Statistical mechanics and applications in condensed matter:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2015
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028302279&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 531 S. graph. Darst. |
| ISBN: | 9781107039407 1107039401 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV042873210 | ||
| 003 | DE-604 | ||
| 005 | 20160808 | ||
| 007 | t| | ||
| 008 | 150916s2015 xx d||| |||| 00||| eng d | ||
| 020 | |a 9781107039407 |9 978-1-107-03940-7 | ||
| 020 | |a 1107039401 |9 1-107-03940-1 | ||
| 035 | |a (OCoLC)923465109 | ||
| 035 | |a (DE-599)BVBBV042873210 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-20 |a DE-29T |a DE-11 |a DE-91G |a DE-634 | ||
| 084 | |a UG 3100 |0 (DE-625)145625: |2 rvk | ||
| 084 | |a PHY 057f |2 stub | ||
| 084 | |a PHY 602f |2 stub | ||
| 100 | 1 | |a DiCastro, Carlo |d 1937- |e Verfasser |0 (DE-588)1077573790 |4 aut | |
| 245 | 1 | 0 | |a Statistical mechanics and applications in condensed matter |c Carlo di Castro ; Roberto Raimondi |
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2015 | |
| 300 | |a XV, 531 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Statistical mechanics | |
| 650 | 0 | 7 | |a Statistische Mechanik |0 (DE-588)4056999-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Statistische Mechanik |0 (DE-588)4056999-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Raimondi, Roberto |d 1963- |e Sonstige |0 (DE-588)1077573995 |4 oth | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028302279&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-028302279 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202 PHY 057f 2016 B 1614 |
|---|---|
| DE-BY-TUM_katkey | 2220556 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040008245101 |
| _version_ | 1821933620489617409 |
| adam_text | Contents
Preface page xi
1 Thermodynamics: a brief overview 1
1.1 Equilibrium states and the empirical temperature 1
1.2 The principles of thermodynamics 5
1.3 Thermodynamic potentials and equilibrium 11
1.4 Thermodynamic stability and availability function 14
1.5 Phase equilibrium 20
1.6 The liquid-gas transition 22
1.7 Problems 26
2 Kinetics 27
2.1 The birth of kinetic theory 27
2.2 The Boltzmann equation 29
2.3 Extension of the Boltzmann equation to quantum systems 34
2.4 The H-theorem and the approach to equilibrium 35
2.5 The Maxwell-Boltzmann distribution 38
2.6 The mean free path for Maxwell-Boltzmann statistics 39
2.7 The Kac model 40
2.8 Problems 43
3 From Boltzmann to Boltzmann-Gibbs 45
3.1 Liouville and Poincaré theorems 45
3.2 Equilibrium statistical mechanics for a gas 47
3.3 Equilibrium statistical mechanics for a generic macroscopic system 50
3.4 The microcanonical ensemble and the entropy 53
3.5 The equipartition theorem 56
3.6 The perfect gas in the microcanonical ensemble 57
3.7 Problems 59
4 More ensembles 60
4.1 The canonical ensemble 60
4.2 The Gibbs entropy 63
4.3 The grand canonical ensemble 64
4.4 Fluctuations of a gas 67
4.5 Problems 68
v
VI
Contents
5 The thermodynamic limit and its thermodynamic stability 69
5.1 The Yang-Lee theorems 70
5.2 Proof of the first theorem 72
6 Density matrix and quantum statistical mechanics 77
6.1 Kinetics for quantum gases 77
6.2 Density matrix for pure states 80
6.3 Density matrix for systems interacting with the environment 81
6.4 Quantum statistical ensembles 82
6.5 Problem 84
7 The quantum gases 85
7.1 The statistical distribution of the quantum gases 85
7.2 The strongly degenerate Fermi gas 88
7.3 The degenerate Bose gas 90
7.4 The Bose and Fermi gases in an harmonic potential 95
7.5 The photon gas 100
7.6 The phonon gas 103
7.7 Problems 106
8 Mean-field theories and critical phenomena 107
8.1 The van der Waals equation and the classical critical indices 107
8.2 The paramagnetic-ferromagnetic transition 112
8.3 The Curie-Weiss theory and the classical critical indices for the
Ising model 115
8.4 Classical linear response theory and fluctuations 121
8.5 Problems 123
9 Second quantization and the Hartree-Fock approximation 124
9.1 Occupation numbers representation 124
9.2 Creation and annihilation operators 125
9.3 Field operators 126
9.4 Basis vectors in terms of the field operators 127
9.5 Observables in second quantization 128
9.6 Equation of motion for field operators 131
9.7 Reduced density matrices 133
9.8 Hartree-Fock method for a Fermi system 135
9.9 Problems 137
10 Linear response and the fluctuation-dissipation theorem in quantum systems:
equilibrium and small deviations 139
