Statistical Mechanics Made Simple A Guide For Students And Researchers
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Statistical Mechanics Made Simple: A Guide For Students And Researchers
Author: Daniel C Mattis
language: en
Publisher: World Scientific Publishing Company
Release Date: 2003-04-08
This book is an elaboration of the author's lecture notes in a graduate course in statistical physics and thermodynamics, augmented by some material suitable for self-teaching as well as for undergraduate study. The first 4 or 5 chapters are suitable for an undergraduate course for engineers and physicists in Thermodynamics and Statistical Physics and include detailed study of the various ensembles and their connections to applied thermodynamics. The Debye law of specific heats and reasons for deviations from the Debye formulas are covered, as are the Einstein theories of Brownian motion, black-body radiation and specific heat of solids. Van der Waals gases and the reason for the apparent failure of his Law of Corresponding States are discussed.The last 5 chapters treat topics of recent interest to researchers, including: the Ising and Potts models, spin waves in ferromagnetic and anti-ferromagnetic media, sound propagation in non-ideal gases and the decay of sound waves, introduction to the understanding of glasses and spin glasses, superfluidity and superconductivity.The selection of material is wide-ranging and the mathematics for handling it completely self-contained, ranging from counting (probability theory) to quantum field theory as used in the study of fermions, bosons and as an adjunct in the solutions of the equations of classical diffusion-reaction theory. In addition to the standard material found in most recent books on statistical physics the constellation of topics covered in this text includes numerous original items:• Generalization of “negative temperature” to interacting spins• Derivation of Gibbs' factor from first principles• Exact free energy of interacting particles in 1D (e.g., classical and quantum Tonk's gas)• Introduction to virial expansions, Equations of State, Correlation Functions and “critical exponents”• Superfluidity in ideal and non-ideal fluids (both Bogolubov and Feynman theories)• Superconductivity: thermodynamical approach and the BCS theory• Derivation of “Central Limit Theorem” and its applications• Boltzmann's “H-Theorem” and the nonlinear Boltzmann equation• Exact solution of nonlinear Boltzmann Equation for electrons in time-dependent electric field and the derivation of Joule heating, transport parameters in crossed electric and magnetic fields, etc.• Frequency spectrum and decay of sound waves in gases• Exact evaluation of free energy and thermodynamic properties of the two-dimensional Ising model in regular and fully frustrated (spin-glass like) lattices• The “zipper” model of crystal fracture or polymer coagulation — calculation of Tc• Potts model in 2D: duality and Tc• “Doi's theory” of diffusion-limited chemical reactions with some exact results — including the evaluation of statistical fluctuations in radioactive decay• Thermodynamic Green Functions and their applications to fermions and bosons with an example drawn from random matrix theory and much more.
Statistical Mechanics Made Simple
This second edition extends and improves on the first, illustrating through myriad examples, the principles and logic used in extending the simple laws of idealised Newtonian physics and quantum physics into the real world of noise and thermal fluctuations.
Theory Of Magnetism Made Simple, The: An Introduction To Physical Concepts And To Some Useful Mathematical Methods
Author: Daniel C Mattis
language: en
Publisher: World Scientific Publishing Company
Release Date: 2006-03-10
This new version of a classic updates much of the material in earlier editions, including the first chapter, on the history of the field. Important modifications reflect major discoveries of the past decades. A historical perspective is maintained throughout. The reader is drawn into the process of discovery: starting with a phenomenon, finding plausible explanations and competing theories — and finally, the solution.The theory of magnetism is practically a metaphor for theoretical physics. The very first quantum many-body theory (Bethe's ansatz) was devised for magnetic chains, just as mean-field theory was invented a century ago by Weiss to explain Curie's Law.The first two chapters of this book are immensely readable, taking us from prehistory to the “spin valves” of the most recent past. Topics in subsequent chapters include: angular momenta and spin (Chapter 3), quantum theory of simple systems, followed by increasingly technical insights into ordered and random systems, thermal fluctuations, phase transitions, chaos and the like. Contemporary developments in nanotechnology now seek to take advantage of the electron's spin as well as of its charge. The time is not far off when nano-circuits made entirely of silicon exhibit such many-body properties as superconductivity or ferromagnetism — without any superconducting materials or magnetic ions being present. The reader of this book will be prepared for such exotic twenty-first century applications.Daniel C Mattis, BS, MS, PhD, Fellow of the American Physical Society (APS), is a frequent lecturer at research institutions and the author of several textbooks and numerous research articles. His expertise includes many-body theory, electrical conductivity, quantum theory of magnetism and most recently, nanotechnology. Prof. Mattis is on the editorial panel for high-temperature superconductivity of the International Journal of Modern Physics B and Modern Physics Letters B, both published by World Scientific. Currently serving as Professor in the Physics department at the University of Utah in Salt Lake City, Utah, USA, at various times he has been visiting Professor at Yale University (New Haven), State University of New York (Buffalo), Temple University (Philadelphia), and served as “Wei-Lun Visiting Professor” at the Chinese University of Hong Kong. A founding member of the “Few-Body Physics” section of the APS, he has also served as Chair of the standing committee of the APS for the “International Freedom of Scientists.”