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E-raamat: Nonequilibrium Statistical Physics [Wiley Online]

(University of Rostock, Germany)
  • Formaat: 382 pages
  • Ilmumisaeg: 13-Mar-2013
  • Kirjastus: Wiley-VCH Verlag GmbH
  • ISBN-10: 3527671390
  • ISBN-13: 9783527671397
Teised raamatud teemal:
  • Wiley Online
  • Hind: 153,31 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Nonequilibrium Statistical PhysicsSuurem pilt
  • Formaat: 382 pages
  • Ilmumisaeg: 13-Mar-2013
  • Kirjastus: Wiley-VCH Verlag GmbH
  • ISBN-10: 3527671390
  • ISBN-13: 9783527671397
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9783527671397
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 prerequisite to describe the evolution of a nonequilibrium state. Different standard 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.
Preface xi
1 Introduction
1(42)
1.1 Irreversibility: The Arrow of Time
2(17)
1.1.1 Dynamical Systems
3(4)
1.1.2 Thermodynamics
7(2)
1.1.3 Ensembles and Probability Distribution
9(2)
1.1.4 Entropy in Equilibrium Systems
11(3)
1.1.5 Fundamental Time Arrows, Units
14(3)
1.1.6 Example: Ideal Quantum Gases
17(2)
1.2 Thermodynamics of Irreversible Processes
19(24)
1.2.1 Quasiequilibrium
39
1.2.2 Statistical Thermodynamics with Relevant Observables
22(3)
1.2.3 Phenomenological Description of Irreversible Processes
25(4)
1.2.4 Example: Reaction Rates
29(2)
1.2.5 Principle of Weakening of Initial Correlations and the Method of Nonequilibrium Statistical Operator
31(7)
Exercises
38(5)
2 Stochastic Processes
43(74)
2.1 Stochastic Processes with Discrete Event Times
42(19)
2.1.1 Potentiality and Options, Chance and Probabilities
43(3)
2.1.2 Stochastic Processes
46(4)
2.1.3 Reduced Probabilities
50(4)
2.1.4 Properties of Probability Distributions: Examples
54(4)
2.1.5 Example: One-Step Process on a Discrete Space-Time Lattice and Random Walk
58(3)
2.2 Birth-and-Death Processes and Master Equation
61(28)
2.2.1 Continuous Time Limit and Master Equation
63(4)
2.2.2 Example: Radioactive Decay
67(2)
2.2.3 Spectral Density and Autocorrelation Functions
69(7)
2.2.4 Example: Continuum Limit of Random Walk and Wiener Process
76(2)
2.2.5 Further Examples for Stochastic One-Step Processes
78(6)
2.2.6 Advanced Example: Telegraph Equation and Poisson Process
84(5)
2.3 Brownian Motion and Langevin Equation
89(28)
2.3.1 Langevin Equation
89(5)
2.3.2 Solution of the Langevin Equation by Fourier Transformation
94(1)
2.3.3 Example Calculations for a Langevin Process on Discrete Time
95(1)
2.3.4 Fokker-Planck Equation
96(9)
2.3.5 Application to Brownian Motion
105(2)
2.3.6 Important Continuous Markov Processes
107(2)
2.3.7 Stochastic Differential Equations and White Noise
109(1)
2.3.8 Applications of Continuous Stochastic Processes
110(3)
Exercises
113(4)
3 Quantum Master Equation
117(40)
3.1 Derivation of the Quantum Master Equation
119(19)
3.1.1 Open Systems Interacting with a Bath
119(5)
3.1.2 Derivation of the Quantum Master Equation
124(3)
3.1.3 Born-Markov and Rotating Wave Approximations
127(5)
3.1.4 Example: Harmonic Oscillator in a Bath
132(3)
3.1.5 Example: Atom Coupled to the Electromagnetic Field
135(3)
3.2 Properties of the Quantum Master Equation and Examples
138(19)
3.2.1 Pauli Equation
138(5)
3.2.2 Properties of the Pauli Equation, Examples
143(3)
3.2.3 Discussion of the Pauli Equation
146(2)
3.2.4 Example: Linear Coupling to the Bath
148(3)
3.2.5 Quantum Fokker-Planck Equation
151(3)
3.2.6 Quantum Brownian Motion and the Classical Limit
154(2)
Exercises
156(1)
4 Kinetic Theory
157(60)
4.1 The Boltzmann Equation
158(28)
4.1.1 Distribution Function
159(4)
4.1.2 Classical Reduced Distribution Functions
163(3)
4.1.3 Quantum Statistical Reduced Distribution Functions
166(3)
4.1.4 The Stoßzahlansatz
169(4)
4.1.5 Derivation of the Boltzmann Equation from the Nonequilibrium Statistical Operator
173(7)
