Nonequilibrium statistical physics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2013
|
| Series: | Physics textbook
|
| Subjects: | |
| Online Access: | Inhaltstext Klappentext Inhaltsverzeichnis |
| Physical Description: | XIII, 382 S. graph. Darst. |
| ISBN: | 3527410872 9783527410873 9783527410927 9783527670574 |
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MARC
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VII
Contents
Preface
XI
Ί
Introduction
1
1.1
Irreversibility:
The Arrow of Time
2
1.1.1
Dynamical Systems
3
1.1.2
Thermodynamics
7
1.1.3
Ensembles and Probability Distribution
9
1.1.4
Entropy in Equilibrium Systems
11
1.1.5
Fundamental Time Arrows, Units
І4
1.1.6
Example
:
Ideal Quantum Gases
17
1.2
Thermodynamics of Irreversible Processes
19
1.2.1
Quasiequilibrium
19
1.2.2
Statistical Thermodynamics with Relevant
Observables
22
1.2.3
Phenomenological Description of Irreversible Processes
25
1.2.4
Example: Reaction Rates
29
1.2.5
Principle of Weakening of Initial Correlations and the Method
of Nonequilibrium Statistical Operator
31
Exercises
38
2
Stochastic Processes
41
2.1
Stochastic Processes with Discrete Event Times
42
2.1.1
Potentiality and Options, Chance and Probabilities
43
2.1.2
Stochastic Processes
46
2.13
Reduced Probabilities
50
2.1.4
Properties of Probability Distributions: Examples
54
2.1.5
Example: One-Step Process on a Discrete Space-Time Lattice and
Random Walk
58
2.2
Birth-and-Death Processes and Master Equation
61
2.2.1
Continuous Time Limit and Master Equation
63
2.2.2
Example: Radioactive Decay
67
2.2.3
Spectral Density and Autocorrelation Functions
69
2.2.4
Example: Continuum Limit of Random Walk and Wiener Process
76
2.2.5
Further Examples for Stochastic One-Step Processes
78
VIII Contents
2.2.6
Advanced Example: Telegraph Equation and
Poisson
Process
84
2.3
Brownian Motion and
Langevin
Equation
89
2.3.1
Langevin Equation
89
2.3.2
Solution of the Langevin Equation by Fourier Transformation
94
2.3.3
Example Calculations for a Langevin Process on Discrete Time
95
23.4
Fokker-Planck Equation
96
2.3.5
Application to Brownian Motion
105
2.3.6
Important Continuous Markov Processes
107
23.7
Stochastic Differential Equations and White Noise
109
2.3.8
Applications of Continuous Stochastic Processes
110
Exercises
113
3
Quantum Master Equation
117
3.1
Derivation of the Quantum Master Equation
119
3.1.1
Open Systems Interacting with a Bath
119
3.1.2
Derivation of the Quantum Master Equation
124
3.1.3
Born-Markov and Rotating Wave Approximations
227
3.1.4
Example: Harmonic Oscillator in a Bath
232
3.1.5
Example: Atom Coupled to the Electromagnetic Field
135
3.2
Properties of the Quantum Master Equation ana Examples
138
3.2.1 Pauli
Equation
138
3.2.2
Properties of the
Pauli
Equation, Examples
143
3.2.3
Discussion of the
Pauli
Equation
146
3.2.4
Example: Linear Coupling to the Bath
148
3.2.5
Quantum Fokker-Planck Equation
151
3.2.6
Quantum Brownian Motion and the Classical Limit
154
Exercises
156
4
Kinetic Theory
157
4.1
The Boltzmann Equation
158
4.1.1
Distribution Function
159
4.1.2
Classical Reduced Distribution Functions
163
4.1.3
Quantum Statistical Reduced Distribution Functions
í
66
4.1.4
The
Stoßzahlansatz 169
4.1.5
Derivation of the Boltzmann Equation from the Nonequilibrium
Statistical Operator
773
4.1.6
Properties of the Boltzmann Equation
180
4.1.7
Example: Hard Spheres
181
4.1.8
Beyond the Boltzmann Kinetic Equation
183
4.2
Solutions of the Boltzmann Equation
186
4.2.1
The Linearized Boltzmann Equation
187
4.2.2
Relaxation Time Method
189
4.2.3
The
Kohier
Variational Principle
194
4.2.4
Example: Thermal Conductivity in Gases
196
Contents
IX
4.3 The Vlasov-Landau
Equation and Hydrodynamic Equations
199
4.3.1
Derivation of the
Vlasov
Equation
199
4.3.2
The Landau Collision Term
201
4.3.3
Example for the
Vlasov
Equation: The
RPA
Dielectric Function
203
A3
Λ
Equations of Hydrodynamics
206
4.3.5
General Remarks to Kinetic Equations
213
Exercises
214
5
Linear Response Theory
217
5.1
Linear Response Theory and Generalized Fluctuation—Dissipation Theorem
(FDT)
218
5.1.1
External Fields and Relevant Statistical Operator
219
5.1.2
Nonequilibrium Statistical Operator for Linear Response
Theory
222
5.1.3
Response Equations and Elimination of
Lagrange
Multipliers
225
5.1.4
Example: Ziman Formula for the Conductivity and Force-Force
Correlation Function
226
5.1.5
The Choice of Relevant
Observables
and the
Kubo
Formula
230
5.2
Generalized Linear Response Approaches
235
5.2.1
Thermal Perturbations
236
5.2.2
Example: Thermoelectric Effects in Plasmas
239
5.2.3
Example: Hopping Conductivity of Localized Electrons
243
5.2.4
Time-Dependent Perturbations
246
5.2.5
Generalized Linear Boltzmann Equation
249
5.2.6
Variational Approach to Transport Coefficients
251
5.2.7
Further Results of Linear Response Theory
254
Exercises
259
6
Quantum Statistical Methods
261
6.1
Perturbation Theory for Many-Particle Systems
262
6.1.1
Equilibrium Statistics of Quantum Gases
262
6.1.2
Three Relations for Elementary Perturbation Expansions
267
6.1.3
Example: Equilibrium Correlation Functions in
Hartree—
Fock
Approximation
274
6.2
Thermodynamic Green's Functions
279
6.2.1
Thermodynamic Green's Functions: Definitions and Properties
280
6.2.2
Green's Function and Spectral Function
285
6.2.3
Example: Thermodynamic Green's Function for the
Ideal Fermi Gas
289
6.2.4
Perturbation Theory for Tliermodynamic Green's Functions
291
6.2.5
