Nonequilibrium statistical mechanics:
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| Format: | Buch |
| Sprache: | English |
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2006
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| Beschreibung: | XIII , 478 S. Ill., graph. Darst. |
| ISBN: | 3527406484 9783527406487 |
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| 100 | 1 | |a Mazenko, Gene F. |e Verfasser |0 (DE-588)132171201 |4 aut | |
| 245 | 1 | 0 | |a Nonequilibrium statistical mechanics |c Gene F. Mazenko |
| 264 | 1 | |a Weinheim |b WILEY-VCH |c 2006 | |
| 300 | |a XIII , 478 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Nonequilibrium statistical mechanics | |
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| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
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Datensatz im Suchindex
| _version_ | 1804135468283985920 |
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| adam_text | Contents
1 Systems
Out of Equilibrium
1
1.1 Problems
of Interest I
1.2
Brownian Motion
6
1.2.1
Fluctuations in Equilibrium
6
1.2.2
Response to Applied Forces
13
1.3
References and Notes
15
1.4
Problems
f
or Chapter
1
Î6
2
Time-Dependent Phenomena in Condensed-Matter Systems
19
2.1
Linear Response Theory
19
2.1.1
General Comments
29
2.1.2
Linear Response Formalism
19
2.1.3
Time-Translational
Invariance
27
2.1.4
Vector Operators
29
2.1.5
Example: The Electrical Conductivity
29
2.1.6
Example: Magnetic Resonance
32
2.1.7
Example: Relaxation From Constrained Equilibrium
37
2.1.8
Field Operators
40
2.1.9
Identification of Couplings
41
2.2
Scattering Experiments
42
2.2.1
Inelastic Neutron Scattering from a Fluid
42
2.2.2
Electron Scattering
49
2.2.3
Neutron Scattering: A More Careful Analysis
50
2.2.4
Magnetic Neutron Scattering
52
2.2.5
Х
-Ray and Light Scattering
55
2.2.6
Summary of Scattering Experiments
57
2.3
References and Notes
58
2.4
Problems for Chapter
2 59
VI
Contents
3
General Properties of Time-Correlation Functions
63
3.1
Fluctuation-Dissipation Theorem
63
3.2
Symmetry Properties of Correlation Functions
67
3.3
Analytic Properties of Response Functions
70
3.4
Symmetries of the Complex Response Function
73
3.5
The Harmonic Oscillator
75
3.6
The Relaxation Function
77
3.7
Summary of Correlation Functions
81
3.8
The Classical Limit
82
3.9
Example: The Electrical Conductivity
83
3.10
Nyquist Theorem
85
3.11
Dissipation
87
3.12
Static Susceptibility (Again)
89
3.13
Sum Rules
91
3.14
References and Notes
96
3.15
Problems for Chapter
3 96
4
Charged Transport
101
4.1
Introduction
101
4.2
The Equilibrium Situation
101
4.3
The Nonequilibrium Case
104
4.3.1
Setting up the Problem
104
4.3.2
Linear Response
106
4.4
The Macroscopic Maxwell Equations
123
4.5
The
Drude
Model
126
4.5.1
Basis for Model
116
4.5.2
Conductivity and Dielectric Function
118
4.5.3
The Current Correlation Function
119
4.6
References and Notes
120
4.7
Problems for Chapter
4 221
5
Linearized
Langevin
and Hydrodynamical Description of
Time-Correlation Functions
123
5.1
Introduction
223
5.2
Spin Diffusion in Itinerant Paramagnets
224
5.2.1
Continuity Equation
224
5.2.2
Constitutive Relation
226
5.2.3
Hydrodynamic Form for Correlation Functions
128
5.2.4
Green-Kubo Formula
230
5.3
Langevin
Equation Approach to the Theory of Irreversible
Processes
234
5.3.1
Choice of Variables
234
Contents
VII
5.3.2
Equations
of
Motion
134
5.3.3
Example:
Heisenberg Ferromagnet 136
5.3.4
Example: Classical Fluid
138
5.3.5
Summary
242
5.3.6
Generalized
Langevin
Equation
142
5.3.7
Memory-Function Formalism
244
5.3.8
Memory-Function Formalism: Summary
247
5.3.9
Second Fluctuation-Dissipation Theorem
