Intermediate Statistical Mechanics
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Intermediate Statistical Mechanics
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Author : Jayanta K Bhattacharjee
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-12-15
Intermediate Statistical Mechanics written by Jayanta K Bhattacharjee and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-15 with Science categories.
In this new textbook, a number of unusual applications are discussed in addition to the usual topics covered in a course on Statistical Physics. Examples are: statistical mechanics of powders, Peierls instability, graphene, Bose-Einstein condensates in a trap, Casimir effect and the quantum Hall effect. Superfluidity and super-conductivity (including the physics of high-temperature superconductors) have also been discussed extensively.The emphasis on the treatment of these topics is pedagogic, introducing the basic tenets of statistical mechanics, with extensive and thorough discussion of the postulates, ensembles, and the relevant statistics. Many standard examples illustrate the microcanonical, canonical and grand canonical ensembles, as well as the Bose-Einstein and Fermi-Dirac statistics.A special feature of this text is the detailed presentation of the theory of second-order phase transitions and the renormalization group, emphasizing the role of disorder. Non-equilibrium statistical physics is introduced via the Boltzmann transport equation. Additional topics covered here include metastability, glassy systems, the Langevin equation, Brownian motion, and the Fokker-Planck equation.Graduate students will find the presentation readily accessible, since the topics have been treated with great deal of care and attention to detail.
Statistical Mechanics An Intermediate Course 2nd Edition
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Author : Elisa Ercolessi
language : en
Publisher: World Scientific Publishing Company
Release Date : 2001-05-17
Statistical Mechanics An Intermediate Course 2nd Edition written by Elisa Ercolessi and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-17 with Science categories.
This book covers the foundations of classical thermodynamics, with emphasis on the use of differential forms of classical and quantum statistical mechanics, and also on the foundational aspects. In both contexts, a number of applications are considered in detail, such as the general theory of response, correlations and fluctuations, and classical and quantum spin systems. In the quantum case, a self-contained introduction to path integral methods is given. In addition, the book discusses phase transitions and critical phenomena, with applications to the Landau theory and to the Ginzburg-Landau theory of superconductivity, and also to the phenomenon of Bose condensation and of superfluidity. Finally, there is a careful discussion on the use of the renormalization group in the study of critical phenomena.
Advanced Statistical Mechanics
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Author : Barry M McCoy
language : en
Publisher: OUP Oxford
Release Date : 2009-12-17
Advanced Statistical Mechanics written by Barry M McCoy and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-17 with Science categories.
Statistical Mechanics is the study of systems where the number of interacting particles becomes infinite. In the last fifty years tremendous advances have been made which have required the invention of entirely new fields of mathematics such as quantum groups and affine Lie algebras. They have engendered remarkable discoveries concerning non-linear differential equations and algebraic geometry, and have produced profound insights in both condensed matter physics and quantum field theory. Unfortunately, none of these advances are taught in graduate courses in statistical mechanics. This book is an attempt to correct this problem. It begins with theorems on the existence (and lack) of order for crystals and magnets and with the theory of critical phenomena, and continues by presenting the methods and results of fifty years of analytic and computer computations of phase transitions. It concludes with an extensive presentation of four of the most important of exactly solved problems: the Ising, 8 vertex, hard hexagon and chiral Potts models.
Advanced Statistical Mechanics
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Author : Jian-Sheng Wang
language : en
Publisher: World Scientific Publishing Company
Release Date : 2021-11-30
Advanced Statistical Mechanics written by Jian-Sheng Wang and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-30 with Science categories.
This short textbook covers roughly 13 weeks of lectures on advanced statistical mechanics at the graduate level. It starts with an elementary introduction to the theory of ensembles from classical mechanics, and then goes on to quantum statistical mechanics with density matrix. These topics are covered concisely and briefly. The advanced topics cover the mean-field theory for phase transitions, the Ising models and their exact solutions, and critical phenomena and their scaling theory. The mean-field theories are discussed thoroughly with several different perspectives -- focusing on a single degree, or using Feynman-Jensen-Bogoliubov inequality, cavity method, or Landau theory. The renormalization group theory is mentioned only briefly. As examples of computational and numerical approach, there is a chapter on Monte Carlo method including the cluster algorithms. The second half of the book studies nonequilibrium statistical mechanics, which includes the Brownian motion, the Langevin and Fokker-Planck equations, Boltzmann equation, linear response theory, and the Jarzynski equality. The book ends with a brief discussion of irreversibility. The topics are supplemented by problem sets (with partial answers) and supplementary readings up to the current research, such as heat transport with a Fokker-Planck approach. Contents: 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 Equalibrium; The Boltzmann Equation; Answers to Selected Problems; Bibliography; Index
Intermediate Statistical Mechanics
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Author : Jayanta K. Bhattacharjee
language : en
Publisher:
Release Date : 2017
Intermediate Statistical Mechanics written by Jayanta K. Bhattacharjee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
Topics In Statistical Mechanics Second Edition
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Author : Brian Cowan
language : en
Publisher: World Scientific
Release Date : 2021-07-23
Topics In Statistical Mechanics Second Edition written by Brian Cowan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-23 with Science categories.