4.1.6 Properties of the Boltzmann Equation
180(1)
4.1.7 Example: Hard Spheres
181(2)
4.1.8 Beyond the Boltzmann Kinetic Equation
183(3)
4.2 Solutions of the Boltzmann Equation
186(13)
4.2.1 The Linearized Boltzmann Equation
187(2)
4.2.2 Relaxation Time Method
189(5)
4.2.3 The Kohler Variational Principle
194(2)
4.2.4 Example: Thermal Conductivity in Gases
196(3)
4.3 The Vlasov-Landau Equation and Hydrodynamic Equations
199(18)
4.3.1 Derivation of the Vlasov Equation
199(2)
4.3.2 The Landau Collision Term
201(2)
4.3.3 Example for the Vlasov Equation: The RPA Dielectric Function
203(3)
4.3.4 Equations of Hydrodynamics
206(7)
4.3.5 General Remarks to Kinetic Equations
213(1)
Exercises
214(3)
5 Linear Response Theory
217(44)
5.1 Linear Response Theory and Generalized Fluctuation-Dissipation Theorem (FDT)
218(17)
5.1.1 External Fields and Relevant Statistical Operator
219(3)
5.1.2 Nonequilibrium Statistical Operator for Linear Response Theory
222(3)
5.1.3 Response Equations and Elimination of Lagrange Multipliers
225(1)
5.1.4 Example: Ziman Formula for the Conductivity and Force-Force Correlation Function
226(4)
5.1.5 The Choice of Relevant Observables and the Kubo Formula
230(5)
5.2 Generalized Linear Response Approaches
235(26)
5.2.1 Thermal Perturbations
236(3)
5.2.2 Example: Thermoelectric Effects in Plasmas
239(4)
5.2.3 Example: Hopping Conductivity of Localized Electrons
243(3)
5.2.4 Time-Dependent Perturbations
246(3)
5.2.5 Generalized Linear Boltzmann Equation
249(2)
5.2.6 Variational Approach to Transport Coefficients
251(3)
5.2.7 Further Results of Linear Response Theory
254(5)
Exercises
259(2)
6 Quantum Statistical Methods
261(76)
6.1 Perturbation Theory for Many-Particle Systems
262(17)
6.1.1 Equilibrium Statistics of Quantum Gases
262(5)
6.1.2 Three Relations for Elementary Perturbation Expansions
267(7)
6.1.3 Example: Equilibrium Correlation Functions in Hartree-Fock Approximation
274(5)
6.2 Thermodynamic Green's Functions
279(21)
6.2.1 Thermodynamic Green's Functions: Definitions and Properties
280(5)
6.2.2 Green's Function and Spectral Function
285(4)
6.2.3 Example: Thermodynamic Green's Function for the Ideal Fermi Gas
289(2)
6.2.4 Perturbation Theory for Thermodynamic Green's Functions
291(6)
6.2.5 Application of the Diagram Rules: Hartree-Fock Approximation
297(3)
6.3 Partial Summation and Many-Particle Phenomena
300(29)
6.3.1 Mean-Field Approximation and Quasiparticle Concept
301(3)
6.3.2 Dyson Equation and Self-Energy
304(3)
6.3.3 Screening Equation and Polarization Function
307(5)
6.3.4 Lowest Order Approximation for the Polarization Function: RPA
312(2)
6.3.5 Bound States
314(4)
6.3.6 Excursus: Solution to the Two-Particle Schrodinger Equation with a Separable Potential
318(6)
6.3.7 Cluster Decomposition and the Chemical Picture
324(5)
6.4 Path Integrals
329(8)
6.4.1 The Onsager-Machlup Function
329(3)
6.4.2 Dirac Equation in 1 + 1 Dimensions
332(3)
Exercises
335(2)
7 Outlook: Nonequilibrium Evolution and Stochastic Processes
337(34)
7.1 Stochastic Models for Quantum Evolution
338(15)
7.1.1 Measuring Process and Localization
339(3)
7.1.2 The Caldeira-Leggett Model and Quantum Brownian Motion
342(3)
7.1.3 Dynamical Reduction Models
345(2)
7.1.4 Stochastic Quantum Electrodynamics
347(2)
7.1.5 Quantum Dynamics and Quantum Evolution
349(4)
7.2 Examples
353(18)
7.2.1 Scattering Theory
353(2)
7.2.2 Bremsstrahlung Emission
355(4)
7.2.3 Radiation Damping
359(1)
7.2.4 The 1/f (Flicker) Noise
360(2)
7.2.5 The Hydrogen Atom in the Radiation Field
362(3)
7.2.6 Comments on Nonequilibrium Statistical Physics
365(6)
References 371(4)
Index 375
Gerd Ropke 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 Ropke has authored over 400 scientific publications on quantum statistics, nonequilibrium statistical 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.
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