247
5.4
Example: The Harmonic Oscillator
149
5.5
Theorem Satisfied by the Static Part of the Memory Function
254
5.6
Separation of Time Scales: The Markoff Approximation
255
5.7
Example: Brownian Motion
256
5.8
The Plateau-Value Problem 25S
5.9
Example: Hydrodynamic Behavior; Spin-Diffusion Revisited
262
5.10
Estimating the Spin-Diffusion Coefficient
265
5.11
References and Notes
270
5.12
Problems for Chapter
5 272
6
Hydrodynamic Spectrum of
Normat
Fluids
175
6.1
Introduction
275
6.2
Selection of Slow Variables
275
6.3
Static Structure Factor
277
6.4
Static Part of the Memory Function
182
6.5
Spectrum of Fluctuations with No Damping
188
6.6
Dynamic Part of the Memory Function
292
6.7
Transverse Modes
292
6.8
Longitudinal Modes
294
6.9
Fluctuation Spectrum Including Damping
296
6.10
References and Notes
202
6.11
Problems for Chapter
6 203
7
Kinetic Theory
205
7.1
Introduction
205
7.2
Boltzmann Equation
206
7.2.1
Ideal Gas Law
206
7.2.2
Mean-Free Path
220
7.2.3
Boltzmann Equation: Kinematics
223
7.2.4
Boltzmann Collision Integral
225
7.2.5
Collisional Invariants
229
7.2.6
Approach to Equilibrium
222
7.2.7
Linearized Boltzmann Collision Integral
223
7.2.8
Kinetic Models
225
VIII Contents
7.2.9
Single-Relaxation-Time Approximation
228
7.2.10
Steady-State Solutions
231
7.3
Traditional Transport Theory
233
7.3.1
Steady-State Currents
233
7.3.2
Thermal Gradients
237
7.3.3
Shear Viscosity
241
7.3.4
Hall Effect
244
7.4
Modern Kinetic Theory
246
7.4.1
Collisionless Theory
250
7.4.2
Noninteracting Gas
252
7.4.3
Vlasov
Approximation
253
7.4.4
Dynamic Part of Memory Function
256
7.4.5
Approximations
257
7.4.6
Transport Coefficients
260
7.5
References and Notes
265
7.6
Problems for Chapter
7 266
8
Critical Phenomena and Broken Symmetry
271
8.1
Dynamic Critical Phenomena
271
8.1.1
Order Parameter as a Slow Variable
271
8.1.2
Examples of Order Parameters
273
8.1.3
Critical Indices and Universality
277
8.1.4
The Scaling Hypothesis
277
8.1.5
Conventional Approximation
279
8.2
More on Slow Variables
283
8.3
Spontaneous Symmetry Breaking and Nambu-Goldstone
Modes
285
8.4
The
Isotropie Ferromagnet 286
8.5 Isotropie Antiferromagnet 290
8.6
Summary
295
8.7
References and Notes
295
8.8
Problems for Chapter
8 296
9
Nonlinear Systems
299
9.1
Historical Background
299
9.2
Motivation
301
9.3
Coarse-Grained Variables and Effective Hamiltonians
302
9.4
Nonlinear Coarse-Grained Equations of Motion
306
9
A.I Generalization of
Langevin
Equation
306
9.4.2
Streaming Velocity
307
9.4.3
Damping Matrix
320
9.4.4
Generalized Fokker-Planck Equation
311
Contents
IX
9.4.5
Nonlinear
Langevin
Equation
322
9.5
Discussion of the Noise
314
9.5.1
General Discussion
314
9.5.2
Gaussian Noise
324
9.5.3
Second Fluctuation-Dissipation Theorem
325
9.6
Summary
326
9.7
Examples of Nonlinear Models
327
9.7.1
TDGL Models
327
9.7.2 Isotropie
Magnets
320
9.7.3
Fluids
322
9.8
Determination of Correlation Functions
326
9.8.1
Formal Arrangements
326
9.8.2
Linearized Theory
329
9.8.3
Mode-Coupling Approximation
329
9.8.4
Long-Time Tails in Fluids
330
9.9
Mode Coupling and the Glass Transition
335
9.10
Mode Coupling and Dynamic Critical Phenomena
336
9.11
References and Notes
336
9.12
Problems for Chapter
9 338
10
Perturbation Theory and the Dynamic Renormalization Group
343
10.1
Perturbation Theory
343
10.1.1
TDGL Model
343
10.1.2
Zeroth-Order Theory
344
10.1.3
Bare Perturbation Theory
345
10.1.4
Fluctuation-Dissipation Theorem
349
10.1.5
Static Limit
352
10.1.6
Temperature Renormalization
356
10.1.7
Self-Consistent
Hartree
Approximation
360
10.1.8
Dynamic Renormalization
362
10.2
Perturbation Theory for the
Isotropie Ferromagnet 369
10.2.1
Equation of Motion
369
10.2.2
