Statistical Mechanics of Disordered Systems
Author | : Anton Bovier |
Publisher | : Cambridge University Press |
Total Pages | : 297 |
Release | : 2006-06-08 |
Genre | : Mathematics |
ISBN | : 0521849918 |
Publisher Description
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Author | : Anton Bovier |
Publisher | : Cambridge University Press |
Total Pages | : 297 |
Release | : 2006-06-08 |
Genre | : Mathematics |
ISBN | : 0521849918 |
Publisher Description
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 | : Véronique Gayrard |
Publisher | : Springer Nature |
Total Pages | : 281 |
Release | : 2019-09-15 |
Genre | : Mathematics |
ISBN | : 3030290778 |
These proceedings of the conference Advances in Statistical Mechanics, held in Marseille, France, August 2018, focus on fundamental issues of equilibrium and non-equilibrium dynamics for classical mechanical systems, as well as on open problems in statistical mechanics related to probability, mathematical physics, computer science, and biology. Statistical mechanics, as envisioned more than a century ago by Boltzmann, Maxwell and Gibbs, has recently undergone stunning twists and developments which have turned this old discipline into one of the most active areas of truly interdisciplinary and cutting-edge research. The contributions to this volume, with their rather unique blend of rigorous mathematics and applications, outline the state-of-the-art of this success story in key subject areas of equilibrium and non-equilibrium classical and quantum statistical mechanics of both disordered and non-disordered systems. Aimed at researchers in the broad field of applied modern probability theory, this book, and in particular the review articles, will also be of interest to graduate students looking for a gentle introduction to active topics of current research.
Author | : Manuel Osvaldo Cáceres |
Publisher | : Springer |
Total Pages | : 568 |
Release | : 2017-03-07 |
Genre | : Science |
ISBN | : 3319515535 |
This textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are described in sections and specific exercises throughout the text, as well as in appendices. Physical-mathematical motivation is the main driving force for the development of this text. It presents the academic topics of probability theory and stochastic processes as well as new educational aspects in the presentation of non-equilibrium statistical theory and stochastic differential equations.. In particular it discusses the problem of irreversibility in that context and the dynamics of Fokker-Planck. An introduction on fluctuations around metastable and unstable points are given. It also describes relaxation theory of non-stationary Markov periodic in time systems. The theory of finite and infinite transport in disordered networks, with a discussion of the issue of anomalous diffusion is introduced. Further, it provides the basis for establishing the relationship between quantum aspects of the theory of linear response and the calculation of diffusion coefficients in amorphous systems.
Author | : Andrea Puglisi |
Publisher | : MDPI |
Total Pages | : 335 |
Release | : 2018-09-04 |
Genre | : Mathematics |
ISBN | : 3038970573 |
This book is a printed edition of the Special Issue "Thermodynamics and Statistical Mechanics of Small Systems" that was published in Entropy
Author | : A. J. Berlinsky |
Publisher | : Springer Nature |
Total Pages | : 609 |
Release | : 2019-10-03 |
Genre | : Science |
ISBN | : 3030281876 |
In a comprehensive treatment of Statistical Mechanics from thermodynamics through the renormalization group, this book serves as the core text for a full-year graduate course in statistical mechanics at either the Masters or Ph.D. level. Each chapter contains numerous exercises, and several chapters treat special topics which can be used as the basis for student projects. The concept of scaling is introduced early and used extensively throughout the text. At the heart of the book is an extensive treatment of mean field theory, from the simplest decoupling approach, through the density matrix formalism, to self-consistent classical and quantum field theory as well as exact solutions on the Cayley tree. Proceeding beyond mean field theory, the book discusses exact mappings involving Potts models, percolation, self-avoiding walks and quenched randomness, connecting various athermal and thermal models. Computational methods such as series expansions and Monte Carlo simulations are discussed, along with exact solutions to the 1D quantum and 2D classical Ising models. The renormalization group formalism is developed, starting from real-space RG and proceeding through a detailed treatment of Wilson’s epsilon expansion. Finally the subject of Kosterlitz-Thouless systems is introduced from a historical perspective and then treated by methods due to Anderson, Kosterlitz, Thouless and Young. Altogether, this comprehensive, up-to-date, and engaging text offers an ideal package for advanced undergraduate or graduate courses or for use in self study.
Author | : Viktor Dotsenko |
Publisher | : Cambridge University Press |
Total Pages | : 236 |
Release | : 2001 |
Genre | : Science |
ISBN | : 0521773407 |
An introductory book on the statistical mechanics of disordered systems, ideal for graduates and researchers.
Author | : Robert H. Swendsen |
Publisher | : Oxford University Press |
Total Pages | : 422 |
Release | : 2012-03 |
Genre | : Mathematics |
ISBN | : 0199646945 |
This text presents statistical mechanics and thermodynamics as a theoretically integrated field of study. It stresses deep coverage of fundamentals, providing a natural foundation for advanced topics. The large problem sets (with solutions for teachers) include many computational problems to advance student understanding.
Author | : Luca Peliti |
Publisher | : Princeton University Press |
Total Pages | : 577 |
Release | : 2024-08-06 |
Genre | : Science |
ISBN | : 0691248451 |
The essential introduction to modern statistical mechanics—now completely updated and expanded Statistical mechanics is one of the most exciting areas of physics today and has applications to subjects ranging from economics and social behavior to algorithmic theory and evolutionary biology. Statistical Mechanics in a Nutshell provides a self-contained introduction to this rapidly developing field. Starting with the basics of kinetic theory and requiring only a background in elementary calculus and mechanics, this concise book discusses the most important developments of recent decades and guides readers to the very threshold of today’s cutting-edge research. Features a new chapter on stochastic thermodynamics with an introduction to the thermodynamics of information—the first treatment of its kind in an introductory textbook Offers a more detailed account of numerical simulations, including simulated annealing and other accelerated Monte Carlo methods The chapter on complex systems now features an accessible introduction to the replica theory of spin glasses and the Hopfield theory of neural networks, with an emphasis on applications Provides a new discussion of defect-mediated transitions and their implications for two-dimensional melting An invaluable resource for graduate students and advanced undergraduates seeking a compact primer on the core ideas of statistical mechanics Solutions manual (available only to instructors)
Author | : Elliott H. Lieb |
Publisher | : Academic Press |
Total Pages | : 580 |
Release | : 2013-09-17 |
Genre | : Science |
ISBN | : 1483218562 |
Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles covers problems of mathematical physics with one-dimensional analogs. The book discusses classical statistical mechanics and phase transitions; the disordered chain of harmonic oscillators; and electron energy bands in ordered and disordered crystals. The text also describes the many-fermion problem; the theory of the interacting boson gas; the theory of the antiferromagnetic linear chains; and the time-dependent phenomena of many-body systems (i.e., classical or quantum-mechanical dynamics). Physicists and mathematicians will find the book invaluable.