拉杰· 帕斯里亚(R. K. Pathria)是一位理论物理学家。他因研究液氦中的超流动性、热力学量的洛伦兹变换、晶格和的严格计算以及相变中的有限尺寸效应而闻名。帕特里亚于1953年和1954年分别获得霍希尔布尔潘贾布大学理学学士和理学硕士学位,并于1957年获得德里大学物理学博士学位。曾任教于他曾在德里大学、麦克马斯特大学、阿尔伯塔大学、昌迪加尔潘贾布大学和滑铁卢大学。于2000 年加入加利福尼亚大学圣地亚哥分校,担任物理学兼职教授。滑铁卢大学授予他“杰出教师奖”和“杰出名誉教授”称号,他还是美国物理学会会员。
保罗·比尔(Paul D. Beale)是一位理论物理学家,科罗拉多大学博尔德分校的物理学教授。专攻统计力学,重点研究相变和临界现象。他的研究工作包括重正化群方法,分子系统的固液相变,以及分子偶极子层中的有序化等。他于1977年以最高荣誉获得北卡罗来纳大学教堂山分校物理学学士学位,并于1982年获得康奈尔大学物理学博士学位。1982—1984年,他在牛津大学理论物理系担任博士后助理研究员。1984年,他加入科罗拉多大学博尔德分校任助理教授,1991年晋升为副教授,1997年晋升为教授。2008—2016年,他担任物理系主任。他还曾担任文理学院自然科学副院长和荣誉项目主任。
目錄:
Preface to the fourth edition
Preface to the third edition
Preface to the second edition
Preface to the first edition
Historical introduction
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
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
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
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
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
5.6. Eigenstate thermalization hypothesis
Problems
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
ldeal 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
ldeal 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
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
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 coeffcients
10.4. General remarks on cluster expansions
10.5. Exact treatment of the second virial coeffcient
10.6. Cluster expansion for a quantum-mechanical system
10.7. Correlations and scattering
Problems
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 theory
11.9. Condensation in Fermi systems
Problems
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. Landaus 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
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
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
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
15.8. Exact equilibrium free energy differences from nonequilibrium measurements
Computer Simulations
16.1. Introduction and statistics
16.2. Monte Carlo simulations
16.3. Molecular dynamics16.3.
16.4. Particle simulations
16.5. Computer simulation caveats
Problems
Appendices
Influence of boundary conditions on the distribution of quantum statesCertain mathematical functions“Volume” and “surface area” of an n-dimensional sphere of radius ROn Bose-Einstein functionsOn Fermi-Dirac functionsA rigorous analysis of the ideal Bose gas and the onset of Bose-Einstein condensationOn Watson functionsThermodynamic relationshipsPseudorandom numbers
Bibliography
Index
內容試閱:
The third edition of Statistical mechanics was published in 201l. The new material added at that time focused on Bose-Einstein condensation and degenerate Fermi gas behavior in ultracold atomic gases, finite-size scaling behavior of Bose-Einstein condensates, thermodynamics of the early universe, chemical equilibrium, Monte Carlo and molecular dynamics simulations, correlation functions and scattering, the fluctuation-dissipation theorem and the dynamical structure factor, phase equilibrium and the Clausius-Clapeyron equation, exact solutions of one-dimensional fluid models, exact solution of the two-dimensional lsing model on a finite lattice, pseudorandom number generators, dozens of new homework problems, and a new appendix with a summary of thermodynamic assemblies and associated statistical ensembles.
The new topics added to this fourth edition are:
Eigenstate thermalization hypothesis: Mark Srednicki, Joshua Deutsch, and others discovered that it is possible for nonintegrable isolated macroscopic quantum many-body systems to equilibrate. This overturned the decades-long presumption that equilibrium behavior of isolated many-body systems was precluded because of the unitary time evolution of pure states. Even though an isolated system as a whole will not equilibrate, most macroscopic many-body systems will display equilibrium behavior for local observables, with the system as a whole serving as the reservoir for each subsystem. This behavior is the quantum equivalent to ergodic behavior in classical systems. The exceptions to this are integrable systems and strongly random systems that display many-body localization.Exact equilibrium free energy differences from nonequilibrium measurements: Christo-pher Jarzynski and Gavin Crooks showed that the average of the quantity exp(-βW) along nonequilibrium paths, where W is the external work done on the system during the transformation, depends only on equilibrium free energy differences, independent of the nonequilibrium path chosen or how far out of equilibrium the system is driven, This property is now used to measure equilibrium free energy differences using nonequilibrium transformations in experiments on physical systems and in computer simulations of model systems.We have rewritten Section 5.1 on the density matrix in coordinate-independent form using Hilbert space vectors and Dirac bra-ket notation.We have expanded Appendix H to include both electric and magnetic free energies and have rewritten equations involving magnetic fields throughout the text to express them in SI units.We have ensured that all of the edits and corrections we made in the 2014 “second printing\ of the third edition were included in this edition.We have added over 30 new end-of-chapter problems.We have made minor edits and corrections throughout the text.
R.K.P expressed his indebtedness to many people at the time of the publication of the first and second editions so, at this time, he simply reiterates his gratitude to them. P.D.B. would like to thank his friends and colleagues at the University of Colorado Boulder for the many conversations he has had with them over the years about physics research and pedagogy, many of whom assisted him with the third or fourth edition: Allan Franklin, Noel Clark, Tom DeGrand, John Price, Chuck Rogers, Michael Dubson, Leo Radzihovsky, Victor Gurarie, Michael Hermele, Rahul Nandkishore, Dan Dessau, Dmitry Reznik, Minhyea Lee, Matthew Glaser, Joseph MacLennan, Kyle McElroy, Murray Holland Heather Lewandowski, John Cumalat, Shantha de Alwis, Alex Conley, Jamie Nagle, PaulRomatschke, Noah Finkelstein, Kathy Perkins, John Blanco, Kevin Stenson, Loren Houg, Meredith Betterton, lvan Smalyukh, Colin West, Eleanor Hodby, and Eric Cornell. In addition to those, special thanks are also due to other colleagues who have read sections of the third or fourth edition manuscript, or offered valuable suggestions: Edmond Meyer Matthew Grau, Andrew Sisler, Michael Foss-Feig, Peter Joot, Jeff justice, Stephen H. White, and Harvey Leff.
P.D.B. would like to express his special gratitude to Raj Kumar Pathria for the honor of being asked to join him as coauthor at the time of publication of the third edition of his highly regarded textbook, He and his wife Erika treasure the friendships they have developed with Raj and his lovely wife Raj Kumari Pathria.
P.D.B. dedicates this edition to Erika, for everything.
R.K.P.
P.D.B.