Graphical Expansion
370
10.2.3
Second Order in Perturbation Theory
374
10.3
The Dynamic Renormalization Group
379
10.3.1
Group Structure
379
10.3.2
TDGL Case
380
10.3.3
Scaling Results
388
10.3.4
Wilson Matching
390
10.3.5 Isotropie
Ferromagnet
392
10.4
Final Remarks
399
10.5
References and Notes
399
X I Contents
10.6
Problems for Chapter
10 400
11
Unstable Growth
403
11.1
Introduction
403
11.2
Langevin
Equation Description
407
11.3
Off-Critical Quenches
411
11.4
Nucleation
413
11.5
Observables
of Interest in Phase-Ordering Systems
416
11.6
Consequences of Sharp Interfaces
428
11.7
Interfacial
motion
420
11.8
Scaling
423
11.9
Theoretical Developments
425
11.9.1
Linear Theory
425
11.9.2
Mean-Field Theory
426
11.9.3
Auxiliary Field Methods
428
11.9
A Auxiliary Field Dynamics
432
11.9.5
The Order Parameter Correlation Function
435
11.9.6
Extension to w-Vector Model
437
11.10
Defect Dynamics
439
11.11
Pattern Forming Systems
445
11.12
References and Notes
446
11.13
Problems for Chapter
11 450
Appendices
A Time-Reversal Symmetry
455
В
Fluid
Poisson
Bracket Relations
461
С
Equilibrium Average of the Phase-Space Density
463
D
Magnetic
Poisson
Bracket Relations
465
E
Noise and the Nonlinear
Langevin
Equation
467
Index
471
|
| adam_txt |
Contents
1 Systems
Out of Equilibrium
1
1.1 Problems
of Interest I
1.2
Brownian Motion
6
1.2.1
Fluctuations in Equilibrium
6
1.2.2
Response to Applied Forces
13
1.3
References and Notes
15
1.4
Problems
f
or Chapter
1
Î6
2
Time-Dependent Phenomena in Condensed-Matter Systems
19
2.1
Linear Response Theory
19
2.1.1
General Comments
29
2.1.2
Linear Response Formalism
19
2.1.3
Time-Translational
Invariance
27
2.1.4
Vector Operators
29
2.1.5
Example: The Electrical Conductivity
29
2.1.6
Example: Magnetic Resonance
32
2.1.7
Example: Relaxation From Constrained Equilibrium
37
2.1.8
Field Operators
40
2.1.9
Identification of Couplings
41
2.2
Scattering Experiments
42
2.2.1
Inelastic Neutron Scattering from a Fluid
42
2.2.2
Electron Scattering
49
2.2.3
Neutron Scattering: A More Careful Analysis
50
2.2.4
Magnetic Neutron Scattering
52
2.2.5
Х
-Ray and Light Scattering
55
2.2.6
Summary of Scattering Experiments
57
2.3
References and Notes
58
2.4
Problems for Chapter
2 59
VI
Contents
3
General Properties of Time-Correlation Functions
63
3.1
Fluctuation-Dissipation Theorem
63
3.2
Symmetry Properties of Correlation Functions
67
3.3
Analytic Properties of Response Functions
70
3.4
Symmetries of the Complex Response Function
73
3.5
The Harmonic Oscillator
75
3.6
The Relaxation Function
77
3.7
Summary of Correlation Functions
81
3.8
The Classical Limit
82
3.9
Example: The Electrical Conductivity
83
3.10
Nyquist Theorem
85
3.11
Dissipation
87
3.12
Static Susceptibility (Again)
89
3.13
Sum Rules
91
3.14
References and Notes
96
3.15
Problems for Chapter
3 96
4
Charged Transport
101
4.1
Introduction
101
4.2
The Equilibrium Situation
101
4.3
The Nonequilibrium Case
104
4.3.1
Setting up the Problem
104
4.3.2
Linear Response
106
4.4
The Macroscopic Maxwell Equations
123
4.5
The
Drude
Model
126
4.5.1
Basis for Model
116
4.5.2
Conductivity and Dielectric Function
118
4.5.3
The Current Correlation Function
119
4.6
References and Notes
120
4.7
Problems for Chapter
4 221
5
Linearized
Langevin
and Hydrodynamical Description of
Time-Correlation Functions
123
5.1
Introduction
223
5.2
Spin Diffusion in Itinerant Paramagnets
224
5.2.1
Continuity Equation
224
5.2.2
Constitutive Relation
226
5.2.3
Hydrodynamic Form for Correlation Functions
128
5.2.4
Green-Kubo Formula
230
5.3
Langevin
Equation Approach to the Theory of Irreversible
Processes
234
5.3.1
Choice of Variables
234
Contents
VII
5.3.2
Equations
of
Motion
134
5.3.3
