Equilibrium statistical physics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2003
|
| Ausgabe: | 2. ed., reprint. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 520 S. Ill., graph. Darst. |
| ISBN: | 9810216416 9810216424 |
Internformat
MARC
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| 100 | 1 | |a Plischke, Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Equilibrium statistical physics |c Michael Plischke ; Birger Bergersen |
| 250 | |a 2. ed., reprint. | ||
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2003 | |
| 300 | |a XV, 520 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1813660686555807744 |
|---|---|
| adam_text |
Contents
Preface
to the First Edition
xi
Preface to the Second Edition
xv
1
Review of Thermodynamics
1
1.1
State Variables and Equations of State
. 2
1.2
Laws of Thermodynamics
. 3
1.2.1
First law
. 4
1.2.2
Second law
. 5
1.3
Thermodynamic Potentials
. 10
1.4
Gibbs Duhem and Maxwell Relations
. 13
1.5
Response Functions
. 15
1.6
Conditions for Equilibrium and Stability
. 17
1.7
Thermodynamics of Phase Transitions
. 19
1.8
Problems
. 23
2
Statistical Ensembles
29
2.1
Isolated Systems: MicrocanonicalEnsemble
. 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
.
4(j
2.5
Maximum Entropy Principle
. 48
2.6
Thermodynamic Variational Principles
. 51
2.7
Problems
. 53
Contents
Mean Field and Landau Theory 61
3.1
Mean Field Theory of the Ising Model
. 63
3.2
Bragg-Williams Approximation
. 65
3.3
Order Disorder Transition
. 69
3.4
Bethe Approximation
. 74
3.5
Critical Behavior of Mean Field Theories
. 77
3.6
Ising Chain: Exact Solution
. 80
3.7
Landau Theory of Phase Transitions
. 86
3.8
Example of Symmetry Considerations: Maier-Saupe Model
. . 89
3.9
Landau Theory of Tricritical Points
. 96
3.10
Landau-Ginzburg Theory for Fluctuations
. 103
3.11
Multicomponent Order Parameters:
η
-Vector
Model
. 107
3.12
Mean Field Theory of Fluids: Van
der Waals
Approach
. 109
3.13
Problems
.
H5
Dense Gases and Liquids
123
4.1
Virial Expansion
. 125
4.2
Distribution Functions
. 131
4.2.1
Pair correlation function
. 131
4.2.2
BBGKY hierarchy
. 137
4.2.3
Ornstein-Zemike equation
. 138
4.3
Perturbation Theory
. 141
4.4
Inhomogeneous Liquids
. 143
4.4.1
Liquid-vapor interface
. 143
4.4.2
Capillary waves
. 149
4.5
Density-Functional Theory
. 151
4.5.1
Functional differentiation
. 151
4.5.2
Free-energy functionals and correlation functions
. 153
4.5.3
Applications
. 159
4.6
Problems
. 161
Critical Phenomena I
163
5.1
Ising Model in Two Dimensions
. 164
5.1.1
Transfer matrix
. 164
5.1.2
Transformation to an interacting fermion problem
. . . 168
5.1.3
Calculation of eigenvalues
. 171
5.1.4
Thermodynamic functions
. 174
5.1.5
Concluding remarks
. 179
5.2
Series Expansions
. 179
Contents
vii
5.2.1
High-temperature expansions
. 180
5.2.2
Low-temperature expansions
. 186
5.2.3
Analysis of series
. 186
5.3
Scaling
. 191
5.3.1
Thermodynamic considerations
. 191
5.3.2
Scaling hypothesis
. 192
5.3.3
Kadanoff block spins
. 195
5.4
Finite-Size Scaling
. 199
5.5
Universality
. 204
5.6
Kosterlitz-Thouless Transition
. 206
5.7
Problems
. 214
β
Critical Phenomena II: The Renormalization Group
217
6.1
The Ising Chain Revisited
. 218
6.2
Fixed Points
. 222
6.3
Position Space Renormalization:
Cumulant
Method
. 228
6.3.1
First-order approximation
. 232
6.3.2
Second-order approximation
. 234
6.4
Other Position Space RenormalizationGroup Methods
. 237
6.4.1
Finite lattice methods
. 237
6.4.2
Adsorbed monolayers: Ising antiferromagnet
. 238
6.4.3
Monte Carlo renormalization
. 243
6.5
Phenomenological Renormalization Group
. 246
6.6
The
е
-Expansion.
