Statistical physics: fundamentals and application to condensed matter ; with lectures, problems and solutions
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| Format: | Book |
| Language: | English |
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Singapore [u.a.]
World Scientific
2015
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| Online Access: | Klappentext Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (pages 609-615) and index |
| Physical Description: | XXV, 621 pages Ill., graph. Darst. |
| ISBN: | 9814696137 9789814696135 9789814696258 |
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| 245 | 1 | 0 | |a Statistical physics |b fundamentals and application to condensed matter ; with lectures, problems and solutions |c Hung T. Diep |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2015 | |
| 300 | |a XXV, 621 pages |b Ill., graph. Darst. | ||
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| adam_text | STATISTICAL PHYSICS
Fundamentals and Application to Condensed Matter
With Lectures, Problems and Solutions
The aim of this book is to provide the fundamentals of statistical physics and its application to condensed matter. The combination of statistical mechanics and quantum mechanics has provided an understanding of properties of matter leading to spectacular
technological innovations and discoveries in condensed matter which have radically changed our daily life.
The book gives the steps to follow to understand fundamental theories and to apply these to real materials.
Contents
ft
Preface vii
Acknowledgments ix
List of Problems xxi
Fundamentals of Statistical Physics 1
1. Basic Concepts and Tools in Statistical Physics 3
1.1 Introduction............................................... 3
1.2 Combinatory analysis....................................... 4
1.2.1 Number of permutations............................. 4
1.2.2 Number of arrangements............................. 4
1.2.3 Number of combinations............................. 5
1.3 Probability................................................ 5
1.3.1 Definition........................................ 5
1.3.2 Fundamental properties............................. 6
1.3.3 Mean values........................................ 7
1.4 Statistical distributions ................................. 9
1.4.1 Binomial distribution.............................. 9
1.4.2 Gaussian distribution............................. 10
1.4.3 Poisson law....................................... 12
1.5 Microstates — Macrostates................................ 13
1.5.1 Microstates — Enumeration......................... 13
1.5.2 Macroscopic states................................ 15
1.5.3 Statistical averages — Ergodic hypothesis .... 15
1.6 Statistical entropy....................................... 16
XI
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58
59
Statistical Physics — Fundamentals and Application to Condensed Matter
1.7 Conclusion ........................................., .
1.8 Problems................................................
Isolated Systems: Micro-Canonical Description
2.1 Introduction............................................
2.2 Fundamental postulate . ................................
2.3 Properties of an isolated system........................
2.3.1 Spontaneous evolution of an isolated system
toward equilibrium .............................
