Statistical Mechanics
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Statistical Mechanics

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ISBN-13:
9780123821898
Einband:
EPUB
Seiten:
744
Autor:
Paul D. Beale
eBook Typ:
Adobe Digital Editions
eBook Format:
EPUB
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Englisch
Beschreibung:

Statistical Mechanics explores the physical properties of matter based on the dynamic behavior of its microscopic constituents. After a historical introduction, this book presents chapters about thermodynamics, ensemble theory, simple gases theory, Ideal Bose and Fermi systems, statistical mechanics of interacting systems, phase transitions, and computer simulations. This edition includes new topics such as BoseEinstein condensation and degenerate Fermi gas behavior in ultracold atomic gases and chemical equilibrium. It also explains the correlation functions and scattering; fluctuationdissipation theorem and the dynamical structure factor; phase equilibrium and the Clausius-Clapeyron equation; and exact solutions of one-dimensional fluid models and two-dimensional Ising model on a finite lattice. New topics can be found in the appendices, including finite-size scaling behavior of Bose-Einstein condensates, a summary of thermodynamic assemblies and associated statistical ensembles, and pseudorandom number generators. Other chapters are dedicated to two new topics, the thermodynamics of the early universe and the Monte Carlo and molecular dynamics simulations. This book is invaluable to students and practitioners interested in statistical mechanics and physics. Bose-Einstein condensation in atomic gasesThermodynamics of the early universeComputer simulations: Monte Carlo and molecular dynamicsCorrelation functions and scatteringFluctuation-dissipation theorem and the dynamical structure factorChemical equilibriumExact solution of the two-dimensional Ising model for finite systemsDegenerate atomic Fermi gasesExact solutions of one-dimensional fluid modelsInteractions in ultracold Bose and Fermi gasesBrownian motion of anisotropic particles and harmonic oscillators
Statistical Mechanics explores the physical properties of matter based on the dynamic behavior of its microscopic constituents. After a historical introduction, this book presents chapters about thermodynamics, ensemble theory, simple gases theory, Ideal Bose and Fermi systems, statistical mechanics of interacting systems, phase transitions, and computer simulations. This edition includes new topics such as BoseEinstein condensation and degenerate Fermi gas behavior in ultracold atomic gases and chemical equilibrium. It also explains the correlation functions and scattering; fluctuationdissipation theorem and the dynamical structure factor; phase equilibrium and the Clausius-Clapeyron equation; and exact solutions of one-dimensional fluid models and two-dimensional Ising model on a finite lattice. New topics can be found in the appendices, including finite-size scaling behavior of Bose-Einstein condensates, a summary of thermodynamic assemblies and associated statistical ensembles, and pseudorandom number generators. Other chapters are dedicated to two new topics, the thermodynamics of the early universe and the Monte Carlo and molecular dynamics simulations. This book is invaluable to students and practitioners interested in statistical mechanics and physics. Bose-Einstein condensation in atomic gasesThermodynamics of the early universeComputer simulations: Monte Carlo and molecular dynamicsCorrelation functions and scatteringFluctuation-dissipation theorem and the dynamical structure factorChemical equilibriumExact solution of the two-dimensional Ising model for finite systemsDegenerate atomic Fermi gasesExact solutions of one-dimensional fluid modelsInteractions in ultracold Bose and Fermi gasesBrownian motion of anisotropic particles and harmonic oscillators
1;Front Cover;12;Statistical Mechanics;4
