Equilibrium statistical physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2007
|
| Edition: | 3. ed., reprint. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 620 S. graph. Darst. |
| ISBN: | 9812561552 9812560483 |
Staff View
MARC
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| 245 | 1 | 0 | |a Equilibrium statistical physics |c Michael Plischke, Birger Bergersen |
| 250 | |a 3. ed., reprint. | ||
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2007 | |
| 300 | |a XVI, 620 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1813660686120648704 |
|---|---|
| adam_text |
Contents
Preface
to the First Edition
xi
Preface to the Second Edition
xiv
Preface to the Third Edition
xv
1
Review of Thermodynamics
1
1.1
State Variables and Equations of State
. 1
1.2
Laws of Thermodynamics
. 3
1.2.1
First law
. 3
1.2.2
Second law
. 5
1.3
Thermodynamic Potentials
. 9
1.4
Gibbs-Duhem and Maxwell Relations
. 12
1.5
Response Functions
. 14
1.6
Conditions for Equilibrium and Stability
. 16
1.7
Magnetic Work
. 18
1.8
Thermodynamics of Phase Transitions
. 20
1.9
Problems
. 24
2
Statistical Ensembles
29
2.1
Isolated Systems: Microcanonical Ensemble
. 30
2.2
Systems at Fixed Temperature: Canonical Ensemble
. 35
2.3
Grand Canonical Ensemble
. 40
2.4
Quantum Statistics
. 43
2.4.1
Harmonic oscillator
. 44
2.4.2
Noninteracting
fermions
. 44
2.4.3
Noninteracting bosons
. 45
2.4.4
Density matrix
. 46
vi
Contents
2.5
Maximum
Entropy Principle
. 48
2.6
Thermodynamic Variational Principles
. 53
2.6.1
Schottky defects in a crystal
. 53
2.7
Problems
. 54
3
Mean Field and Landau Theory
63
3.1
Mean Field Theory of the Ising Model
. 64
3.2
Bragg-Williams Approximation
. 67
3.3
A Word of Warning
. 69
3.4
Bethe Approximation
. 71
3.5
Critical Behavior of Mean Field Theories
. 74
3.6
Ising Chain: Exact Solution
. 77
3.7
Landau Theory of Phase Transitions
. 83
3.8
Symmetry Considerations
. 86
3.8.1
Potts model
. 87
3.9
Landau Theory of Tricritical Points
. 90
3.10
Landau-Ginzburg Theory for Fluctuations
. 94
ЗЛІ
Multicomponent Order Parameters: n-Vector Model
. 98
3.12
Problems
. 100
4
Applications of Mean Field Theory
109
4.1
Order-Disorder Transition
. 110
4.2
Maier-Saupe Model
. 114
4.3
Blume-Emery-Griffiths Model
. 120
4.4
Mean Field Theory of Fluids: van
der Waals
Approach
. 123
4.5
Spruce Budworm Model
. 129
4.6
A Non-Equilibrium System: Two Species Asymmetric Exclusion
Model
. 132
4.7
Problems
. 137
5
Dense Gases and Liquids
143
5.1
Virial Expansion
. 145
5.2
Distribution Functions
. 151
5.2.1
Pair correlation function
. 151
5.2.2
BBGKY hierarchy
. 157
5.2.3
Ornstein-Zernike equation
. 158
5.3
Perturbation Theory
. 161
5.4
inhomogeneous Liquids
. 163
5.4.1
Liquid-vapor interface
. 164
Contents
vii
5.4.2
Capillary waves
. 169
5.5
Density-Functional Theory
. 171
5.5.1
Functional differentiation
. 171
5.5.2
Free-energy functionals and correlation functions
. 174
5.5.3
Applications
. 179
5.6
Problems
. 181
6
Critical Phenomena I
183
6.1
Ising Model in Two Dimensions
. 184
6.1.1
Transfer matrix
. 184
6.1.2
Transformation to an interacting fermion problem
. . . 188
6.1.3
Calculation of eigenvalues
. 191
6.1.4
Thermodynamic functions
. 194
6.1.5
Concluding remarks
. 199
6.2
Series Expansions
. 199
6.2.1
High-temperature expansions
. 200
6.2.2
Low-temperature expansions
. 206
6.2.3
Analysis of series
. 206
6.3
Scaling
. 211
6.3.1
Thermodynamic considerations
. 211
6.3.2
Scaling hypothesis
. 212
6.3.3
Kadanoff block spins
. 215
6.4
Finite-Size Scaling
. 218
6.5
Universality
. 223
6.6
Kosterlitz-Thouless Transition
. 226
6.7
Problems
. 233
7
Critical Phenomena II: The Renormalization Group
237
7.1
The Ising Chain Revisited
. 238
7.2
Fixed Points
. 242
7.3
An Exactly Solvable Model: Ising Spins on a Diamond Fractal
248
7.4
Position Space Renormali2ation:
Cumulant
Method
. 258
7.4.1
First-order approximation
. 262
7.4.2
Second-order approximation
. 264
7.5
Other Position Space Renormalization
Group Methods