2.3.2 Exchanges of heat and volume....................
2.3.3 Exchange of particles...........................
2.3.4 Statistical distribution of an internal variable . . .
2.4 Phase space — Density of states.........................
2.4.1 Density of states...............................
2.4.2 Density of states of free quantum particles . . . .
2.4.3 Density of states of free classical particles...
2.5 Applications of the micro-canonical method..............
2.5.1 Example 1: two-level systems ...................
2.5.2 Example 2: Classical ideal gas..................
2.6 Conclusion .............................................
2.7 Problems ...............................................
Systems at a Constant Temperature: Canonical Description
3.1 Canonical probability ..................................
3.2 Partition function
3.3 Properties of a system at a constant temperature........
3.4 Statistical distribution of an internal variable........
3.5 Spontaneous evolution of a canonical system ............
3.5.1 Criterion for equilibrium.......................
3.5.2 Direction of spontaneous evolution..............
3.6 Applications of the canonical method....................
3.6.1 Systems of identical independent particles . . . .
3.6.2 Classical ideal gas.............................
3.6.3 Two-level systems...............................
3.6.4 Theorem of equipartition of energy..............
3.7 Conclusion .............................................
3.8 Problems................................................
Contents xiii
4. Open Systems at Constant Temperature:
Grand-Canonical Description 65
4.1 Introduction............................................. 65
4.2 Grand-canonical probability.............................. 65
4.3 Grand partition function Z — Grand potential J........... 67
4.4 General properties of grand-canonical systems............ 68
4.5 Spontaneous evolution of a grand-canonical system .... 70
4.6 Systems of identical, independent particles.............. 72
4.6.1 Factorization of Z............................... 73
4.6.2 Bose-Einstein distribution....................... 74
4.6.3 Fermi-Dirac distribution......................... 74
4.6.4 Maxwell-Boltzmann distribution................... 75
4.7 Applications of the grand-canonical method............... 75
4.7.1 Classical ideal gas.............................. 75
4.7.2 Two-level systems................................ 76
4.8 Conclusion .............................................. 78
4.9 Problems................................................. 78
5. Free Fermi Gas 83
5.1 Introduction............................................. 83
5.2 Fermi-Dirac distribution................................. 83
5.3 General properties of a free Fermi gas................... 84
5.3.1 General formulas ................................ 84
5.3.2 Formulas for large systems....................... 86
5.4 Properties of a free Fermi gas at T = 0.................. 88
5.4.1 Fermi energy..................................... 88
5.4.2 Total average kinetic energy..................... 89
5.5 Properties of a free Fermi gas at low temperatures .... 89
5.5.1 Sommerfeldes expansion........................... 89
5.5.2 Chemical potential, average energy and calorific
capacity......................................... 90
5.6 Free Fermi gas at the high-temperature limit............. 90
5.7 Applications............................................. 91
5.7.1 Paramagnetism of conducting electrons in metals 91
5.7.2 Thermo-ionic emission ........................... 93
5.8 Conclusion .............................................. 94
5.9 Problems................................................. 94
xiv Statistical Physics — Fundamentals and Application to Condensed Matter
6. Free Boson Gas 97
6.1 Introduction............................................. 97
6.2 Bose-Einstein distribution............................... 97
6.3 General properties of a free boson gas................... 98
6.3.1 General formulas ................................ 98
6.3.2 Formulas for large systems...................... 100
6.4 High-temperature limit.................................. 101
6.5 Bose-Einstein condensation.............................. 102
6.6 Properties at temperatures higher than Tb .............. 103
6.7 Applications........................................... 106
6.7.1 Photons: black-body radiation................... 106
6.7.2 Helium-4........................................ 110
6.8 Conclusion ............................................. Ill
6.9 Problems................................................ Ill
7. Systems of Interacting Particles: Method of Second Quantization 113
7.1 Introduction............................................ 113
7.2 First quantization: symmetric and antisymmetric wave
functions .............................................. 114
7.3 Representation of microstates by occupation numbers . . 118
7.4 Second quantization: the case of bosons................. 119
7.4.1 Hamiltonian in second quantization.............. 119
7.4.2 Properties of boson operators .................. 123
7.5 Second quantization: the case of fermions............... 124
7.6 Field operators........................................ 127
7.7 Hartree-Fock approximation.............................. 129
7.8 Conclusion ............................................. 132
7.9 Problems ............................................... 132
Application to Condensed Matter 135
8. Symmetry in Crystalline Solids 137
8.1 Crystalline symmetry .................................. 137
8.2 Reciprocal lattices..................................... 139
8.3 Wave-vector space — Brillouin zones..................... 142
8.4 Sum rules............................................... 144
8.5 Fourier analysis........................................ 146
8.6 Representation in fc-space.............................. 148
8.7 Conclusion ............................................. 148
Contents
xv
8.8 Problems................................................. 148
9. Interacting Atoms in Crystals: Phonons 151
9.1 Introduction............................................. 151
9.2 Vibrations in one dimension.............................. 153
9.2.1 Equation of motion................................ 153
9.2.2 Dispersion relation .............................. 154
9.3 Vibrations in two and three dimensions................... 155
9.4 Quantization of vibration: phonons....................... 159