3;Copyright;5
4;Table of Contents;6
5;Preface to the Third Edition;14
6;Preface to the Second Edition;18
7;Preface to the First Edition;20
8;Historical Introduction;22
9;Chapter 1. The Statistical Basis of Thermodynamics;28
9.1;1.1 The macroscopic and the microscopic states;28
9.2;1.2 Contact between statistics and thermodynamics: physical significance of the number O(N, V, E);30
9.3;1.3 Further contact between statistics and thermodynamics;33
9.4;1.4 The classical ideal gas;36
9.5;1.5 The entropy of mixing and the Gibbs paradox;43
9.6;1.6 The "correct" enumeration of the microstates;47
9.7;Problems;49
10;Chapter 2. Elements of Ensemble Theory;52
10.1;2.1 Phase space of a classical system;52
10.2;2.2 Liouville's theorem and its consequences;54
10.3;2.3 The microcanonical ensemble;57
10.4;2.4 Examples;59
10.5;2.5 Quantum states and the phase space;62
10.6;Problems;64
11;Chapter 3. The Canonical Ensemble;66
11.1;3.1 Equilibrium between a system and a heat reservoir;67
11.2;3.2 A system in the canonical ensemble;68
11.3;3.3 Physical significance of the various statistical quantities in the canonical ensemble;77
11.4;3.4 Alternative expressions for the partition function;79
11.5;3.5 The classical systems;81
11.6;3.6 Energy fluctuations in the canonical ensemble: correspondence with the microcanonical ensemble;85
11.7;3.7 Two theorems - the "equipartition" and the "virial";88
11.8;3.8 A system of harmonic oscillators;92
11.9;3.9 The statistics of paramagnetism;97
11.10;3.10 Thermodynamics of magnetic systems: negative temperatures;104
11.11;Problems;110
12;Chapter 4. The Grand Canonical Ensemble;118
12.1;4.1 Equilibrium between a system and a particle-energy reservoir;118
12.2;4.2 A system in the grand canonical ensemble;120
12.3;4.3 Physical significance of the various statistical quantities;122
12.4;4.4 Examples;125
12.5;4.5 Density and energy fluctuations in the grand canonical ensemble: correspondence with other ensembles;130
12.6;4.6 Thermodynamic phase diagrams;132
12.7;4.7 Phase equilibrium and the Clausius-Clapeyron equation;136
12.8;Problems;138
13;Chapter 5. Formulation of Quantum Statistics;142
13.1;5.1 Quantum-mechanical ensemble theory: the density matrix;142
13.2;5.2 Statistics of the various ensembles;146
13.3;5.3 Examples;149
13.4;5.4 Systems composed of indistinguishable particles;155
13.5;5.5 The density matrix and the partition function of a system of free particles;160
13.6;Problems;166
14;Chapter 6. The Theory of Simple Gases;168
14.1;6.1 An ideal gas in a quantum-mechanical microcanonical ensemble;168
14.2;6.2 An ideal gas in other quantum-mechanical ensembles;173
14.3;6.3 Statistics of the occupation numbers;176
14.4;6.4 Kinetic considerations;179
14.5;6.5 Gaseous systems composed of molecules with internal motion;182
14.6;6.6 Chemical equilibrium;197
14.7;Problems;200
15;Chapter 7. Ideal Bose Systems;206
15.1;7.1 Thermodynamic behavior of an ideal Bose gas;207
15.2;7.2 Bose-Einstein condensation in ultracold atomic gases;218
15.3;7.3 Thermodynamics of the blackbody radiation;227
15.4;7.4 The field of sound waves;232
15.5;7.5 Inertial density of the sound field;239
15.6;7.6 Elementary excitations in liquid helium II;242
15.7;Problems;250
16;Chapter 8. Ideal Fermi Systems;258
16.1;8.1 Thermodynamic behavior of an ideal Fermi gas;258
16.2;8.2 Magnetic behavior of an ideal Fermi gas;265
16.3;8.3 The electron gas in metals;274
16.4;8.4 Ultracold atomic Fermi gases;285
16.5;8.5 Statistical equilibrium of white dwarf stars;286
16.6;8.6 Statistical model of the atom;291
16.7;Problems;296
17;Chapter 9. Thermodynamics of the Early Universe;302
17.1;9.1 Observational evidence of the Big Bang;302
17.2;9.2 Evolution of the temperature of the universe;307
17.3;9.3 Relativistic electrons, positrons, and neutrinos ;309
17.4;9.4 Neutron fraction;312
17.5;9.5 Annihilation of the positrons and electrons;314
17.6;9.6 Neutrino temperature;316
17.7;9.7 Primordial nucleosynthesis;317
17.8;