Building on the material learned by students in their first few years of study, Topics in Statistical Mechanics (Second Edition) presents an advanced level course on statistical and thermal physics. It begins with a review of the formal structure of statistical mechanics and thermodynamics considered from a unified viewpoint. There is a brief revision of non-interacting systems, including quantum gases and a discussion of negative temperatures. Following this, emphasis is on interacting systems. First, weakly interacting systems are considered, where the interest is in seeing how small interactions cause small deviations from the non-interacting case. Second, systems are examined where interactions lead to drastic changes, namely phase transitions. A number of specific examples is given, and these are unified within the Landau theory of phase transitions. The final chapter of the book looks at non-equilibrium systems, in particular the way they evolve towards equilibrium. This is framed within the context of linear response theory. Here fluctuations play a vital role, as is formalised in the fluctuation-dissipation theorem.The second edition has been revised particularly to help students use this book for self-study. In addition, the section on non-ideal gases has been expanded, with a treatment of the hard-sphere gas, and an accessible discussion of interacting quantum gases. In many cases there are details of Mathematica calculations, including Mathematica Notebooks, and expression of some results in terms of Special Functions.
Statistical Physics Of Polymers
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Author : Toshihiro Kawakatsu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Statistical Physics Of Polymers written by Toshihiro Kawakatsu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
This book is an introductory textbook on the statistical mechanics of poly mers and complex fluids aimed at senior undergraduate and graduate stu dents and non-specialist researchers who are starting research in this field. Modern statistical mechanics on polymers and complex fluids is based on many fields, such as chemical physics, statistical mechanics, quantum me chanics, stochastic processes, theory of phase transitions, hydrodynamics, rheology, and so on. This book provides an overview of the basic concepts and methods used in current research on the physics of polymers and complex fluids. Using simple but essential examples, we describe how to derive the physical properties of polymers theoretically, focusing on the structure and dynamics on mesoscopic scales. Here, the term 'mesoscopic scales' means intermediate lengths and time scales between the microscopic atomic scale and the macroscopic scale. Properties on mesoscopic scales are the central issue of the physics of polymers and complex fluids, because these materials are well characterized by spatiotemporal structures on these scales, where we can extract universal properties that are independent of the microscopic details of the system.
Statistical Physics
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Author : Josef Honerkamp
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-19
Statistical Physics written by Josef Honerkamp and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-19 with Science categories.
The application of statistical methods to physics is essential. This unique book on statistical physics offers an advanced approach with numerous applications to the modern problems students are confronted with. Therefore the text contains more concepts and methods in statistics than the student would need for statistical mechanics alone. Methods from mathematical statistics and stochastics for the analysis of data are discussed as well. The book is divided into two parts, focusing first on the modeling of statistical systems and then on the analysis of these systems. Problems with hints for solution help the students to deepen their knowledge. The third edition has been updated and enlarged with new sections deepening the knowledge about data analysis. Moreover, a customized set of problems with solutions is accessible on the Web at extras.springer.com.
Statistical Mechanics
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Author : Franz Schwabl
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Statistical Mechanics written by Franz Schwabl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
In addition to a deductive approach to equilibrium statistics and thermodynamics based on a single hypothesis - the form of the microcanonical density matrix - this book treats the most important elements of non-equilibrium phenomena. Intermediate calculations are presented in complete detail. Problems at the end of each chapter help students to consolidate their understanding of the material. Beyond the fundamentals, this text demonstrates the breadth of the field and its great variety of applications. Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications to critical dynamics, as well as fundamental considerations of irreversibility, are discussed. The text will be useful for advanced students of physics and other natural sciences; a basic knowledge of quantum mechanics is presumed.
Mathematical Foundations Of Statistical Mechanics
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Author : A. Ya. Khinchin
language : en
Publisher: Courier Corporation
Release Date : 2013-01-17
Mathematical Foundations Of Statistical Mechanics written by A. Ya. Khinchin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-17 with Mathematics categories.
Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Reduction to the Problem of the Theory of Probability; and more.