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### Paul D. Beale

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3rd Edition - February 28, 2011

Author: Paul D. Beale

eBook ISBN:

9 7 8 - 0 - 1 2 - 3 8 2 1 8 9 - 8

Statistical Mechanics explores the physical properties of matter based on the dynamic behavior of its microscopic constituents. After a historical introduction, this book presents… Read more

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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 gases
- Thermodynamics of the early universe
- Computer simulations: Monte Carlo and molecular dynamics
- Correlation functions and scattering
- Fluctuation-dissipation theorem and the dynamical structure factor
- Chemical equilibrium
- Exact solution of the two-dimensional Ising model for finite systems
- Degenerate atomic Fermi gases
- Exact solutions of one-dimensional fluid models
- Interactions in ultracold Bose and Fermi gases
- Brownian motion of anisotropic particles and harmonic oscillators

Graduate and Advanced Undergraduate Students in Physics. Researchers in the field of Statisical Physics

Chapter 1: The Statistical Basis of Thermodynamics

1.1 The macroscopic and the microscopic states

1.2 Contact between statistics and thermodynamics: physical significance of the number Ω(N, V, E)

1.3 Further contact between statistics and thermodynamics

1.4 The classical ideal gas

1.5 The entropy of mixing and the Gibbs paradox

1.6 The “correct” enumeration of the microstates

Problems

Chapter 2: Elements of Ensemble Theory

2.1 Phase space of a classical system

2.2 Liouville’s theorem and its consequences

2.3 The microcanonical ensemble

2.4 Examples

2.5 Quantum states and the phase space

Problems

Chapter 3: The Canonical Ensemble

3.1 Equilibrium between a system and a heat reservoir

3.2 A system in the canonical ensemble

3.3 Physical significance of the various statistical quantities in the canonical ensemble

3.4 Alternative expressions for the partition function

3.5 The classical systems

3.6 Energy fluctuations in the canonical ensemble: correspondence with the microcanonical ensemble

3.7 Two theorems — the “equipartition” and the “virial”

3.8 A system of harmonic oscillators

3.9 The statistics of paramagnetism

3.10 Thermodynamics of magnetic systems: negative temperatures

Problems

Chapter 4: The Grand Canonical Ensemble

4.1 Equilibrium between a system and a particle-energy reservoir

4.2 A system in the grand canonical ensemble

4.3 Physical significance of the various statistical quantities

4.4 Examples

4.5 Density and energy fluctuations in the grand canonical ensemble: correspondence with other ensembles

4.6 Thermodynamic phase diagrams

4.7 Phase equilibrium and the Clausius–Clapeyron equation

Problems

Chapter 5: Formulation of Quantum Statistics

5.1 Quantum-mechanical ensemble theory: the density matrix

5.2 Statistics of the various ensembles

5.3 Examples

5.4 Systems composed of indistinguishable particles

5.5 The density matrix and the partition function of a system of free particles

Problems

Chapter 6: The Theory of Simple Gases

6.1 An ideal gas in a quantum-mechanical microcanonical ensemble

6.2 An ideal gas in other quantum-mechanical ensembles

6.3 Statistics of the occupation numbers

6.4 Kinetic considerations

6.5 Gaseous systems composed of molecules with internal motion

6.6 Chemical equilibrium

Problems

Chapter 7: Ideal Bose Systems

7.1 Thermodynamic behavior of an ideal Bose gas

7.2 Bose-Einstein condensation in ultracold atomic gases

7.3 Thermodynamics of the blackbody radiation

7.4 The field of sound waves

7.5 Inertial density of the sound field

7.6 Elementary excitations in liquid helium II

Problems

Chapter 8: Ideal Fermi Systems

8.1 Thermodynamic behavior of an ideal Fermi gas

8.2 Magnetic behavior of an ideal Fermi gas

8.3 The electron gas in metals

8.4 Ultracold atomic Fermi gases

8.5 Statistical equilibrium of white dwarf stars

8.6 Statistical model of the atom

Problems

Chapter 9: Thermodynamics of the Early Universe

9.1 Observational evidence of the Big Bang

9.2 Evolution of the temperature of the universe

9.3 Relativistic electrons, positrons, and neutrinos

9.4 Neutron fraction

9.5 Annihilation of the positrons and electrons

9.6 Neutrino temperature

9.7 Primordial nucleosynthesis

9.8 Recombination

9.9 Epilogue

Problems

Chapter 10: Statistical Mechanics of Interacting Systems: The Method of Cluster Expansions