249
6.6.1
The Gaussian model
. 251
6.6.2
The S4 model
. 255
6.6.3
Critical exponents to order
e
. 258
6.6.4
Conclusion
. 264
6.7
Problems
. 265
7
Simulations
271
7.1
Molecular Dynamics
. 272
7.2
Monte Carlo Method
. 277
7.2.1
Markov processes
. 277
7.2.2
Detailed balance and the Metropolis algorithm
. 279
7.2.3
Histogram methods
. 282
7.3
Data Analysis
. 284
7.3.1
Fluctuations
. 284
7.3.2
Error estimates
. 286
yjjj Contents
7.3.3
Extrapolation to the thermodynamic limit
. 287
7.4
The Hopfield Model of Neural Nets
. 290
7.5
Simulated Quenching and Annealing
. 295
7.6
Problems
. 298
8
Polymers and Membranes
301
8.1
Linear Polymers
. 302
8.1.1
The freely jointed chain
. 304
8.1.2
The Gaussian chain
. 307
8.2
Excluded Volume Effects:
Flory
Theory
. 309
8.3
Polymers and the n-Vector Model
. 313
8.4
Dense Polymer Solutions
. 317
8.5
Membranes
. 323
8.5.1
Phantom membranes
. 324
8.5.2
Self-avoiding membranes
. 327
8.5.3
Liquid membranes
. 332
8.6
Problems
. 336
9
Quantum Fluids
339
9.1
Bose
Condensation
. 339
9.2
Superfluidity
. 347
9.2.1
Qualitative features of superfluidity
. 347
9.2.2
Bogoliubov theory of the 4He excitation spectrum
. . . 356
9.3
Superconductivity
. 359
9.3.1
Cooper problem
. 360
9.3.2
BCS ground state
. 361
9.3.3
Finite-temperature BCS theory
. 365
9.3.4
Landau-Ginzburg theory of superconductivity
. 369
9.4
Problems
. 373
10
Linear Response Theory
377
10.1
Exact Results
. 378
10.1.1
Generalized susceptibility and the structure factor
. . . 378
10.1.2
Thermodynamic properties
. 385
10.1.3
Sum rules and inequalities
. 386
10.2
Mean Field Response
. 388
10.2.1
Dielectric function of the electron gas
. 389
10.2.2
Weakly interacting
Bose
gas
.391
10.2.3
Excitations of the
Heisenberg ferromagnet.393
Contents ix
10.2.4
Screening and plasmons
. 396
10.2.5
Exchange and correlation energy
. 402
10.2.6
Phonons in metals
. 404
10.3
Entropy Production, the
Kubo
Formula, and the Onsager Rela¬
tions for Transport Coefficients
. 406
10.3.1
Kubo
formula
. 406
10.3.2
Entropy production and generalized currents and forces
408
10.3.3
Microscopic reversibility: Onsager relations
. 410
10.4
The Boltzmann Equation
. 414
10.4.1
Fields, drift and collisions
. 414
10.4.2
DC conductivity of a metal
. 417
10.4.3
Thermal conductivity and thermoelectric effects
. 419
10.5
Problems
. 423
11
Disordered Systems
429
11.1
Single-Particle States in Disordered Systems
. 431
11.1.1
Electron states in one dimension
. 432
11.1.2
Transfer matrix
. 433
11.1.3
Localization in three dimensions
. 439
11.1.4
Density of states
. 441
11.2
Percolation
. 446
11.2.1
Scaling theory of percolation
. 448
11.2.2
Series expansions and renormalization group
. 451
11.2.3
Conclusion
. 453
11.3
Phase Transitions in Disordered Materials
. 454
11.3.1
Statistical formalism and the replica trick
. 455
11.3.2
Nature of phase transitions
. 458
11.4
Strongly Disordered Systems
. 463
11.4.1
Molecular glasses
. 463
11.4.2
Spin glasses
. 465
11.4.3
Sherrington-Kirkpatrick model
. 470
11.5
Problems
. 476
Appendix: Occupation Number Representation
481
Bibliography
495
Index |
| any_adam_object | 1 |
| author | Plischke, Michael Bergersen, Birger 1891-1977 |
| author_GND | (DE-588)1059369338 |
| author_facet | Plischke, Michael Bergersen, Birger 1891-1977 |
| author_role | aut aut |
| author_sort | Plischke, Michael |
| author_variant | m p mp b b bb |
| building | Verbundindex |
| bvnumber | BV035321481 |
| classification_rvk | UG 3100 |
| classification_tum | PHY 057f |
| ctrlnum | (OCoLC)635166379 (DE-599)BVBBV035321481 |
| discipline | Physik |
| edition | 2. ed., reprint. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV035321481 |
| illustrated | Illustrated |
| indexdate | 2024-10-23T00:00:14Z |
| institution | BVB |
| isbn | 9810216416 9810216424 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017126053 |
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| physical | XV, 520 S. Ill., graph. Darst. |
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| publisher | World Scientific |
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| spelling | Plischke, Michael Verfasser aut Equilibrium statistical physics Michael Plischke ; Birger Bergersen 2. ed., reprint. Singapore [u.a.] World Scientific 2003 XV, 520 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier 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 1\p (DE-588)4123623-3 Lehrbuch gnd-content Statistische Thermodynamik (DE-588)4126251-7 s DE-604 Kritisches Phänomen (DE-588)4165788-3 s Statistische Mechanik (DE-588)4056999-8 s Statistische Physik (DE-588)4057000-9 s 2\p DE-604 Gleichgewichtstheorie (DE-588)4071876-1 s 3\p DE-604 Bergersen, Birger 1891-1977 Verfasser (DE-588)1059369338 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017126053&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 Bergersen, Birger 1891-1977 Equilibrium statistical physics 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 | 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 | 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=017126053&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT plischkemichael equilibriumstatisticalphysics AT bergersenbirger equilibriumstatisticalphysics |