9.4.1 Normal coordinates, vibration energy.............. 159
9.4.2 Quantization of vibration......................... 160
9.5 Thermal properties of phonons............................ 162
9.5.1 Density of modes ................................. 163
9.5.2 Einstein model and Debye model ................... 164
9.6 Phonons in a condensed gas of Helium-4................... 168
9.7 Conclusion .............................................. 172
9.8 Problems................................................. 173
10. Systems of Interacting Electrons — Fermi Liquids 177
10.1 Introduction............................................ 177
10.2 Gas of interacting electrons............................. 177
10.2.1 Kinetic and exchange energies..................... 181
10.2.2 Effective mass.................................... 184
10.3 Gas of interacting electrons by second quantization .... 184
10.3.1 Kinetic energy.................................... 187
10.3.2 Energy at first-order perturbation................ 188
10.3.3 Energy at second-order perturbation............... 189
10.4 Fermi Liquids............................................ 193
10.5 Kondo effect ............................................ 195
10.6 Conclusion .............................................. 196
10.7 Problems................................................. 196
11. Electrons in Crystalline Solids: Energy Bands 201
11.1 Wave function of an electron in a periodic potential: Bloch
function................................................. 202
11.2 Theory of almost-free electrons.......................... 204
11.2.1 One-dimensional case...............................204
11.2.2 Calculation of the energy correction.............. 207
xvi Statistical Physics — Fundamentals and Application to Condensed Matter
11.2.3 Interpretation of the forbidden band gap............ 209
11.2.4 Three-dimensional case.............................. 210
11.3 Electrons in a periodic potential: the central equation . . 212
11.3.1 Band filling: classification of materials .......... 214
11.3.2 Semiconductors...................................... 215
11.4 Tight-Binding Approximation................................ 219
11.4.1 One-dimensional case................................ 219
11.4.2 Three-dimensional case.............................. 224
11.4.3 Velocity, acceleration, effective mass.............. 225
11.5 Conclusion ................................................ 226
11.6 Problems................................................... 228
12. Systems of Interacting Spins: Magnons 235
12.1 Spin models................................................ 235
12.1.1 Heisenberg model.................................... 235
12.1.2 Ising, XY and Potts models ......................... 237
12.2 Spin waves in ferromagnets................................. 239
12.2.1 Classical treatment................................. 239
12.2.2 Quantum theory...................................... 244
12.2.3 Properties at low temperatures...................... 247
12.3 Other magnets.............................................. 250
12.3.1 Antiferromagnets.................................... 250
12.3.2 Ferrimagnets........................................ 250
12.3.3 Helimagnets......................................... 250
12.3.4 Frustrated magnets................................. 252
12.4 Conclusion .............................................. 254
12.5 Problems .................................................. 254
13. Systems of Interacting Spins: Phase Transitions 259
13.1 Introduction........................................... 259
13.2 Generalities............................................... 260
13.2.1 Order parameter..................................... 260
13.2.2 Order of the phase transition....................... 262
13.2.3 Correlation function — Correlation length .... 262
13.2.4 Critical exponents.................................. 263
13.2.5 Universality class.................................. 264
13.3 Ferromagnetism in mean-field theory........................ 266
13.3.1 Mean-field equation................................. 266
Contents xvii
13.3.2 Critical temperature ............................ 269
13.3.3 Specific heat.................................... 271
13.3.4 Susceptibility................................... 272
13.3.5 Validity of mean-field theory.................... 274
13.3.6 Improved mean-field theory: Bethe’s approximation 274
13.4 Landau-Ginzburg theory.................-.............. 276
13.4.1 Mean-field critical exponents.................... 277
13.4.2 Correlation function............................. 278
13.4.3 Corrections to mean-field theory................. 280
13.5 Renormalization group................................... 282
13.5.1 Transformation of renormalization group — Fixed
point............................................ 282
13.5.2 Renormalization group applied to an Ising chain . 285
13.5.3 MigdahKadanoff decimation method and Migdah
Kadanoif bond-moving approximation............... 287
13.6 Transfer matrix method applied to an Ising chain........ 291
13.7 Phase transition in some particular systems............. 293
13.7.1 Exactly solved spin systems ..................... 293
13.7.2 Kosterlitz-Thouless transition . . .............. 294
13.7.3 Frustrated spin systems.......................... 294
13.8 Conclusion ............................................. 295
13.9 Problems................................................ 295
14. Superconductivity 301
14.1 Introduction............................................ 301
14.2 Properties of conventional superconductors.............. 302
14.3 Ginzburg-Landau theory of superconductivity............. 303
14.4 Superconductors of type II ............................. 310
14.5 Bardeen-Cooper-Schrieffer theory........................ 314
14.5.1 Electron-phonon interaction...................... 314
14.5.2 Cooper electron pairs — BCS Hamiltonian .... 317
14.5.3 Ground-state wave function ...................... 321
14.6 High-temperature superconductivity...................... 323
14.7 Conclusion ............................................. 324
14.8 Problems ............................................... 325
15. Transport in Metals and Semiconductors 327
15.1 Introduction............................................ 327
xviii Statistical Physics — Fundamentals and Application to Condensed Matter
15.2 Boltzmann’s equation..................................... 327
