Lectures on statistical mechanics:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
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New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2020]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xix, 287 Seiten Illustrationen, Diagramme |
| ISBN: | 9789811224577 9789811225543 |
Internformat
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| 245 | 1 | 0 | |a Lectures on statistical mechanics |c Berthold-Georg Englert, National University of Singapore, Singapore |
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| 653 | |a STATISTISCHE MECHANIK | ||
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| 653 | |a STATISTICAL MECHANICS | ||
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Datensatz im Suchindex
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| adam_text | Contents Preface vii Glossary xiii Miscellanea................................................................................... xiii Latin alphabet ............................................................................. xiv Greek alphabet and Greek-Latin combinations............................. xviii A note on units............................................................................. xix 1. Review of Selected Topics inThermodynamics 1.1 Four laws of thermodynamics............................................ 1.1.1 The Minus-First Law................................................ 1.1.2 The Zeroth Law......................................................... 1.1.3 The First Law............................................................ 1.1.4 The Second Law......................................................... 1.1.5 Temperature.............................................................. 1.2 Ideal gas................................................................................ 1.3 Maximum property of the entropy.................................... 1.4 Minimum property of the energy....................................... 1.5 The Second Law and thermal equilibrium........................ 1.6 Thermodynamical potentials: Free energy, enthalpy, free enthalpy................................................................................ 1.7 Heat capacities of the ideal gas.......................................... 1.8 Minimum property of the free energy................................. 1.9 Maxwell
relations................................................................. 1.10 Heat capacities.................................................................... 1.11 Gibbs-Duhem relation........................................................ 1.12 Stability criteria; coexisting phases.................................... 1.13 Gibbs phase rule................................................................. ІХ 1 2 2 3 4 5 7 8 12 13 14 16 20 22 24 26 30 33 39
t Lectures 1.14 1.15 1.16 1.17 1.18 2. 3. on Statistical Mechanics Clausius-Clapeyron equation................................................. Phase transition; Maxwell construction.................................. Van der Waals gas................................................................... Coexisting phases: Entropy, heatcapacity............................. Interfaces.................................................................................. 43 46 ^ 57 64 Statistical ensembles 69 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 70 72 73 77 79 85 87 88 89 93 The benefit of large numbers .............................................. Ergodic principle................................................................... Microcanonica] ensemble....................................................... Correct Boltzmann counting................................................. Canonical ensemble................................................................ Other ensembles ................................................................... Gibbs’s entropy formula....................................................... Grand canonical ensemble.................................................... Fluctuating particle numbers.............................................. Gibbs’s entropy formula as a basic statement................... Ideal gases 97 3.1 3.2 3.3 Getting started...................................................................... 97 Occupation numbers; bosons; fermions............................... 98 Average occupation numbers
.............................................. 100 3.3.1 Bosons......................................................................... 100 3.3.2 Fermions...................................................................... 102 3.3.3 Dilute-gas limit.......................................................... 103 3.4 Photon gas............................................................................ 105 3.5 Phonon gas............................................................................ 108 3.6 Bose-Einstein condensation................................................. 112 3.7 Fermion gas............................................................................ 120 3.8 Electron gas in a metal.......................................................... 126 3.9 Pressure and energy density................................................. 130 3.10 The Third Law...................................................................... 131 4. Systems with interaction 133 4.1 Thomas-Fermi model............................................................. 133 4.2 One-dimensional Ising model .............................................. 140 4.3 Renormalization group method (Ising chain)...................... 149 4.4 Renormalization group method (Ising square lattice) ... 153 4.5 Order-disorder phase transition........................................... 159
Contents 4.6 4.7 4.8 xi Onsager’s solution .............................................................. 162 Three-dimensional Ising model. Spontaneous magnetization 164 Mean-field approximation................................................... 166 5. Perturbation theory 5.1 Large and small contributions............................................. 5.2 Gibbs-Bogolyubov inequality............................................. 5.2.1 Example: Ising model (mean-field approximation) . 5.2.2 Quantum aspects...................................................... 5.3 Peierls inequality................................................................. 5.4 Minimum principle for the free energy.............................. 5.5 Ising chain with next-next-neighbors interaction............... 5.6 Ising model and two-state quantum system..................... 171 171 172 173 174 178 180 183 187 6. Real gases 191 6.1 Interacting atoms................................................................. 191 6.2 Clusters................................................................................ 193 6.3 Cluster expansion; viriai expansion.................................... 198 6.4 Finite volume, finite number of particles........................... 200 6.5 Second viriai coefficient: van der Waals gas.........................202 7. Stochastic processes 205 7.1 Random jumps.................................................................... 205 7.1.1 Recurrence relation; generating function...................206 7.1.2 Example: Symmetric one-unit jumps.........................208 7.2 Asymptotic
