON INTRAVALLEY SCATTERING BY
ACOUSTIC PHONONS . 133 9.3.2 ELECTRON INTRAVALLEY SCATTERING BY
OPTICAL PHONONS . 140 9.3.3 ELECTRON INTERVALLEY SCATTERING 142 9.3.4
HOLE INTRABAND SCATTERING BY ACOUSTIC PHONONS 143 9.3. XII CONTENTS 9.7
ALLOY SCATTERING 158 9.8 CARRIER-CARRIER INTERACTION 159 9.9 RELATIVE
IMPORTANCE OF THE DIFFERENT SCATTERING MECHANISMS . 160 10 BOLTZMANN
EQUATION 163 10.1 THE DISTRIBUTION FUNCTION 163 10.1.1 MEAN QUANTITIES
164 10.2 ELEMENTARY DERIVATION OF THE BOLTZMANN EQUATION 165 10.3 THE
COLLISION INTEGRAL - DETAILED BALANCE 167 10.4 MOMENT METHOD 168 10.4.1
ZERO-ORDER MOMENT: CONTINUITY EQUATION 169 10.4.2 FIRST-ORDER MOMENT 171
10.4.3 DRIFT-DIFFUSION EQUATION 173 10.4.4 HIGHER-ORDER MOMENTS:
HYDRODYNAMIC EQUATIONS 176 10.5 CHAMBERS' INTEGRAL EQUATION 177 10.5.1
PATH VARIABLES 177 10.5.2 CHAMBERS' INTEGRAL EQUATION 179 11 LINEAR
TRANSPORT 181 11.1 LINEARIZATION OF BOLTZMANN EQUATION 181 11.2
RELAXATION-TIME APPROXIMATION 183 11.3 LINEAR TRANSPORT PROPERTIES IN A
"SIMPLE SEMICONDUCTOR" . 184 11.3.1 OHMIC MOBILITY 184 11.3.2
MATTHIESSEN RULE 187 11.3.3 MAGNETOTRANSPORT 188 11.3.4 HALL EFFECT 192
11.4 HIGH-MAGNETIC-FIELD EFFECTS 197 11.5 EVALUATION OF THE MOMENTUM
RELAXATION TIMES 198 11.5.1 RELAXATION TIME FOR VELOCITY-RANDOMIZING
COLLISIONS . 198 11.5.2 RELAXATION TIME FOR ELASTIC COLLISIONS 199 11.6
MOBILITIES 201 11.6.1 ACOUSTIC-PHONON SCATTERING, DEFORMATION POTENTIAL,
ELASTIC 201 11.6.2 OPTICAL-PHONON SCATTERING, DEFORMATION POTENTIAL .
202 11.6. CONTENTS XIII 13 NONLINEAR TRANSPORT 219 13.1 HOT ELECTRONS
220 13.1.1 THE WARM ELECTRON REGION 224 13.2 ELECTRON-ELECTRON
COLLISIONS AND THE HEATED AND DRIFTED MAXWELL DISTRIBUTION 225 13.3
ANISOTROPY OF TRANSPORT COEFFICIENTS 225 13.4 NEGATIVE DIFFERENTIAL
MOBILITY AND GUNN EFFECT 227 13.5 HIGH-FIELD DIFFUSIVITY 229 13.5.1
INTERVALLEY DIFFUSION 230 13.6 TRANSIENT TRANSPORT 233 13.7 HOT PHONONS
235 13.8 ULTRAFAST SPECTROSCOPY 235 14 MONTE CARLO SIMULATION OF BULK
ELECTRON TRANSPORT 237 14.1 THE MONTE CARLO METHOD 237 14.2 DIRECT MONTE
CARLO SIMULATION 239 14.2.1 A TYPICAL MONTE CARLO PROGRAM FOR
HOMOGENEOUS, STATIONARY TRANSPORT 240 14.2.2 TIME- AND SPACE-DEPENDENT
PHENOMENA - ENSEMBLE MC 245 14.2.3 DIFFUSION 247 14.2.4 OHMIC MOBILITY
248 14.2.5 ELECTRON-ELECTRON INTERACTION AND DEGENERATE STATISTICS 249
14.2.6 IMPACT IONIZATION 251 14.2.7 VARIANCE-REDUCING TECHNIQUES 251
14.2.8 FULL-BAND MONTE CARLO 252 14.3 FORMAL MONTE CARLO SOLUTION OF THE
BE - WEIGHTED MONTE CARLO 254 14.3.1 MONTE CARLO EVALUATION OF SUMS AND
INTEGRALS 254 14.3.2 THE INTEGRAL BOLTZMANN EQUATION WITH APPROXIMATE
TOTAL SCATTERING RATE 257 14.3.3 THE NEUMANN EXPANSION 258 14.3.4
SAMPLING 260 15 BULK TRANSPORT PROPERTIES OF MAIN SEMICONDUCTORS 26 XIV
CONTENTS PART III QUANTUM TRANSPORT IN BULK SEMICONDUCTORS 16 QUANTUM
TRANSPORT IN HOMOGENEOUS SYSTEMS 285 16.1 INTRODUCTION TO QUANTUM
TRANSPORT 285 16.1.1 SEMICLASSICAL TRANSPORT AND QUANTUM PHYSICS 285
16.1.2 FROM REVERSIBLE DYNAMICS TO IRREVERSIBLE BOLTZMANN EQUATION 286
16.1.3 COHERENCE, DEPHASING, AND ENTANGLEMENT 289 16.1.4 WHEN IS QUANTUM
TRANSPORT NECESSARY? 290 16.2 THE DENSITY MATRIX 293 16.3 REDUCED
DENSITY MATRIX 296 16.4 KUBO FORMULA 297 16.5 THE PATH-INTEGRAL APPROACH
301 17 THE WIGNER-FUNCTION APPROACH TO QUANTUM TRANSPORT . 305 17.1
INTRODUCTION 305 17.2 DEFINITION AND MAIN PROPERTIES 306 17.2.1
WEYL-WIGNER TRANSFORMATION 306 17.2.2 TRANSFORMATION BETWEEN THE MATRIX
ELEMENTS OF AN OPERATOR AND ITS WEYL-WIGNER TRANSFORM 307 17.2.3
DEFINITION OF THE WIGNER FUNCTION 308 17.2.4 MAIN PROPERTIES 309 17.3
COHERENT EVOLUTION OF THE WIGNER FUNCTION 311 17.4 DYNAMICAL EQUATIONS
OF THE WIGNER FUNCTION 312 17.4.1 MOYAL EXPANSION 315 17.5
ELECTRON-PHONON INTERACTION 316 17.6 WIGNER PATHS AND MC SIMULATION 320
17.6.1 INTEGRAL EQUATION 320 17.6.2 NEUMANN EXPANSION AND WIGNER PATHS
322 17.6.3 MONTE CARLO SIMULATION 324 17.7 TWO-TIME WIGNER FUNCTION 327
17.8 MANY-PARTICLE WIGNER FUNCTION 328 PART IV TRANSPORT IN
SEMICONDUCTOR STRUCTURES 18 INHOMOGENEOUS AND OPEN SYSTEMS: ELECTRONIC
DEVICES . CONTENTS XV 18.3.3 SOLAR CELLS 344 18.3.4 LIGHT-EMITTING
DIODES 345 18.4 THE BIPOLAR JUNCTION TRANSISTOR 347 18.5
METAL-SEMICONDUCTOR JUNCTIONS, SCHOTTKY BARRIER DIODE 349 18.6
FIELD-EFFECT TRANSISTORS 351 18.7 DEVICE SIMULATION 355 18.7.1
DRIFT-DIFFUSION MODELS 356 18.7.2 HYDRODYNAMIC MODELS 359 18.7.3 MONTE
CARLO SIMULATIONS 360 19 LOW-DIMENSIONAL STRUCTURES 363 19.1 EPITAXIAL
HETEROSTRUCTURES 363 19.2 QUANTUM WELLS 366 19.2.1 ELECTRON STATES 366
19.2.2 TRANSPORT 370 19.2.3 MULTIPLE QUANTUM WELLS 376 19.3 QUANTUM
WIRES 376 19.4 QUANTUM DOTS 379 19.4.1 TRANSPORT: COULOMB BLOCKADE 380
19.5 SUPERLATTICES 382 19.5.1 MINIBANDS 382 19.5.2 TRANSPORT: BLOCH
OSCILLATIONS 384 19.5.3 WANNIER-STARK LADDER 385 19.5.4 NEGATIVE
DIFFERENTIAL CONDUCTIVITY 386 19.6 APPLICATIONS 386 20 CARBON NANOTUBES
389 20.1 INTRODUCTION 389 20.2 STRUCTURE 389 20.3 ELECTRON STATES: BANDS
393 20.4 ELECTRON TRANSPORT 396 21 COHERENT TRANSPORT IN MESOSCOPIC
STRUCTURES 401 21.1 LANDAUER-BUETTIKER THEORY OF TRANSPORT 401 21.2 POINT
CONTACTS 408 21.3 QUANTUM HALL EFFECT 409 21.4 AHARONOV-BOHM
OSCILLATIONS 417 21.5 LOCALIZATION 420 21.6 WEAK LOCALIZATION - QUANTUM
CORRECTIONS 423 21.7 UNIVERSAL CONDUCTION FLUCTUATIONS 424 21. XVI
CONTENTS PART V QUANTUM TRANSPORT WITH NONEQUILIBRIUM GREEN FUNCTIONS 23
SECOND-QUANTIZATION FORMALISM 441 23.1 MANY-PARTICLE WAVEFUNCTIONS 441
23.1.1 EXPANSION IN SYMMETRIC WAVEFUNCTIONS 443 23.2 VECTOR SPACE OF
MANY-PARTICLE STATES 444 23.2.1 CREATION AND ANNIHILATION OPERATORS 445
23.2.2 FIELD OPERATORS 446 23.3 FROM FIRST TO SECOND QUANTIZATION 448
23.4 DYNAMICS 449 23.5 COMMUTATIONS AT DIFFERENT TIMES FOR
NON-INTERACTING PARTICLES 450 23.6 FIELD OPERATORS IN MOMENTUM AND