10.1 Linear response 139
10.2 The response to an electromagnetic field and gauge invariance 143
Contents
10.3 The principle of detailed balance and the fluctuation-dissipation theorem 145
10.4 Onsager’s symmetry relations 148
10.5 Generalized fluctuations theorem and minimum availability function 149
10.6 Problems 154
11 Brownian motion and transport in disordered systems 155
11.1 Einstein’s theory of Brownian motion 155
11.2 Langevin’s theory of Brownian motion 158
11.3 The Johnson-Nyquist noise 160
11.4 Transport description in the disordered Fermi gas 162
11.5 Problems 169
12 Fermi liquids 170
12.1 Temperature range of application and quasiparticles 170
12.2 Equilibrium properties 173
12.3 Transport properties 177
12.4 Problems 185
13 The Landau theory of second order phase transitions 186
13.1 Spontaneous symmetry breaking, order parameter and the classical
critical indices 186
13.2 Fluctuations and Ginzburg criterion for the validity of
mean-field theories 189
13.3 First order transition and tricritical point 191
13.4 Continuous symmetries and the lower critical dimensionality 195
13.5 Problem 197
14 The Landau-Wilson model for critical phenomena 198
14.1 The Gaussian transformation 198
14.2 The Gaussian approximation 201
14.3 Hydrodynamics for the isotropic ferromagnet 203
15 Superfluidity and superconductivity 205
15.1 Introduction 205
15.2 The Landau criterion 206
15.3 Phenomenology of superfluid 4He 207
15.4 Phenomenology of superconductors 214
15.5 The condensation criterion and the order parameter 218
15.6 Order parameter and symmetry 223
15.7 The Landau-Ginzburg equations 235
15.8 The Bogoliubov model for superfluidity 242
15.9 The microscopic theory of superconductivity 245
15.10 Crossover between BCS and Bose-Einstein condensation 255
viii
Contents
15.11 Superfluid 3He 260
15.12 High temperature superconductivity: a brief presentation 266
15.13 Problems 273
16 Scaling theory 275
16.1 The scaling laws 275
16.2 On the existence of ODLRO at low dimension 283
16.3 Dynamical scaling 285
16.4 Problem 289
17 The renormalization group approach 290
17.1 General properties of the renormalization group 291
17.2 The Kadanoff-Wilson transformation 295
17.3 Derivation of the RG equations 299
17.4 Field-theoretic renormalization group 307
17.5 Problems 317
18 Thermal Green functions 318
18.1 The Matsubara Green function 318
18.2 The thermal Green function for Fermi and Bose gases 321
18.3 The connection with the time-dependent Green function at finite
temperature 323
18.4 The physical meaning of the poles of the Green function 326
18.5 The perturbative expansion of the Matsubara Green function 331
18.6 The statistical Wick theorem 333
18.7 Diagrammatic expansion of the one-particle thermal Green function and
the thermodynamic potential 335
18.8 The Dyson equation 341
18.9 Thermal density and current response functions 346
18.10 The Ward identity 348
18.11 Problems 351
19 The microscopic foundations of Fermi liquids 352
19.1 Scattering amplitudes 352
19.2 The static and dynamic limit of the truncated vertex function 355
19.3 Response functions and Fermi liquid parameters 356
20 The Luttinger liquid 358
20.1 The breakdown of the Fermi liquid in one dimension 358
20.2 The Tomonaga-Luttinger (TL) model 359
20.3 The Dyson equation, conservation laws and Ward identities 365
20.4 Remarks about renormalization 370
20.5 Problems 374
IX
Contents
21 Quantum interference effects in disordered electron systems 375
21.1 Experimental evidence of anomalous disorder effects 376
21.2 The Anderson transition and quantum interference 378
21.3 The scaling theory of the metal-insulator transition 380
21.4 The quantum theory of the disordered Fermi gas 383
21.5 A few remarks on the experiments 396
21.6 Electron-electron interaction in the presence of disorder 397
21.7 Quantum theory of the disordered Fermi liquid 406
21.8 The renormalization group flow of the disordered
Fermi liquid 413
21.9 Problems 420
Appendix A The central limit theorem 422
Appendix B Some useful properties of the Euler Gamma function 424
AppendixC Proof of the second theorem of Yang and Lee 426
Appendix D The most probable distribution for the quantum gases 428
Appendix E Fermi—Diracand Bose—Einstein integrals 430
Appendix F The Fermi gas in a uniform magnetic field: Landau diamagnetism 433
AppendixG Ising and gas-lattice models 436
AppendixH Sum over discrete Matsubara frequencies 438
Appendix I Two-fluid hydrodynamics: a few hints 439
Appendix J The Cooper problem in the theory of superconductivity 441
Appendix K Superconductive fluctuation phenomena 443
