Wang J. Advanced Statistical Mechanics 2022

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Wang J. Advanced Statistical Mechanics 2022

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Textbook in PDF format Statistical mechanics is a fundamental subject that every graduate student of physics needs to learn. It is fundamental as physical systems cannot exist in isolation, either because of small but definite interactions with other parts of the world or interactions among similar entities, such as a collection of gas molecules. This book arises out of many years of teaching of a course known as “Advanced Statistical Mechanics.” This book, parallel to the taught course, will begin by reviewing the basics of equilibrium statistical mechanics. The materials should already have been learned in an under graduate statistical mechanics class. Thus, the coverage will be somewhat formal and brief. We will then go on to interacting systems, such as the van der Waals gas and the Ising model, with mean-field theories of phase transi tions, and certain exact methods. The second part of the book will contain more advanced topics of nonequilibrium statistical mechanics, which covers Brownian motion, Langevin equations, Fokker-Planck equations, Kubo’s linear response theory, Boltzmann equations, and the Jarzynski equality. The book, as a whole, offers a semester’s worth of contents — about 13 weeks of lectures. I have also collected a good number of problems which should be helpful to students in reinforcing fundamental concepts. Preface Thermodynamics Foundation of Statistical Mechanics, Statistical Ensembles Quantum Statistical Mechanics Phase Transitions, van der Waals Equation Ising Models and Mean-Field Theories Ising Models: Exact Methods Critical Exponents, Scaling, and Renormalization Group Monte Carlo Methods Brownian Motion — Langevin and Fokker-Planck Equations Systems Near and Far from Equilibrium — Linear Response Theory and Jarzynski Equality The Boltzmann Equation