Example:
Heisenberg Ferromagnet 136
5.3.4
Example: Classical Fluid
138
5.3.5
Summary
242
5.3.6
Generalized
Langevin
Equation
142
5.3.7
Memory-Function Formalism
244
5.3.8
Memory-Function Formalism: Summary
247
5.3.9
Second Fluctuation-Dissipation Theorem
247
5.4
Example: The Harmonic Oscillator
149
5.5
Theorem Satisfied by the Static Part of the Memory Function
254
5.6
Separation of Time Scales: The Markoff Approximation
255
5.7
Example: Brownian Motion
256
5.8
The Plateau-Value Problem 25S
5.9
Example: Hydrodynamic Behavior; Spin-Diffusion Revisited
262
5.10
Estimating the Spin-Diffusion Coefficient
265
5.11
References and Notes
270
5.12
Problems for Chapter
5 272
6
Hydrodynamic Spectrum of
Normat
Fluids
175
6.1
Introduction
275
6.2
Selection of Slow Variables
275
6.3
Static Structure Factor
277
6.4
Static Part of the Memory Function
182
6.5
Spectrum of Fluctuations with No Damping
188
6.6
Dynamic Part of the Memory Function
292
6.7
Transverse Modes
292
6.8
Longitudinal Modes
294
6.9
Fluctuation Spectrum Including Damping
296
6.10
References and Notes
202
6.11
Problems for Chapter
6 203
7
Kinetic Theory
205
7.1
Introduction
205
7.2
Boltzmann Equation
206
7.2.1
Ideal Gas Law
206
7.2.2
Mean-Free Path
220
7.2.3
Boltzmann Equation: Kinematics
223
7.2.4
Boltzmann Collision Integral
225
7.2.5
Collisional Invariants
229
7.2.6
Approach to Equilibrium
222
7.2.7
Linearized Boltzmann Collision Integral
223
7.2.8
Kinetic Models
225
VIII Contents
7.2.9
Single-Relaxation-Time Approximation
228
7.2.10
Steady-State Solutions
231
7.3
Traditional Transport Theory
233
7.3.1
Steady-State Currents
233
7.3.2
Thermal Gradients
237
7.3.3
Shear Viscosity
241
7.3.4
Hall Effect
244
7.4
Modern Kinetic Theory
246
7.4.1
Collisionless Theory
250
7.4.2
Noninteracting Gas
252
7.4.3
Vlasov
Approximation
253
7.4.4
Dynamic Part of Memory Function
256
7.4.5
Approximations
257
7.4.6
Transport Coefficients
260
7.5
References and Notes
265
7.6
Problems for Chapter
7 266
8
Critical Phenomena and Broken Symmetry
271
8.1
Dynamic Critical Phenomena
271
8.1.1
Order Parameter as a Slow Variable
271
8.1.2
Examples of Order Parameters
273
8.1.3
Critical Indices and Universality
277
8.1.4
The Scaling Hypothesis
277
8.1.5
Conventional Approximation
279
8.2
More on Slow Variables
283
8.3
Spontaneous Symmetry Breaking and Nambu-Goldstone
Modes
285
8.4
The
Isotropie Ferromagnet 286
8.5 Isotropie Antiferromagnet 290
8.6
Summary
295
8.7
References and Notes
295
8.8
Problems for Chapter
8 296
9
Nonlinear Systems
299
9.1
Historical Background
299
9.2
Motivation
301
9.3
Coarse-Grained Variables and Effective Hamiltonians
302
9.4
Nonlinear Coarse-Grained Equations of Motion
306
9
A.I Generalization of
Langevin
Equation
306
9.4.2
Streaming Velocity
307
9.4.3
Damping Matrix
320
9.4.4
Generalized Fokker-Planck Equation
311
Contents
IX
9.4.5
Nonlinear
Langevin
Equation
322
9.5
Discussion of the Noise
314
9.5.1
General Discussion
314
9.5.2
Gaussian Noise
324
9.5.3
Second Fluctuation-Dissipation Theorem
325
9.6
Summary
326
9.7
Examples of Nonlinear Models
327
9.7.1
TDGL Models
327
9.7.2 Isotropie
Magnets
320
9.7.3
Fluids
322
9.8
Determination of Correlation Functions
326
9.8.1
Formal Arrangements
326
9.8.2
Linearized Theory
329
9.8.3
Mode-Coupling Approximation
329
9.8.4
Long-Time Tails in Fluids
330
9.9
Mode Coupling and the Glass Transition
335
9.10
Mode Coupling and Dynamic Critical Phenomena
336
9.11
References and Notes
336
9.12
Problems for Chapter
9 338
10
Perturbation Theory and the Dynamic Renormalization Group
343
10.1
Perturbation Theory
343
10.1.1
TDGL Model
343
10.1.2
Zeroth-Order Theory
344
10.1.3
Bare Perturbation Theory
345
10.1.4
Fluctuation-Dissipation Theorem