Appendix L Diagrammatic aspects of the exact solution of the Tomonaga-Luttinger model 450
Appendix M Details on the theory of the disordered Fermi liquid 458
Appendix N Answers to problems 467
References
Index
511
527
|
| any_adam_object | 1 |
| author | DiCastro, Carlo 1937- |
| author_GND | (DE-588)1077573790 (DE-588)1077573995 |
| author_facet | DiCastro, Carlo 1937- |
| author_role | aut |
| author_sort | DiCastro, Carlo 1937- |
| author_variant | c d cd |
| building | Verbundindex |
| bvnumber | BV042873210 |
| classification_rvk | UG 3100 |
| classification_tum | PHY 057f PHY 602f |
| ctrlnum | (OCoLC)923465109 (DE-599)BVBBV042873210 |
| discipline | Physik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01539nam a2200373 c 4500</leader><controlfield tag="001">BV042873210</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160808 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">150916s2015 xx d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107039407</subfield><subfield code="9">978-1-107-03940-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1107039401</subfield><subfield code="9">1-107-03940-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)923465109</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042873210</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UG 3100</subfield><subfield code="0">(DE-625)145625:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 057f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 602f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">DiCastro, Carlo</subfield><subfield code="d">1937-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1077573790</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Statistical mechanics and applications in condensed matter</subfield><subfield code="c">Carlo di Castro ; Roberto Raimondi</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2015</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 531 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Statistical mechanics</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Statistische Mechanik</subfield><subfield code="0">(DE-588)4056999-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Statistische Mechanik</subfield><subfield code="0">(DE-588)4056999-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Raimondi, Roberto</subfield><subfield code="d">1963-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)1077573995</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028302279&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028302279</subfield></datafield></record></collection> |
| id | DE-604.BV042873210 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T17:22:05Z |
| institution | BVB |
| isbn | 9781107039407 1107039401 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028302279 |
| oclc_num | 923465109 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-20 DE-29T DE-11 DE-91G DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-20 DE-29T DE-11 DE-91G DE-BY-TUM DE-634 |
| physical | XV, 531 S. graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spellingShingle | DiCastro, Carlo 1937- Statistical mechanics and applications in condensed matter Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd |
| subject_GND | (DE-588)4056999-8 |
| title | Statistical mechanics and applications in condensed matter |
| title_auth | Statistical mechanics and applications in condensed matter |
| title_exact_search | Statistical mechanics and applications in condensed matter |
| title_full | Statistical mechanics and applications in condensed matter Carlo di Castro ; Roberto Raimondi |
| title_fullStr | Statistical mechanics and applications in condensed matter Carlo di Castro ; Roberto Raimondi |
| title_full_unstemmed | Statistical mechanics and applications in condensed matter Carlo di Castro ; Roberto Raimondi |
| title_short | Statistical mechanics and applications in condensed matter |
| title_sort | statistical mechanics and applications in condensed matter |
| topic | Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Statistical mechanics Statistische Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028302279&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dicastrocarlo statisticalmechanicsandapplicationsincondensedmatter AT raimondiroberto statisticalmechanicsandapplicationsincondensedmatter |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Physik
| Signatur: |
0202 PHY 057f 2016 B 1614
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |