Intermediate statistical mechanics:
Saved in:
| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2016]
[New Delhi] Hindustan Book Agency |
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| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverzeichnis: Seiten 405-412 |
| Physical Description: | xiv, 423 Seiten Diagramme |
| ISBN: | 9789813201149 |
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| adam_text | Contents
/1
Preface v
Acknowledgments vii
1 Statistical Mechanics: The Basics X
1.1 Prom Micro to Macro......................................... 1
1.2 Equilibrium Distribution.................................. 8
1.3 Boltzmann’s Hypothesis...................................... 9
1.4 Dynamics, Dynamical Systems and Chaos...................... 12
1.5 The Prevalence of Chaos ................................... 20
1.6 Quantum Dynamics........................................... 23
1.7 Problems for Chapter 1..................................... 26
2 The Microcanonical Ensemble 27
2.1 Examples................................................... 27
2.1.1 The Ideal Gas......................................... 27
2.1.2 An ideal solid......*............................... 29
2.1.3 General oscillators................................... 30
2.1.4 Magnetic moments in an external field................. 32
2.1.5 The quantum solid..................................... 34
2.1.6 The quantum free particle............................. 37
2.2 Additivity of Entropy and Microcanonical Ensemble.......... 38
2.3 Shannon Entropy ........................................... 40
2.4 Problems for Chapter 2................................... 41
3 Other Ensembles 43
3.1 Canonical Ensemble......................................... 43
3.2 Alternative Derivation..................................... 48
3.3 Varying Number of Particles................................ 51
3.4 Grand Canonical Ensemble................................... 53
3.5 Energy Fluctuation in Grand Canonical Ensemble............. 55
3.6 Physical Interpretation of Q . ............................ 57
3.7 Problems for Chapter 3..................................... 58
61
61
62
65
66
66
67
68
68
68
69
73
76
77
77
78
80
81
83
87
91
91
95
100
105
106
110
111
113
116
119
119
120
121
Non-interacting Systems
4.1 Calculational Procedure for Canonical Ensemble .
4.2 Ideal Gas.......................................
4.3 Ideal Gas in Grand Canonical Ensemble...........
4.4 Space-dependent Distribution....................
4.4.1 In a Gravitational Potential...............
4.4.2 In a Centrifuge............................
4.5 Oscillators in Contact with Heat Bath .......
4.5.1 Classical Oscillators......................
4.5.2 Quantum Oscillators........................
4.6 Specific Heat of Solids.........................
4.7 Model for Paramagnetism.........................
4.8 Electronic Energy in a Monoatomic Gas...........
4.9 Diatomic Molecules..............................
4.9.1 Heteronuclear Molecules....................
4.9.2 Homonuclear Molecules......................
4.10 Solid-vapour Equilibrium........................
4.11 Saha Ionization Formula.........................
4.12 Statistical Mechanics of Powders (Edwards’ Model)
4.13 Problems for Chapter 4..........................
Interacting Classical Systems
5.1 The Non-ideal Gas...............................
5.2 Linked Cluster Expansion........................
5.3 Van der Waals Equation of State.................
5.4 Existence of Phase Transitions..................
5.5 Correlation Functions...........................
5.6 Ising Model.....................................
5.6.1 Exact Solution in One Dimension............
5.6.2 Approximate Method for Any Dimensions . .
5.7 Problems for Chapter 5 .........................
Quantum Statistics
6.1 Introduction....................................
6.2 Quantum Distribution Functions..................
6.2.1 Fermions...................................
6.2.2 Bosons.....................................
6.3 Equation of State...............................
6.4 Entropy of the Quantum Ideal Gas................
6.5 Chemical Potential in Two Dimensions............
6.6 Problems for Chapter 6..........................
Contents xi
7 Fermi Distribution: Examples 135
7.1 Degenerate Fermi Gas........................................ 135
7.2 White Dwarfs................................................ 136
7.3 Specific Heat of an Electron Gas......................... 140
7.4 One Dimensional Metal: Effect of Periodic Lattice Structure 143
7.4.1 Energy Levels for a Periodic Potential................ 143
7.4.2 Fermi Level and Density of States................... 146
7.4.3 Specific Heat.......................................... 147
7.4.4 Peierls’ Instability................................... 148
7.5 Emission of Electrons from a Metal Surface.................. 150
7.6 Correlations in a Fermi Gas............................... . 152
7.7 Electrons in Graphene ...................................... 153
7.7.1 The Tight-binding Approximation........................ 154
7.7.2 Application to Graphene................................ 157
7.8 Problems for Chapter 7..................................... 161
8 Electrons in a Magnetic Field 163
8.1 Introduction................................................ 163
8.2 Magnetic Properties at T = 0............................... 165
8.2.1 Intrinsic Magnetic Moment.............................. 166
8.2.2 Orbital Magnetic Moment................................ 168
8.3 Magnetic Properties at T » TF .............................. 170
8.4 De Haas - Van Alphen Effect: T — 0.......................... 171
8.5 Quantum Hall Effect......................................... 172
8.5.1 Integer Hall Effect.................................... 172
8.5.2 Fractional Hall effect................................. 179
9 Bose-Einstein Distribution: Examples 181
9.1 Bose-Einstein Condensation.................................. 181
9.1.1 The Condensation Point................................. 181
9.1.2 Order of the Transition................................ 183
9.1.3 Near the Transition Point.............................. 186
9.1.4 Experimental Observation of the Transition: Bosons in a
Trap................................................... 190
9.1.5 Interaction Effects in BEC............................. 193
9.2 Two Important Phenomena..................................... 195
9.2.1 Black Body Radiation and Stefan-Boltzmann law .... 195
9.2.2 Casimir Effect ........................................ 199
9.3 Superfluidity of Helium-4................................... 200
9.3.1 General Characteristics................................ 200
9.3.2 The Energy Spectrum.................................... 203
9.3.3 Occurrence of Superfluidity............................ 206
9.4 Problems for Chapter 9...................................... 208
xii Contents
10 Superconductivity 211
10.1 Introduction............................................... 211
10.2 Pairing Theory: Qualitative............................... 213
10.3 Origin of the Attractive Interaction....................... 221
10.4 Cooper Instability......................................... 223
10.5 A Different Pairing: High Temperature Superconductivity in
Cuprates................................................... 225
11 Phase Transitions 231
11.1 Introduction............................................... 231
11.2 Transfer Matrix for the 2D Ising Model..................... 234
11.2.1 The Conversion to a Quantum Problem.................. 234
11.2.2 The Transition Temperature ........................... 238
11.2.3 The Specific Heat .................................... 241
11.3 Planar Model and Heisenberg Model.......................... 244
11.4 Statistical Mechanics and Field Theory..................... 246
11.5 Kac-Hubbard-Stratonovich Transformation.................... 250
11.6 Critical Phenomena: Scaling Laws........................... 252
12 Landau Theory and Related Models 259
12.1 Landau Theory.............................................. 259
12.2 The Gaussian Model......................................... 263
12.3 The Spherical Limit........................................ 264
13 The Renormalization Group 269
13.1 Renormalization Group in Real Space........................ 269
13.1.1 Introduction ....................................... 269
13.1.2 One-dimensional Ising Model......................... 271
13.1.3 Two-dimensional Ising Model......................... 273
13.2 Renormalization Group in Momentum Space.................... 276
13.3 Fixed Points and Scaling Laws.............................. 277
13.4 Application to the Gaussian Model........................ 282
13.5 Application to the Landau-Ginzburg Model................... 283
14 Disordered Systems 291
14.1 Introduction............................................... 291
14.2 Models with Quenched Disorder.............................. 293
14.3 Electron Localization in Disordered Systems................ 298
15 Transport Equation - I 305
15.1 Introduction............................................... 305
15.2 Distribution Function...................................... 306
15.3 In the Absence of Collisions............................... 307
15.4 In the Presence of Collisions.............................. 309
Contents xiii
16 Transport Equation - II 315
16.1 Introduction.............................................. 315
16.2 Interaction without Collisions............................ 316
16.3 Collisions with Fixed Scatterers ........................ . 319
16.4 Binary Collisions.......................................... 322
16.5 The H-theorem.............................................. 326
17 Transport Equation - III 327
17.1 A Theorem.................................................. 327
17.2 Transport Equation for Conserved Quantities................ 328
17.3 Equations of Hydrodynamics................................. 331
18 Transport Equation - IV 335
18.1 Form of the Transport Equation for Quantum Particles . . . 335
18.1.1 Fermions ............................................. 336
18.1.2 Bosons............................................... 336
18.2 Equilibrium Distribution................................... 337
18.3 Approach to Equilibrium (F^O but no Collisions) ........... 339