349
10.1.5
Static Limit
352
10.1.6
Temperature Renormalization
356
10.1.7
Self-Consistent
Hartree
Approximation
360
10.1.8
Dynamic Renormalization
362
10.2
Perturbation Theory for the
Isotropie Ferromagnet 369
10.2.1
Equation of Motion
369
10.2.2
Graphical Expansion
370
10.2.3
Second Order in Perturbation Theory
374
10.3
The Dynamic Renormalization Group
379
10.3.1
Group Structure
379
10.3.2
TDGL Case
380
10.3.3
Scaling Results
388
10.3.4
Wilson Matching
390
10.3.5 Isotropie
Ferromagnet
392
10.4
Final Remarks
399
10.5
References and Notes
399
X I Contents
10.6
Problems for Chapter
10 400
11
Unstable Growth
403
11.1
Introduction
403
11.2
Langevin
Equation Description
407
11.3
Off-Critical Quenches
411
11.4
Nucleation
413
11.5
Observables
of Interest in Phase-Ordering Systems
416
11.6
Consequences of Sharp Interfaces
428
11.7
Interfacial
motion
420
11.8
Scaling
423
11.9
Theoretical Developments
425
11.9.1
Linear Theory
425
11.9.2
Mean-Field Theory
426
11.9.3
Auxiliary Field Methods
428
11.9
A Auxiliary Field Dynamics
432
11.9.5
The Order Parameter Correlation Function
435
11.9.6
Extension to w-Vector Model
437
11.10
Defect Dynamics
439
11.11
Pattern Forming Systems
445
11.12
References and Notes
446
11.13
Problems for Chapter
11 450
Appendices
A Time-Reversal Symmetry
455
В
Fluid
Poisson
Bracket Relations
461
С
Equilibrium Average of the Phase-Space Density
463
D
Magnetic
Poisson
Bracket Relations
465
E
Noise and the Nonlinear
Langevin
Equation
467
Index
471 |
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| author | Mazenko, Gene F. |
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| discipline | Physik |
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| illustrated | Illustrated |
| index_date | 2024-07-02T15:05:11Z |
| indexdate | 2024-07-09T20:40:59Z |
| institution | BVB |
| isbn | 3527406484 9783527406487 |
| language | English |
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| physical | XIII , 478 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
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| publisher | WILEY-VCH |
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| spelling | Mazenko, Gene F. Verfasser (DE-588)132171201 aut Nonequilibrium statistical mechanics Gene F. Mazenko Weinheim WILEY-VCH 2006 XIII , 478 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonequilibrium statistical mechanics Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Nichtgleichgewichtsstatistik (DE-588)4136220-2 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2686585&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014872967&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mazenko, Gene F. Nonequilibrium statistical mechanics Nonequilibrium statistical mechanics Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd |
| subject_GND | (DE-588)4136220-2 (DE-588)4123623-3 |
| title | Nonequilibrium statistical mechanics |
| title_auth | Nonequilibrium statistical mechanics |
| title_exact_search | Nonequilibrium statistical mechanics |
| title_exact_search_txtP | Nonequilibrium statistical mechanics |
| title_full | Nonequilibrium statistical mechanics Gene F. Mazenko |
| title_fullStr | Nonequilibrium statistical mechanics Gene F. Mazenko |
| title_full_unstemmed | Nonequilibrium statistical mechanics Gene F. Mazenko |
| title_short | Nonequilibrium statistical mechanics |
| title_sort | nonequilibrium statistical mechanics |
| topic | Nonequilibrium statistical mechanics Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd |
| topic_facet | Nonequilibrium statistical mechanics Nichtgleichgewichtsstatistik Lehrbuch |
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