. 267
7.5.1
Finite lattice methods
. 267
7.5.2
Adsorbed monolayers: king antiferromagnet
. 268
7.5.3
Monte Carlo renormalization
. 272
viii
Contents
7.6
Phenomenological
Renormałization
Group
. 275
7.7
The
є
-Expansion
. 279
7.7.1
The Gaussian model
. 281
7.7.2
The S4 model
. 284
7.7.3
Conclusion
. 290
Appendix: Second Order
Cumulant
Expansion
. 292
7.8
Problems
. 295
8
Stochastic Processes
303
8.1
Markov Processes and the Master Equation
. 304
8.2
Birth and Death Processes
. 306
8.3
Branching Processes
. 309
8.4
Fokker-Planck Equation
. 313
8.5
Fokker-Planck Equation with Several Variables: SIR Model
. . 316
8.6
Jump Moments for Continuous Variables
. 321
8.6.1
Brownian motion
. 323
8.6.2
Rayleigh and Kramers equations
. 326
8.7
Diffusion, First Passage and Escape
. 328
8.7.1
Natural boundaries: The Kimura-Weiss model for
genetic drift
. 329
8.7.2
Artificial boundaries
. 331
8.7.3
First passage time and escape probability
. 332
8.7.4
Kramers escape rate
. 337
8.8
Transformations of the Fokker-Planck Equation
. 340
8.8.1
Heterogeneous diffusion
. 340
8.8.2
Transformation to the
Schrödinger
equation
. 343
8.9
Problems
. 345
9
Simulations
349
9.1
Molecular Dynamics
. 350
9.1.1
Conservative molecular dynamics
. 351
9.1.2
Brownian dynamics
. 353
9.1.3
Data analysis
. 355
9.2
Monte Carlo Method
. 357
9.2.1
Discrete time Markov processes
. 358
9.2.2
Detailed balance and the Metropolis algorithm
. 359
9.2.3
Histogram methods
. 363
9.3
Data Analysis
. 365
9.3.1
Fluctuations
. 365
Contents ix
9.3.2
Error estimates
. 367
9.3.3
Extrapolation to the thermodynamic limit
. 368
9.4
The Hopfield Model of Neural Nets
. 371
9.5
Simulated Quenching and Annealing
. 376
9.6
Problems
. 379
10
Polymers and Membranes
383
10.1
Linear Polymers
. 384
10.1.1
The freely jointed chain
. 386
10.1.2
The Gaussian chain
. 389
10.2
Excluded Volume Effects:
Flory
Theory
. 391
10.3
Polymers and the n-Vector Model
. 395
10.4
Dense Polymer Solutions
. 400
10.5
Membranes
. 405
10.5.1
Phantom membranes
. 406
10.5.2
Self-avoiding membranes
. 409
10.5.3
Liquid membranes
. 415
10.6
Problems
. 418
11
Quantum Fluids
421
11.1
Bose
Condensation
. 422
11.2
Superfluidity
. 430
11.2.1
Qualitative features of superfluidity
. 430
11.2.2
Bogoliubov theory of the 4He excitation spectrum
. . . 439
11.3
Superconductivity
. 442
11.3.1
Cooper problem
. 443
11.3.2
BCS ground state
. 445
11.3.3
Finite-temperature BCS theory
. 449
11.3.4
Landau-Ginzburg theory of superconductivity
. 453
11.4
Problems
. 456
12
Linear Response Theory
461
12.1
Exact Results
. 462
12.1.1
Generalized susceptibility and the structure factor
. . . 462
12.1.2
Thermodynamic properties
. 469
12.1.3
Sum rules and inequalities
. 470
12.2
Mean Field Response
. 472
12.2.1
Dielectric function of the electron gas
. 473
12.2.2
Weakly interacting
Bose
gas
. 475
x
Contents
12.2.3
Excitations
of the
Heisenberg ferromagnet. 477
12.2.4
Screening and plasmons
. 480
12.2.5
Exchange and correlation energy
. 486
12.2.6
Phonons in metals
. 487
12.3
Entropy Production, the
Kubo
Formula, and the Onsager Rela¬
tions for Transport Coefficients
. 490
12.3.1
Kubo
formula
. 490
12.3.2
Entropy production and generalized currents and forces
492
12.3.3
Microscopic reversibility: Onsager relations
. 494
12.4
The Boltzmann Equation
. 498
12.4.1
Fields, drift and collisions
. 498
12.4.2
DC conductivity of a metal
. 500
12.4.3
Thermal conductivity and thermoelectric effects
. 503
12.5
Problems
. 507
13
Disordered Systems
513
13.1
Single-Particle States in Disordered Systems
. 515
13.1.1
Electron states in one dimension
. 516
13.1.2
Transfer matrix
. 517
13.1.3
Localization in three dimensions
. 523
13.1.4
Density of states
. 525
13.2
Percolation
. 530
13.2.1
Scaling theory of percolation
. 533
13.2.2
Series expansions and renormalization group
. 536
13.2.3
Rigidity percolation
. 540
13.2.4
Conclusion
. 542
13.3
Phase Transitions in Disordered Materials
. 542
13.3.1
Statistical formalism and the replica trick
