Volume 5.

This volume is a compilation of carefully selected questions at the PhD qualifying exam level, including many actual questions from Columbia University, University of Chicago, MIT, State University of New York at Buffalo, Princeton University, University of Wisconsin and the University of California at Berkeley over a twenty-year period. Topics covered in this book include the laws of thermodynamics, phase changes, Maxwell-Boltzmann statistics and kinetic theory of gases.This latest edition has been updated with more problems and solutions and the original problems have also been modernized, excluding outdated questions and emphasizing those that rely on calculations. The problems range from fundamental to advanced in a wide range of topics on thermodynamics and statistical physics, easily enhancing the student's knowledge through workable exercises. Simple-to-solve problems play a useful role as a first check of the student's level of knowledge whereas difficult problems will challenge the student's capacity on finding the solutions.

A thorough understanding of statistical mechanics depends strongly on the insights and manipulative skills that are acquired through the solving of problems. Problems on Statistical Mechanics provides over 120 problems with model solutions, illustrating both basic principles and applications that range from solid-state physics to cosmology. An introductory chapter provides a summary of the basic concepts and results that are needed to tackle the problems, and also serves to establish the notation that is used throughout the book. The problems themselves occupy five chapters, progressing from the simpler aspects of thermodynamics and equilibrium statistical ensembles to the more challenging ideas associated with strongly interacting systems and nonequilibrium processes. Comprehensive solutions to all of the problems are designed to illustrate efficient and elegant problem-solving techniques. Where appropriate, the authors incorporate extended discussions of the points of principle that arise in the course of the solutions. The appendix provides useful mathematical formulae.

The material for these volumes has been selected from 20 years of examination questions for graduate students at the University of California at Berkeley, Columbia University, University of Chicago, MIT, SUNY at Buffalo, Princeton University and the University of ...

Newtonian mechanics : dynamics of a point mass (1001-1108) - Dynamics of a system of point masses (1109-1144) - Dynamics of rigid bodies (1145-1223) - Dynamics of deformable bodies (1224-1272) - Analytical mechanics : Lagrange's equations (2001-2027) - Small oscillations (2028-2067) - Hamilton's canonical equations (2068-2084) - Special relativity (3001-3054).

Statistical mechanics is concerned with defining the thermodynamic properties of a macroscopic sample in terms of the properties of the microscopic systems of which it is composed. The previous book Introduction to Statistical Mechanics provided a clear, logical, and self-contained treatment of equilibrium statistical mechanics starting from Boltzmann's two statistical assumptions, and presented a wide variety of applications to diverse physical assemblies. An appendix provided an introduction to non-equilibrium statistical mechanics through the Boltzmann equation and its extensions. The coverage in that book was enhanced and extended through the inclusion of many accessible problems. The current book provides solutions to those problems. These texts assume only introductory courses in classical and quantum mechanics, as well as familiarity with multi-variable calculus and the essentials of complex analysis. Some knowledge of thermodynamics is also assumed, although the analysis starts with an appropriate review of that topic. The targeted audience is first-year graduate students and advanced undergraduates, in physics, chemistry, and the related physical sciences. The goal of these texts is to help the reader obtain a clear working knowledge of the very useful and powerful methods of equilibrium statistical mechanics and to enhance the understanding and appreciation of the more advanced texts.

Well respected and widely used, this volume presents problems and full solutions related to a wide range of topics in thermodynamics, statistical physics, and statistical mechanics. The text is intended for instructors, undergraduates, and graduate students of mathematics, physics, chemistry, and engineering. Twenty-eight chapters, each prepared by an expert, proceed from simpler to more difficult subjects. Similarly, the early chapters are easier than the later ones, making the book ideal for independent study. Subjects begin with the laws of thermodynamics and statistical theory of information and of ensembles, advancing to the ideal classical gases of polyatomic molecules, non-electrolyte liquids and solutions, and surfaces. Subsequent chapters explore imperfect classical and quantum gas, phase transitions, cooperative phenomena, Green function methods, the plasma, transport in gases and metals, Nyquist's theorem and its generalizations, stochastic methods, and many other topics.

Nobel Laureate's brilliant attempt to develop a simple, unified standard method of dealing with all cases of statistical thermodynamics — classical, quantum, Bose-Einstein, Fermi-Dirac, etc.

This book develops in detail the statistical foundations of nonequilibrium thermodynamics, based on the mathematical theory of Brownian motion. Author Bernard H. Lavenda demonstrates that thermodynamic criteria emerge in the limit of small thermal fluctuations and in the Gaussian limit where means and modes of the distribution coincide. His treatment assumes the theory of Brownian motion to be a general and practical model of irreversible processes that are inevitably influenced by random thermal fluctuations. This unifying approach permits the extraction of widely applicable principles from the analysis of specific models. Arranged by argument rather than theory, the text is based on the premises that random thermal fluctuations play a decisive role in governing the evolution of nonequilibrium thermodynamic processes and that they can be viewed as a dynamic superposition of many random events. Intended for nonmathematicians working in the areas of nonequilibrium thermodynamics and statistical mechanics, this book will also be of interest to chemical physicists, condensed matter physicists, and readers in the area of nonlinear optics.

This book addresses problems in three main developments in modern condensed matter physics– namely topological superconductivity, many-body localization and strongly interacting condensates/superfluids–by employing fruitful analogies from classical mechanics. This strategy has led to tangible results, firstly in superconducting nanowires: the density of states, a smoking gun for the long sought Majorana zero mode is calculated effortlessly by mapping the problem to a textbook-level classical point particle problem. Secondly, in localization theory even the simplest toy models that exhibit many-body localization are mathematically cumbersome and results rely on simulations that are limited by computational power. In this book an alternative viewpoint is developed by describing many-body localization in terms of quantum rotors that have incommensurate rotation frequencies, an exactly solvable system. Finally, the fluctuations in a strongly interacting Bose condensate and superfluid, a notoriously difficult system to analyze from first principles, are shown to mimic stochastic fluctuations of space-time due to quantum fields. This analogy not only allows for the computation of physical properties of the fluctuations in an elegant way, it sheds light on the nature of space-time. The book will be a valuable contribution for its unifying style that illuminates conceptually challenging developments in condensed matter physics and its use of elegant mathematical models in addition to producing new and concrete results.