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This 2006 textbook provides a concise introduction to the key concepts and tools of statistical mechanics. It also covers advanced topics such as non-relativistic quantum field theory and numerical methods. After introducing classical analytical techniques, such as cluster expansion and Landau theory, the authors present important numerical methods with applications to magnetic systems, Lennard-Jones fluids and biophysics. Quantum statistical mechanics is discussed in detail and applied to Bose-Einstein condensation and topics in astrophysics and cosmology. In order to describe emergent phenomena in interacting quantum systems, canonical non-relativistic quantum field theory is introduced and then reformulated in terms of Feynman integrals. Combining the authors' many years' experience of teaching courses in this area, this textbook is ideal for advanced undergraduate and graduate students in physics, chemistry and mathematics.
This book deals with the basic principles and techniques of nonequilibrium statistical mechanics. The importance of this subject is growing rapidly in view of the advances being made, both experimentally and theoretically, in statistical physics, chemical physics, biological physics, complex systems and several other areas. The presentation of topics is quite self-contained, and the choice of topics enables the student to form a coherent picture of the subject. The approach is unique in that classical mechanical formulation takes center stage. The book is of particular interest to advanced undergraduate and graduate students in engineering departments.
Key features include an elementary introduction to probability, distribution functions, and uncertainty; a review of the concept and significance of energy; and various models of physical systems. 1968 edition.
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.
Statistical Mechanics discusses the fundamental concepts involved in understanding the physical properties of matter in bulk on the basis of the dynamical behavior of its microscopic constituents. The book emphasizes the equilibrium states of physical systems. The text first details the statistical basis of thermodynamics, and then proceeds to discussing the elements of ensemble theory. The next two chapters cover the canonical and grand canonical ensemble. Chapter 5 deals with the formulation of quantum statistics, while Chapter 6 talks about the theory of simple gases. Chapters 7 and 8 examine the ideal Bose and Fermi systems. In the next three chapters, the book covers the statistical mechanics of interacting systems, which includes the method of cluster expansions, pseudopotentials, and quantized fields. Chapter 12 discusses the theory of phase transitions, while Chapter 13 discusses fluctuations. The book will be of great use to researchers and practitioners from wide array of disciplines, such as physics, chemistry, and engineering.
This concise, elementary treatment illustrates the ways in which an atomic-molecular perspective yields new insights and powers operative in the realms of macroscopic thermodynamics. Starting with an analysis of some very simple microcanonical ensembles, it proceeds to the Boltzmann distribution law and a systematic exploration of the proper formulation, evaluation, and application of partition functions. The concepts of equilibrium and entropy thus acquire new significance, and readers discover how thermodynamic parameters may be calculated from spectroscopic data. Encompassing virtually all of the forms of statistical mechanics customary to undergraduate physical chemistry books, this brief text requires prior acquaintance with only the rudiments of the calculus and a few of the simplest propositions of classical thermodynamics. Appropriate for introductory college chemistry courses, it further lends itself to use as a supplementary text for independent study by more advanced students.
Elementary concepts in statistics and probability - The ising model and the lattice gas - Elements of thermodynamics - Statistical mechanics - The world of bosons - All about fermions : theories of metals, superconductors, semiconductors - Kinetic theory - The transfer matrix - Some uses of quantum field theory in statistical physics.
This unique and consistent mathematical treatise contains a deductive description of equilibrium statistics and thermodynamics. The most important elements of non-equilibrium phenomena are also treated. In addition to the fundamentals, the text tries to show how large the area of statistical mechanics is and how many applications can be found here. Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications in critical dynamics, as well as fundamental thoughts of irreversibility are discussed. The text will be useful for advanced students in physics and other sciences who have profound knowledge of quantum mechanics.