gaussian distribution....................................... 210 7.3 Poisson processes................................................................. 212 7.4 Brownian motion: Langevin’s random force.........................215 7.5 Autocorrelation function..................................................... 217 7.6 Fluctuations and dissipation................................................ 222 7.7 Dynamics in phase space..................................................... 222 7.8 Brownian motion: Fokker-Planck equation........................ 226 7.8.1 Expected values........................................................ 226 7.8.2 Generating function................................................... 228 7.8.3 Green’s function........................................................ 233 Exercises with Hints 237 Exercises for Chapters 1-7........................................................... 237 Hints............................................................................................... 263 Index 275
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| adam_txt |
Contents Preface vii Glossary xiii Miscellanea. xiii Latin alphabet . xiv Greek alphabet and Greek-Latin combinations. xviii A note on units. xix 1. Review of Selected Topics inThermodynamics 1.1 Four laws of thermodynamics. 1.1.1 The Minus-First Law. 1.1.2 The Zeroth Law. 1.1.3 The First Law. 1.1.4 The Second Law. 1.1.5 Temperature. 1.2 Ideal gas. 1.3 Maximum property of the entropy. 1.4 Minimum property of the energy. 1.5 The Second Law and thermal equilibrium. 1.6 Thermodynamical potentials: Free energy, enthalpy, free enthalpy. 1.7 Heat capacities of the ideal gas. 1.8 Minimum property of the free energy. 1.9 Maxwell
relations. 1.10 Heat capacities. 1.11 Gibbs-Duhem relation. 1.12 Stability criteria; coexisting phases. 1.13 Gibbs phase rule. ІХ 1 2 2 3 4 5 7 8 12 13 14 16 20 22 24 26 30 33 39
t Lectures 1.14 1.15 1.16 1.17 1.18 2. 3. on Statistical Mechanics Clausius-Clapeyron equation. Phase transition; Maxwell construction. Van der Waals gas. Coexisting phases: Entropy, heatcapacity. Interfaces. 43 46 ^ 57 64 Statistical ensembles 69 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 70 72 73 77 79 85 87 88 89 93 The benefit of large numbers . Ergodic principle. Microcanonica] ensemble. Correct Boltzmann counting. Canonical ensemble. Other ensembles . Gibbs’s entropy formula. Grand canonical ensemble. Fluctuating particle numbers. Gibbs’s entropy formula as a basic statement. Ideal gases 97 3.1 3.2 3.3 Getting started. 97 Occupation numbers; bosons; fermions. 98 Average occupation numbers
. 100 3.3.1 Bosons. 100 3.3.2 Fermions. 102 3.3.3 Dilute-gas limit. 103 3.4 Photon gas. 105 3.5 Phonon gas. 108 3.6 Bose-Einstein condensation. 112 3.7 Fermion gas. 120 3.8 Electron gas in a metal. 126 3.9 Pressure and energy density. 130 3.10 The Third Law. 131 4. Systems with interaction 133 4.1 Thomas-Fermi model. 133 4.2 One-dimensional Ising model . 140 4.3 Renormalization group method (Ising chain). 149 4.4 Renormalization group method (Ising square lattice) . 153 4.5 Order-disorder phase transition. 159
Contents 4.6 4.7 4.8 xi Onsager’s solution . 162 Three-dimensional Ising model. Spontaneous magnetization 164 Mean-field approximation. 166 5. Perturbation theory 5.1 Large and small contributions. 5.2 Gibbs-Bogolyubov inequality. 5.2.1 Example: Ising model (mean-field approximation) . 5.2.2 Quantum aspects. 5.3 Peierls inequality. 5.4 Minimum principle for the free energy. 5.5 Ising chain with next-next-neighbors interaction. 5.6 Ising model and two-state quantum system. 171 171 172 173 174 178 180 183 187 6. Real gases 191 6.1 Interacting atoms. 191 6.2 Clusters. 193 6.3 Cluster expansion; viriai expansion. 198 6.4 Finite volume, finite number of particles. 200 6.5 Second viriai coefficient: van der Waals gas.202 7. Stochastic processes 205 7.1 Random jumps. 205 7.1.1 Recurrence relation; generating function.206 7.1.2 Example: Symmetric one-unit jumps.208 7.2 Asymptotic
gaussian distribution. 210 7.3 Poisson processes. 212 7.4 Brownian motion: Langevin’s random force.215 7.5 Autocorrelation function. 217 7.6 Fluctuations and dissipation. 222 7.7 Dynamics in phase space. 222 7.8 Brownian motion: Fokker-Planck equation. 226 7.8.1 Expected values. 226 7.8.2 Generating function. 228 7.8.3 Green’s function. 233 Exercises with Hints 237 Exercises for Chapters 1-7. 237 Hints. 263 Index 275 |
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| index_date | 2024-07-03T17:29:32Z |
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| language | English |
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| spelling | Englert, Berthold-Georg 1953- Verfasser (DE-588)13834504X aut Lectures on statistical mechanics Berthold-Georg Englert, National University of Singapore, Singapore New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2020] xix, 287 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf STATISTISCHE MECHANIK MÉCANIQUE STATISTIQUE STATISTICAL MECHANICS Statistische Mechanik (DE-588)4056999-8 s DE-604 Erscheint auch als Online-Ausgabe 978-981-122-458-4 Erscheint auch als Online-Ausgabe 978-981-122-459-1 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=032724556&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title_auth | Lectures on statistical mechanics |
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| title_full | Lectures on statistical mechanics Berthold-Georg Englert, National University of Singapore, Singapore |
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| title_full_unstemmed | Lectures on statistical mechanics Berthold-Georg Englert, National University of Singapore, Singapore |
| title_short | Lectures on statistical mechanics |
| title_sort | lectures on statistical mechanics |
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| topic_facet | Statistische Mechanik |
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