ENERGY SPACE 451 24 INTRODUCTION TO GREEN FUNCTIONS 453 24.1 GFS FROM
DIFFERENTIAL EQUATIONS TO MANY-BODY THEORY 453 24.1.1 GF OF SCHROEDINGER
EQUATION 453 24.1.2 THE EVOLUTION OPERATOR AS GREENIAN 455 24.1.3 GREEN
FUNCTIONS FOR A ONE-PARTICLE SYSTEM 456 24.1.4 SINGLE-PARTICLE GREEN
FUNCTIONS IN MANY-PARTICLE SYSTEMS 458 24.2 GREEN FUNCTIONS IN MOMENTUM
AND ENERGY SPACE 460 24.3 EQUILIBRIUM GFS FOR NONLNTERACTING PARTICLES
461 24.4 GREEN FUNCTIONS AND MEAN QUANTITIES 465 24.5 SPECTRAL DENSITY
466 24.5.1 RELATION BETWEEN G AND G AND THE SPECTRAL DENSITY AT
EQUILIBRIUM 466 25 WICK*MATSUBARA THEOREMS 469 25.1 TIME-ORDERED
PRODUCTS, NORMAL PRODUCTS, AND CONTRACTIONS. 469 25.2 WICK THEOREM 471
25.2.1 LEMMA : 471 25.2. CONTENTS XVII 26.4 PARTICLE-PARTICLE
INTERACTION 485 26.5 ELECTRON-PHONON INTERACTION 486 26.6 SELF-ENERGY
AND DYSON EQUATION 488 26.6.1 MATRIX FORMULATION OF G AND OF DYSON
EQUATION 489 26.6.2 DYSON EQUATIONS FOR SEPARATE GFS 491 26.6.3 (FE, UJ)
REPRESENTATION 493 26.7 ELECTRON-PHONON SELF-ENERGY 496 27
NONEQUILIBRIUM GREEN FUNCTIONS APPLIED TO TRANSPORT: QUANTUM BOLTZMANN
EQUATION 497 27.1 THE EQUATIONS FOR G (R, T,R', T') AND G R (R, T,R',T')
498 27.2 THE EQUATIONS FOR G (R,T,K,U}) AND G T (R,T,K,UI) 500 27.3
GRADIENT-EXPANSION APPROXIMATION 502 27.4 EQUATIONS FOR LINEAR RESPONSE
IN HOMOGENEOUS SYSTEMS IN STEADY STATE 508 28 NONEQUILIBRIUM GREEN
FUNCTIONS APPLIED TO TRANSPORT: MESOSCOPIC SYSTEMS 513 28.1 GFS FOR THE
TIME-INDEPENDENT SCHROEDINGER EQUATION 514 28.2 GF FOR A PERFECT,
INFINITE, TWO-DIMENSIONAL WIRE 516 28.3 FROM GREEN FUNCTION TO S MATRIX
517 28.4 FINITE-DIFFERENCE SCHEME FOR THE CONDUCTOR GF 519 28.5 THE
EFFECT OF THE LEADS 521 28.6 CONDUCTANCE 525 PART VI APPENDICES A |
any_adam_object | 1 |
author | Jacoboni, Carlo |
author_facet | Jacoboni, Carlo |
author_role | aut |
author_sort | Jacoboni, Carlo |
author_variant | c j cj |
building | Verbundindex |
bvnumber | BV036745445 |
classification_rvk | UP 1100 UP 3200 |
classification_tum | PHY 672f |
ctrlnum | (OCoLC)699882503 (DE-599)DNB1000032175 |
dewey-full | 537.6226 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 537 - Electricity and electronics |
dewey-raw | 537.6226 |
dewey-search | 537.6226 |
dewey-sort | 3537.6226 |
dewey-tens | 530 - Physics |
discipline | Physik |
format | Book |
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id | DE-604.BV036745445 |
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indexdate | 2024-07-20T10:50:12Z |
institution | BVB |
isbn | 9783642105852 |
language | English |
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oclc_num | 699882503 |
open_access_boolean | |
owner | DE-83 DE-11 DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-20 DE-703 |
owner_facet | DE-83 DE-11 DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-20 DE-703 |