15.2.1 Classical formulation............................. 328
15.2.2 Quantum formulation............................... 329
15.3 Linearized Boltzmann’s equation.......................... 331
15.3.1 Explicit linearized terms......................... 331
15.3.2 Relaxation-time approximation..................... 332
15.4 Applications in general transport problems .............. 333
15.4.1 Heat current...................................... 333
15.4.2 Thermo-electric current........................... 333
15.4.3 Electric conductivity............................. 336
15.4.4 Thermal conductivity.............................. 336
15.4.5 Seebeck effect.................................... 337
15.4.6 Peltier effect.................................... 337
15.5 Resistivity.............................................. 337
15.6 Spin-independent transport in metals — Ohm’s law . . . 338
15.7 Transport in strong electric fields — Hot electrons .... 340
15.8 Transport in semiconductors ............................. 345
15.8.1 Motion of electrons in applied fields — Hall effect 345
15.8.2 Calculation of the diffusion coefficient by the
Boltzmann’s equation.............................. 350
15.8.3 Transport in semiconductors: Gunn’s effect ... 353
15.8.4 Conductivity in extrinsic semiconductors —
Doping effects.................................... 357
15.8.5 Doped semiconductors: generation, recombination, equation of continuity.............................. 360
15.8.6 p — n junctions — Diodes.......................... 363
15.9 Spin transport in magnetic materials..................... 367
15.10 Conclusion .............................................. 368
15.11 Problems................................................. 368
Solutions of Problems 375
Solutions of Problems of Part 1 377
16.1 Solutions of problems of chapter 1....................... 377
16.2 Solutions of problems of chapter 2....................... 385
16.3 Solutions of problems of chapter 3........................406
16.4 Solutions of problems of chapter 4........................422
16.5 Solutions of problems of chapter 5....................... 437
Contents xix
16.6 Solutions of problems of chapter 6....................... 449
16.7 Solutions of problems of chapter 7....................... 456
Solutions of Problems of Part 2 465
17.1 Solutions of problems of chapter 8....................... 465
17.2 Solutions of problems of chapter 9 ...................... 469
17.3 Solutions of problems of chapter 10...................... 481
17.4 Solutions of problems of chapter 11...................... 495
17.5 Solutions of problems of chapter 12...................... 507
17.6 Solutions of problems of chapter 13 . . ................. 523
17.7 Solutions of problems of chapter 14...................... 535
17.8 Solutions of problems of chapter 15...................... 548
Appendices 571
Appendix A Mathematical Complements and Table of Constants 573
A.l Volume of a sphere in n dimensions......................... 573
A.2 Stirling formula........................................... 574
A.3 Gaussian integrals......................................... 574
A.4 r function................................................. 575
A.5 C series or Riemann’s series............................... 575
A.6 Other formulas ............................................ 575
A.7 Universal constants........................................ 576
Appendix B Sommerfeld’s Expansion at Low Temperatures 577
Appendix C Origin of the Heisenberg Model 579
Appendix D Hubbard Model: Superexchange 583
Appendix E Kosterlitz-Thouless Phase Transition 591
Appendix F Low- and High-Temperature Expansions of the
Ising Model 599
F.l The case of the square lattice............................. 599
F.2 The case of the triangular and honeycomb lattices .... 604
Bibliography 609
Index 617
|
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| publisher | World Scientific |
| record_format | marc |
| spelling | Diep, Hung T. Verfasser aut Statistical physics fundamentals and application to condensed matter ; with lectures, problems and solutions Hung T. Diep Singapore [u.a.] World Scientific 2015 XXV, 621 pages Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (pages 609-615) and index Statistical physics Condensed matter / Statistical methods 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 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=028313973&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext 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=028313973&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diep, Hung T. Statistical physics fundamentals and application to condensed matter ; with lectures, problems and solutions Statistical physics Condensed matter / Statistical methods Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4057000-9 (DE-588)4123623-3 |
| title | Statistical physics fundamentals and application to condensed matter ; with lectures, problems and solutions |
| title_auth | Statistical physics fundamentals and application to condensed matter ; with lectures, problems and solutions |
| title_exact_search | Statistical physics fundamentals and application to condensed matter ; with lectures, problems and solutions |
| title_full | Statistical physics fundamentals and application to condensed matter ; with lectures, problems and solutions Hung T. Diep |
| title_fullStr | Statistical physics fundamentals and application to condensed matter ; with lectures, problems and solutions Hung T. Diep |
| title_full_unstemmed | Statistical physics fundamentals and application to condensed matter ; with lectures, problems and solutions Hung T. Diep |
| title_short | Statistical physics |
| title_sort | statistical physics fundamentals and application to condensed matter with lectures problems and solutions |
| title_sub | fundamentals and application to condensed matter ; with lectures, problems and solutions |
| topic | Statistical physics Condensed matter / Statistical methods Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Statistical physics Condensed matter / Statistical methods Statistische Physik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028313973&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028313973&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT diephungt statisticalphysicsfundamentalsandapplicationtocondensedmatterwithlecturesproblemsandsolutions |