Application of the Diagram Rules:
Hartree—
Fock Approximation
297
6.3
Partial Summation and Many-Particle Phenomena
300
6.3.1
Mean-Field Approximation and Quasiparticle Concept
301
6.3.2
Dyson Equation and Self-Energy
304
6.3.3
Screening Equation and Polarization Function
307
Contents
6.3.4
Lowest
Order Approximation
for the Polarization Function:
RPA
312
6.3.5
Bound States
314
6.3.6
Excursus: Solution to the Two-Particle
Schrödinger
Equation with a
Separable Potential
318
6.3.7
Cluster Decomposition and the Chemical Picture
324
6.4
Path Integrals
329
6.4.1
The Onsager—Machlup Function
329
6.4.2
Dirac Equation in
1 + 1
Dimensions
332
Exercises
335
7
Outlook: Nonequilibrium Evolution and Stochastic Processes
337
7.1
Stochastic Models for Quantum Evolution
338
7.1.1
Measuring Process and Localization
339
7.1.2
The Caldeira-Leggett Model and Quantum Brownian Motion
342
7.1.3
Dynamical Reduction Models
345
7.1.4
Stochastic Quantum Electrodynamics
347
7.1.5
Quantum Dynamics and Quantum Evolution
349
7.2
Examples
353
7.2.1
Scattering Theory
3 53
7.2.2 Bremsstrahlung
Emission
355
7.2.3
Radiation Damping
359
7.2.4
The
1
//(Flicker) Noise
360
7.2.5
The Hydrogen Atom in the Radiation Field
362
7.2.6
Comments on Nonequilibrium Statistical Physics
365
References
372
Index
375
Authored by a well-known expert in the field of nonequilibrium
statistical physics, this book is a coherent presentation of the subject
suitable for masters and PhD students, as well as postdocs in physics
and related disciplines.
Starting from a general discussion of irreversibility and entropy, the
method of nonequilibrium statistical operator is presented as a general
concept. Stochastic processes are introduced as a necessary prerequi¬
site to describe the evolution of a nonequilibrium state. Different stan¬
dard approaches such as master equations, kinetic equations and linear
response theory, are derived after special assumptions. This allows for
an insight into the problems of nonequilibrium physics, a discussion
of the limits of the approaches, and suggestions for improvements.
The method of thermodynamic Green's function is outlined that allows
for the systematic quantum statistical treatment of many-body systems.
Applications and typical examples are given, as well as fully worked
problems.
From the contents:
Introduction
Stochastic processes
Quantum Master Equation
Kinetic Theory
Linear Response Theory
Quantum Statistical Methods
Outlook: Nonequilibrium evolution
and stochastic processes
Gera
Röpke
is professor of Theoretical Physics at the University of Rostock, Germany.
Having obtained his academic degrees from the University of Leipzig, he spent most of his
career working at the Technical University Dresden before the appointment at Rostock.
Professor
Röpke
has authored over
400
scientific publications on quantum statistics, non-
equiiibrium
statistka!
mechanics, plasma physics and nuclear theory, including several
monographs, and he received different awards. He is a member of the
Saxonian
Academy
of Sciences and external member of the Max-Planck Society. |
| any_adam_object | 1 |
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| discipline | Physik |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV040898508 |
| illustrated | Illustrated |
| indexdate | 2024-08-21T00:37:50Z |
| institution | BVB |
| isbn | 3527410872 9783527410873 9783527410927 9783527670574 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025878029 |
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| physical | XIII, 382 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
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| publisher | Wiley-VCH |
| record_format | marc |
| series2 | Physics textbook |
| spelling | Röpke, Gerd 1941- Verfasser (DE-588)135700167 aut Nonequilibrium statistical physics Gerd Röpke Weinheim Wiley-VCH 2013 XIII, 382 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics textbook Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Nichtgleichgewichtsstatistik (DE-588)4136220-2 s DE-604 Erscheint auch als Online-Ausgabe, EPUB 978-3-527-67059-8 Erscheint auch als Online-Ausgabe, MOBI 978-3-527-67058-1 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4033943&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025878029&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025878029&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Röpke, Gerd 1941- Nonequilibrium statistical physics Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd |
| subject_GND | (DE-588)4136220-2 (DE-588)4123623-3 |
| title | Nonequilibrium statistical physics |
| title_auth | Nonequilibrium statistical physics |
| title_exact_search | Nonequilibrium statistical physics |
| title_full | Nonequilibrium statistical physics Gerd Röpke |
| title_fullStr | Nonequilibrium statistical physics Gerd Röpke |
| title_full_unstemmed | Nonequilibrium statistical physics Gerd Röpke |
| title_short | Nonequilibrium statistical physics |
| title_sort | nonequilibrium statistical physics |
| topic | Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd |
| topic_facet | Nichtgleichgewichtsstatistik Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4033943&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=025878029&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025878029&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ropkegerd nonequilibriumstatisticalphysics |