18.4 Effect of Collisions in a Fermion Gas...................... 340
18.5 Collision Term for Bosons.................................. 344
19 Metastable States 347
19.1 Introduction............................................... 347
19.2 A Phenomenological Approach................................ 348
19.3 Decay of Metastable States ................................ 350
19.4 Beyond Metastability: Glasses.............................. 352
20 Langevin Equations 357
20.1 Introduction............................................... 357
20.2 An Example with Oscillators................................ 358
20.3 Gaussian Distribution and the Central Limit Theorem .... 360
20.4 Langevin Equation.......................................... 365
20.5 Langevin Equation and Equilibrium.......................... 367
20.6 Brownian Motion ........................................... 369
20.7 Quantum Langevin Equation................................. 375
21 Fokker-Planck Equations 379
21.1 Introduction............................................... 379
21.2 Fokker-Planck Equation: Derivation......................... 380
21.3 The General Solution....................................... 383
21.4 Metastable State and the Lowest Eigenvalue................. 387
21.5 Passage to Equilibrium of a Non-equilibrium State.......... 389
21.5.1 Regime - I: Diffusion................................. 391
21.5.2 Regime - II: “Scaling” or “Sliding”................... 392
21.5.3 Regime-Ill: Kramers .................................. 393
21.6 Diffusion in a Periodic Potential.......................... 394
xiv Contents
22 Fluctuation Dissipation Theorem 397
22.1 Introduction............................................... 397
22.2 The General Case........................................... 398
22.3 Jarzynski Equality........................................ 403
References 405
Index
413
In this new textbook, a number of unusual applications are discussed in addition.to the
usual topics covered in a course on Statistical Physics. Examples are: statistical mechanics
of powders, Peierls instability, graphene, Bose-Einstein condensates in a trap, Casimir
effect and the quantum Hall effect. Superfluidity and super-conductivity (including the
physics of high-temperature superconductors) have also been discussed extensively.
The emphasis on the treatment of these topics is pedagogic, introducing the basic
tenets of statistical mechanics, with extensive-and thorough discussion of the
postulates, ensembles, and the relevant statistics. Many standard examples illustrate
the microcanonical, canonical and grand canonical ensembles, as well as the Bose-
Einstein and Fermi-Dirac statistics.
A special feature of this text is the detailed presentation of the theory of second-order
phase transitions and the renormalization group, emphasizing the role of disorder.
Non-equilibrium statistical physics is introduced via the Boltzmann transport equation.
Additional topics covered here include metastability, glassy systems, the Langevin
equation, Brownian motion, and the Fokker-Planck equation.
■ Graduate students will find the presentation readily accessible, since the topics have
been treated with great deal of care and attention to detail.
4»
%
World Scientific
www.worldscientific.com -
10312 he .
ISBN 978-981-3201-14-9
|
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| spelling | Bhattacharjee, Jayanta K. Verfasser aut Intermediate statistical mechanics Jayanta Bhattacharjee (Harish-Chandra Research Institute, Allahabad, India), Dhruba Banerjee (Jadavpur University, India) New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2016] [New Delhi] Hindustan Book Agency xiv, 423 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis: Seiten 405-412 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 Banerjee, Dhruba Verfasser aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029775858&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029775858&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Bhattacharjee, Jayanta K. Banerjee, Dhruba Intermediate statistical mechanics Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4057000-9 (DE-588)4123623-3 |
| title | Intermediate statistical mechanics |
| title_auth | Intermediate statistical mechanics |
| title_exact_search | Intermediate statistical mechanics |
| title_full | Intermediate statistical mechanics Jayanta Bhattacharjee (Harish-Chandra Research Institute, Allahabad, India), Dhruba Banerjee (Jadavpur University, India) |
| title_fullStr | Intermediate statistical mechanics Jayanta Bhattacharjee (Harish-Chandra Research Institute, Allahabad, India), Dhruba Banerjee (Jadavpur University, India) |
| title_full_unstemmed | Intermediate statistical mechanics Jayanta Bhattacharjee (Harish-Chandra Research Institute, Allahabad, India), Dhruba Banerjee (Jadavpur University, India) |
| title_short | Intermediate statistical mechanics |
| title_sort | intermediate statistical mechanics |
| topic | Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Statistische Physik Lehrbuch |
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