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Statistical Mechanics Made Simple by Daniel Charles Mattis Pdf
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.
Statistical Mechanics Made Simple by Daniel Charles Mattis,Robert H. Swendsen Pdf
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.
Statistical Mechanics Made Simple by Daniel C Mattis,Robert Swendsen Pdf
This second edition extends and improves on the first, already an acclaimed and original treatment of statistical concepts insofar as they impact theoretical physics and form the basis of modern thermodynamics. This book illustrates through myriad examples the principles and logic used in extending the simple laws of idealized Newtonian physics and quantum physics into the real world of noise and thermal fluctuations. In response to the many helpful comments by users of the first edition, important features have been added in this second, new and revised edition. These additions allow a more coherent picture of thermal physics to emerge. Benefiting from the expertise of the new co-author, the present edition includes a detailed exposition — occupying two separate chapters — of the renormalization group and Monte-Carlo numerical techniques, and of their applications to the study of phase transitions. Additional figures have been included throughout, as have new problems. A new Appendix presents fully worked-out solutions to representative problems; these illustrate various methodologies that are peculiar to physics at finite temperatures, that is, to statistical physics. This new edition incorporates important aspects of many-body theory and of phase transitions. It should better serve the contemporary student, while offering to the instructor a wider selection of topics from which to craft lectures on topics ranging from thermodynamics and random matrices to thermodynamic Green functions and critical exponents, from the propagation of sound in solids and fluids to the nature of quasiparticles in quantum liquids and in transfer matrices.
Statistical Mechanics Made Simple by Daniel C Mattis Pdf
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.
Thermodynamics and Statistical Mechanics by Phil Attard Pdf
The account of thermodynamics and statistical mechanics in Thermodynamics and Statistical Mechanics is based on entropy and its maximization. Building from first principles, it gives a transparent explanation of the physical behaviour of equilibrium thermodynamic systems, and it presents a comprehensive, self-contained account of the modern mathematical and computational techniques of statistical mechanics. This field of study is of vital importance to researchers, lecturers and students alike. Dr Attard is a well-known researcher in statistical mechanics who has made significant contributions to this field. His book offers a fresh perspective on the foundations of statistical thermodynamics. It includes a number of new results and novel derivations, and provides an intriguing alternative to existing monographs. Especially of note are the simple graphs and figures that illustrate the text throughout and the logical organization of the material. Thermodynamics and Statistical Mechanics will be an invaluable and comprehensive reference manual for research scientists. This text can be used as a complement to existing texts and for supplementary reading. Offers a fresh perspective on the foundations of statistical thermodynamics Includes a number of new results and novel derivations, and provides an intriguing alternative to existing monographs Simple graphs and figures illustrate the text throughout Logical organization of material An invaluable and comprehensive reference manual for research scientists Can be used as a complement to existing texts and for supplementary reading
Advanced Statistical Mechanics by Barry M McCoy Pdf
McCoy presents the advances made in statistical mechanics over the last 50 years, including mathematical theorems on order and phase transitions, numerical and series computations of phase diagrams and solutions for important solvable models such as Ising and 8 vortex.
Statistical Mechanics for the Liquid State by Jean-Louis Bretonnet Pdf
In a simple and accessible form, this book presents a unified approach to the physics of the liquid state, both in and out of equilibrium. It discerns, behind the seemingly anarchistic proliferation of phenomena observable in the liquid state, the sequence of causes and effects and, where appropriate, the underlying rules that preside over the general principles. The book begins by introducing the fundamental concepts of statistical mechanics, such as classical and quantum mechanics, probability theory, and the kinetic theory of gases, before moving on to discuss theoretical methods in order to contextualise the study of liquids. The last final section is devoted to ordering in complex fluids. It includes detailed technical notes and explicit calculations, and will appeal to graduate students in physics and chemistry. It will also be of interest the reader interested in statistical mechanics and their application to the physics of dense matter. This book will certainly become an indispensable reference for students and researchers who wish to become familiar with a multifaceted process looking towards new horizons.
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.
Statistical Mechanics in a Nutshell by Luca Peliti Pdf
A concise introduction to statistical mechanics Statistical mechanics is one of the most exciting areas of physics today, and it also has applications to subjects as diverse as economics, social behavior, algorithmic theory, and evolutionary biology. Statistical Mechanics in a Nutshell offers the most concise, self-contained introduction to this rapidly developing field. Requiring only a background in elementary calculus and elementary mechanics, this book starts with the basics, introduces the most important developments in classical statistical mechanics over the last thirty years, and guides readers to the very threshold of today's cutting-edge research. Statistical Mechanics in a Nutshell zeroes in on the most relevant and promising advances in the field, including the theory of phase transitions, generalized Brownian motion and stochastic dynamics, the methods underlying Monte Carlo simulations, complex systems—and much, much more. The essential resource on the subject, this book is the most up-to-date and accessible introduction available for graduate students and advanced undergraduates seeking a succinct primer on the core ideas of statistical mechanics. Provides the most concise, self-contained introduction to statistical mechanics Focuses on the most promising advances, not complicated calculations Requires only elementary calculus and elementary mechanics Guides readers from the basics to the threshold of modern research Highlights the broad scope of applications of statistical mechanics
Statistical Mechanics of Liquids and Solutions by Roland Kjellander Pdf
The statistical mechanical theory of liquids and solutions is a fundamental area of physical sciences with important implications for many industrial applications. This book shows how you can start from basic laws for the interactions and motions of microscopic particles and calculate how macroscopic systems of these particles behave, thereby explaining properties of matter at the scale that we perceive. Using this microscopic, molecular approach, the text emphasizes clarity of physical explanations for phenomena and mechanisms relevant to fluids, addressing the structure and behavior of liquids and solutions under various conditions. A notable feature is the author’s treatment of forces between particles that include nanoparticles, macroparticles, and surfaces. The book also provides an expanded, in-depth treatment of polar liquids and electrolytes.
Equilibrium Statistical Mechanics by E. Atlee Jackson Pdf
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.
Equilibrium and Non-equilibrium Statistical Mechanics by Carolyn M. Van Vliet Pdf
This book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round.
In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.
Learning is one of the things that humans do naturally, and it has always been a challenge for us to understand the process. Nowadays this challenge has another dimension as we try to build machines that are able to learn and to undertake tasks such as datamining, image processing and pattern recognition. We can formulate a simple framework, artificial neural networks, in which learning from examples may be described and understood. The contribution to this subject made over the last decade by researchers applying the techniques of statistical mechanics is the subject of this book. The authors provide a coherent account of various important concepts and techniques that are currently only found scattered in papers, supplement this with background material in mathematics and physics and include many examples and exercises to make a book that can be used with courses, or for self-teaching, or as a handy reference.
