Lectures On Mathematical Statistical Mechanics
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| Author | : Robert Adolʹfovich Minlos |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 114 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821813374 |
This book presents a mathematically rigorous approach to the main ideas and phenomena of statistical physics. The introduction addresses the physical motivation, focusing on the basic concept of modern statistical physics, that is the notion of Gibbsian random fields. Properties of Gibbsian fields are analysed in two ranges of physical parameters: "regular" (corresponding to high-temperature and low-density regimes) where no phase transition is exhibited, and "singular" (low temperature regimes) where such transitions occur. Next, a detailed approach to the analysis of the phenomena of phase transitions of the first kind, the Pirogov-Sinai theory, is presented. The author discusses this theory in a general way and illustrates it with the example of a lattice gas with three types of particles. The conclusion gives a brief review of recent developments arising from this theory. The volume is written for the beginner, yet advanced students will benefit from it as well. The book will serve nicely as a supplementary textbook for course study. The prerequisites are an elementary knowledge of mechanics, probability theory and functional analysis.
| Author | : Sacha Friedli |
| Publisher | : Cambridge University Press |
| Total Pages | : 643 |
| Release | : 2017-11-23 |
| Genre | : Mathematics |
| ISBN | : 1107184827 |
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
| Author | : John Cardy |
| Publisher | : Cambridge University Press |
| Total Pages | : 180 |
| Release | : 2008-12-11 |
| Genre | : Mathematics |
| ISBN | : 9780521715140 |
This self-contained volume introduces modern methods of statistical mechanics in turbulence, with three harmonised lecture courses by world class experts.
| Author | : George D.J. Phillies |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 441 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461212642 |
This textbook for graduates and advanced undergraduates in physics and physical chemistry covers the major areas of statistical mechanics and concludes with the level of current research. It begins with the fundamental ideas of averages and ensembles, focusing on classical systems described by continuous variables such as position and momentum, and using the ideal gas as an example. It then turns to quantum systems, beginning with diatomic molecules and working up through blackbody radiation and chemical equilibria. The discussion of equilibrium properties of systems of interacting particles includes such techniques as cluster expansions and distribution functions and uses non-ideal gases, liquids, and solutions. Dynamic behavior -- treated here more extensively than in other texts -- is discussed from the point of view of correlation functions. The text concludes with the problem of diffusion in a suspension of interacting hard spheres and what can be learned about such a system from scattered light. Intended for a one-semester course, the text includes several "asides" on topics usually omitted from introductory courses, as well as numerous exercises.
| Author | : Martin Loebl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 187 |
| Release | : 2010-02-16 |
| Genre | : Science |
| ISBN | : 3834893293 |
The book first describes connections between some basic problems and technics of combinatorics and statistical physics. The discrete mathematics and physics terminology are related to each other. Using the established connections, some exciting activities in one field are shown from a perspective of the other field. The purpose of the book is to emphasize these interactions as a strong and successful tool. In fact, this attitude has been a strong trend in both research communities recently. It also naturally leads to many open problems, some of which seem to be basic. Hopefully, this book will help making these exciting problems attractive to advanced students and researchers.
| Author | : Oliver Bühler |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 165 |
| Release | : 2006-10-12 |
| Genre | : Mathematics |
| ISBN | : 0821842323 |
This book provides a rapid overview of the basic methods and concepts in mechanics for beginning Ph.D. students and advanced undergraduates in applied mathematics or related fields. It is based on a graduate course given in 2006-07 at the Courant Institute of Mathematical Sciences. Among other topics, the book introduces Newton's law, action principles, Hamilton-Jacobi theory, geometric wave theory, analytical and numerical statistical mechanics, discrete and continuous quantum mechanics, and quantum path-integral methods. The focus is on fundamental mathematical methods that provide connections between seemingly unrelated subjects. An example is Hamilton-Jacobi theory, which appears in the calculus of variations, in Fermat's principle of classical mechanics, and in the geometric theory of dispersive wavetrains. The material is developed in a sequence of simple examples and the book can be used in a one-semester class on classical, statistical, and quantum mechanics. Some familiarity with differential equations is required but otherwise the book is self-contained. In particular, no previous knowledge of physics is assumed. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
| Author | : M. G. Bowler |
| Publisher | : Newnes |
| Total Pages | : 131 |
| Release | : 2012-12-02 |
| Genre | : Science |
| ISBN | : 0080984053 |
Lectures on Statistical Mechanics
| Author | : Kerson Huang |
| Publisher | : World Scientific |
| Total Pages | : 159 |
| Release | : 2005-05-30 |
| Genre | : Science |
| ISBN | : 9814481068 |
This book introduces an approach to protein folding from the point of view of kinetic theory. There is an abundance of data on protein folding, but few proposals are available on the mechanism driving the process. Here, presented for the first time, are suggestions on possible research directions, as developed by the author in collaboration with C C Lin.The first half of this invaluable book contains a concise but relatively complete review of relevant topics in statistical mechanics and kinetic theory. It includes standard topics such as thermodynamics, the Maxwell-Boltzmann distribution, and ensemble theory. Special discussions include the dynamics of phase transitions, and Brownian motion as an illustration of stochastic processes.The second half develops topics in molecular biology and protein structure, with a view to discovering mechanisms underlying protein folding. Attention is focused on the energy flow through the protein in its folded state. A mathematical model, based on the Brownian motion of coupled harmonic oscillators, is worked out in the appendix.
| Author | : Aleksandr I?Akovlevich Khinchin |
| Publisher | : Courier Corporation |
| Total Pages | : 212 |
| Release | : 1949-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780486601472 |
Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.
| Author | : Wolfgang Pauli |
| Publisher | : Courier Corporation |
| Total Pages | : 162 |
| Release | : 2000-01-01 |
| Genre | : Science |
| ISBN | : 9780486414614 |
Examines basic concepts and the First Law, Second Law, equilibria, Nernst's Heat Theorem, and the kinetic theory of gases. Includes an index and a wealth of figures. An important resource for students and physicists, it can be read independently by those who wish to focus on individual topics. 1973 edition.