10.1 Cluster expansion for a classical gas

10.2 Virial expansion of the equation of state

10.3 Evaluation of the virial coefficients

10.4 General remarks on cluster expansions

10.5 Exact treatment of the second virial coefficient

10.6 Cluster expansion for a quantum-mechanical system

10.7 Correlations and scattering

Problems

Chapter 11: Statistical Mechanics of Interacting Systems: The Method of Quantized Fields

11.1 The formalism of second quantization

11.2 Low-temperature behavior of an imperfect Bose gas

11.3 Low-lying states of an imperfect Bose gas

11.4 Energy spectrum of a Bose liquid

11.5 States with quantized circulation

11.6 Quantized vortex rings and the breakdown of superfluidity

11.7 Low-lying states of an imperfect Fermi gas

11.8 Energy spectrum of a Fermi liquid: Landau’s phenomenological theory21

11.9 Condensation in Fermi systems

Problems

Chapter 12: Phase Transitions: Criticality, Universality, and Scaling

12.1 General remarks on the problem of condensation

12.2 Condensation of a van der Waals gas

12.3 A dynamical model of phase transitions

12.4 The lattice gas and the binary alloy

12.5 Ising model in the zeroth approximation

12.6 Ising model in the first approximation

12.7 The critical exponents

12.8 Thermodynamic inequalities

12.9 Landau’s phenomenological theory

12.10 Scaling hypothesis for thermodynamic functions

12.11 The role of correlations and fluctuations

12.12 The critical exponents ν and η

12.13 A final look at the mean field theory

Problems

Chapter 13: Phase Transitions: Exact (or Almost Exact) Results for Various Models

13.1 One-dimensional fluid models

13.2 The Ising model in one dimension

13.3 The n-vector models in one dimension

13.4 The Ising model in two dimensions

13.5 The spherical model in arbitrary dimensions

13.6 The ideal Bose gas in arbitrary dimensions

13.7 Other models

Problems

Chapter 14: Phase Transitions: The Renormalization Group Approach

14.1 The conceptual basis of scaling

14.2 Some simple examples of renormalization

14.3 The renormalization group: general formulation

14.4 Applications of the renormalization group

14.5 Finite-size scaling

Problems

Chapter 15: Fluctuations and Nonequilibrium Statistical Mechanics

15.1 Equilibrium thermodynamic fluctuations

15.2 The Einstein–Smoluchowski theory of the Brownian motion

15.3 The Langevin theory of the Brownian motion

15.4 Approach to equilibrium: the Fokker–Planck equation

15.5 Spectral analysis of fluctuations: the Wiener–Khintchine theorem

15.6 The fluctuation–dissipation theorem

15.7 The Onsager relations

Problems

Chapter 16: Computer Simulations

16.1 Introduction and statistics

16.2 Monte Carlo simulations

16.3 Molecular dynamics

16.4 Particle simulations

16.5 Computer simulation caveats

Problems

- No. of pages: 744
- Language: English
- Published: February 28, 2011
- Imprint: Academic Press
- eBook ISBN: 9780123821898

PB

Paul D. Beale is a Professor of Physics at the University of Colorado Boulder. He earned a B.S. in Physics with Highest Honors at the University of North Carolina Chapel Hill in 1977, and Ph.D. in Physics from Cornell University in 1982. He served as a postdoctoral research associate at the Department of Theoretical Physics at Oxford University from 1982-1984. He joined the faculty of the University of Colorado Boulder in 1984 as an assistant professor, was promoted to associate professor in 1991, and professor in 1997. He served as the Chair of the Department of Physics from 2008-2016. He also served as Associate Dean for Natural Sciences in the College of Arts and Sciences, and Director of the Honors Program. He is currently Director of the Buffalo Bicycle Classic, the largest scholarship fundraising event in the State of Colorado. Beale is a theoretical physicist specializing in statistical mechanics, with emphasis on phase transitions and critical phenomena. His work includes renormalization group methods, finite-size scaling in spin models, fracture modes in random materials, dielectric breakdown in metal-loaded dielectrics, ferroelectric switching dynamics, exact solutions of the finite two-dimensional Ising model, solid-liquid phase transitions of molecular systems, and ordering in layers of molecular dipoles. His current interests include scalable parallel pseudorandom number generators, and interfacing quantum randomness with cryptographically secure pseudorandom number generators. He is coauthor with Raj Pathria of the third and fourth editions of the graduate physics textbook Statistical Mechanics. The Boulder Faculty Assembly has honored him with the Excellence in Teaching and Pedagogy Award, and the Excellence in Service and Leadership Award. Beale is a private pilot and an avid cyclist. He is married to Erika Gulyas, and has two children: Matthew and Melanie.

Affiliations and expertise

Professor of Physics, University of Colorado, Boulder, USA