. 544
13.3.2
Nature of phase transitions
. 546
13.4
Strongly Disordered Systems
. 551
13.4.1
Molecular glasses
. 552
13.4.2
Spin glasses
. 554
13.4.3
Sherrington-Kirkpatrick model
. 558
13.5
Problems
. 565
A Occupation Number Representation
569
Bibliography
583
Index
603 |
| any_adam_object | 1 |
| author | Plischke, Michael |
| author_GND | (DE-588)1059369338 |
| author_facet | Plischke, Michael |
| author_role | aut |
| author_sort | Plischke, Michael |
| author_variant | m p mp |
| building | Verbundindex |
| bvnumber | BV036965363 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.8 |
| callnumber-search | QC174.8 |
| callnumber-sort | QC 3174.8 |
| callnumber-subject | QC - Physics |
| classification_rvk | UG 3100 |
| classification_tum | PHY 050f |
| ctrlnum | (OCoLC)254851772 (DE-599)BVBBV036965363 |
| dewey-full | 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 3. ed., reprint. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV036965363 |
| illustrated | Illustrated |
| indexdate | 2024-10-23T00:00:14Z |
| institution | BVB |
| isbn | 9812561552 9812560483 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020880175 |
| oclc_num | 254851772 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XVI, 620 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Plischke, Michael Verfasser aut Equilibrium statistical physics Michael Plischke, Birger Bergersen 3. ed., reprint. Singapore [u.a.] World Scientific 2007 XVI, 620 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier aStatistical physics vTextbooks aCritical phenomena (Physics) vTextbooks Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Kritisches Phänomen (DE-588)4165788-3 gnd rswk-swf Statistische Thermodynamik (DE-588)4126251-7 gnd rswk-swf Gleichgewichtstheorie (DE-588)4071876-1 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistische Physik (DE-588)4057000-9 s DE-604 Kritisches Phänomen (DE-588)4165788-3 s Statistische Mechanik (DE-588)4056999-8 s 1\p DE-604 Statistische Thermodynamik (DE-588)4126251-7 s 2\p DE-604 Gleichgewichtstheorie (DE-588)4071876-1 s 3\p DE-604 Bergersen, Birger 1891-1977 Sonstige (DE-588)1059369338 oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020880175&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Plischke, Michael Equilibrium statistical physics aStatistical physics vTextbooks aCritical phenomena (Physics) vTextbooks Statistische Mechanik (DE-588)4056999-8 gnd Kritisches Phänomen (DE-588)4165788-3 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd Gleichgewichtstheorie (DE-588)4071876-1 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4056999-8 (DE-588)4165788-3 (DE-588)4126251-7 (DE-588)4071876-1 (DE-588)4057000-9 (DE-588)4123623-3 |
| title | Equilibrium statistical physics |
| title_auth | Equilibrium statistical physics |
| title_exact_search | Equilibrium statistical physics |
| title_full | Equilibrium statistical physics Michael Plischke, Birger Bergersen |
| title_fullStr | Equilibrium statistical physics Michael Plischke, Birger Bergersen |
| title_full_unstemmed | Equilibrium statistical physics Michael Plischke, Birger Bergersen |
| title_short | Equilibrium statistical physics |
| title_sort | equilibrium statistical physics |
| topic | aStatistical physics vTextbooks aCritical phenomena (Physics) vTextbooks Statistische Mechanik (DE-588)4056999-8 gnd Kritisches Phänomen (DE-588)4165788-3 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd Gleichgewichtstheorie (DE-588)4071876-1 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | aStatistical physics vTextbooks aCritical phenomena (Physics) vTextbooks Statistische Mechanik Kritisches Phänomen Statistische Thermodynamik Gleichgewichtstheorie Statistische Physik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020880175&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT plischkemichael equilibriumstatisticalphysics AT bergersenbirger equilibriumstatisticalphysics |