physical | XXVI, 588 S. Ill., graph. Darst. 24 cm |
publishDate | 2010 |
publishDateSearch | 2010 |
publishDateSort | 2010 |
publisher | Springer |
record_format | marc |
series | Springer series in solid-state sciences |
series2 | Springer series in solid-state sciences |
spelling | Jacoboni, Carlo Verfasser aut Theory of electron transport in semiconductors a pathway from elementary physics to nonequilibrium green functions Carlo Jacoboni Berlin [u.a.] Springer 2010 XXVI, 588 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer series in solid-state sciences 165 Literaturangaben Halbleiter (DE-588)4022993-2 gnd rswk-swf Elektronentransport (DE-588)4014344-2 gnd rswk-swf Halbleiter (DE-588)4022993-2 s Elektronentransport (DE-588)4014344-2 s DE-604 Springer series in solid-state sciences 165 (DE-604)BV000016582 165 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3423612&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020662819&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Jacoboni, Carlo Theory of electron transport in semiconductors a pathway from elementary physics to nonequilibrium green functions Springer series in solid-state sciences Halbleiter (DE-588)4022993-2 gnd Elektronentransport (DE-588)4014344-2 gnd |
subject_GND | (DE-588)4022993-2 (DE-588)4014344-2 |
title | Theory of electron transport in semiconductors a pathway from elementary physics to nonequilibrium green functions |
title_auth | Theory of electron transport in semiconductors a pathway from elementary physics to nonequilibrium green functions |
title_exact_search | Theory of electron transport in semiconductors a pathway from elementary physics to nonequilibrium green functions |
title_full | Theory of electron transport in semiconductors a pathway from elementary physics to nonequilibrium green functions Carlo Jacoboni |
title_fullStr | Theory of electron transport in semiconductors a pathway from elementary physics to nonequilibrium green functions Carlo Jacoboni |
title_full_unstemmed | Theory of electron transport in semiconductors a pathway from elementary physics to nonequilibrium green functions Carlo Jacoboni |
title_short | Theory of electron transport in semiconductors |
title_sort | theory of electron transport in semiconductors a pathway from elementary physics to nonequilibrium green functions |
title_sub | a pathway from elementary physics to nonequilibrium green functions |
topic | Halbleiter (DE-588)4022993-2 gnd Elektronentransport (DE-588)4014344-2 gnd |
topic_facet | Halbleiter Elektronentransport |
url | http://deposit.dnb.de/cgi-bin/dokserv?id=3423612&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020662819&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV000016582 |
work_keys_str_mv | AT jacobonicarlo theoryofelectrontransportinsemiconductorsapathwayfromelementaryphysicstononequilibriumgreenfunctions |