Statistical Mechanics of Classical and Disordered Systems

Statistical Mechanics of Classical and Disordered Systems
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.

Exact Methods in Low-dimensional Statistical Physics and Quantum Computing

Exact Methods in Low-dimensional Statistical Physics and Quantum Computing
Author: Stephane Ouvry
Publisher: Oxford University Press
Total Pages: 651
Release: 2010-04-22
Genre: Language Arts & Disciplines
ISBN: 0199574618

Low-dimensional statistical models are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book of lectures by international leaders in the field sets these issues into a larger and more coherent theoretical perspective than is currently available.

Disordered Systems and Biological Organization

Disordered Systems and Biological Organization
Author: E. Bienenstock
Publisher: Springer Science & Business Media
Total Pages: 407
Release: 2012-12-06
Genre: Computers
ISBN: 3642826571

The NATO workshop on Disordered Systems and Biological Organization was attended, in march 1985, by 65 scientists representing a large variety of fields: Mathematics, Computer Science, Physics and Biology. It was the purpose of this interdisciplinary workshop to shed light on the conceptual connections existing between fields of research apparently as different as: automata theory, combinatorial optimization, spin glasses and modeling of biological systems, all of them concerned with the global organization of complex systems, locally interconnected. Common to many contributions to this volume is the underlying analogy between biological systems and spin glasses: they share the same properties of stability and diversity. This is the case for instance of primary sequences of biopo Iymers I ike proteins and nucleic acids considered as the result of mutation-selection processes [P. W. Anderson, 1983] or of evolving biological species [G. Weisbuch, 1984]. Some of the most striking aspects of our cognitive apparatus, involved In learning and recognttlon [J. Hopfield, 19821, can also be described in terms of stability and diversity in a suitable configuration space. These interpretations and preoccupations merge with those of theoretical biologists like S. Kauffman [1969] (genetic networks) and of mathematicians of automata theory: the dynamics of networks of automata can be interpreted in terms of organization of a system in multiple possible attractors. The present introduction outlInes the relationships between the contributions presented at the workshop and brIefly discusses each paper in its particular scientific context.

Statistical Mechanics of Lattice Systems

Statistical Mechanics of Lattice Systems
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.

Thermodynamics and Statistical Mechanics

Thermodynamics and Statistical Mechanics
Author: Phil Attard
Publisher: Academic Press
Total Pages: 444
Release: 2002-07-24
Genre: Science
ISBN: 9780120663217

Isolated systems and thermal equilibrium -- Various reservoirs -- Probability and the general formalism -- Classical statistical mechanics -- Ideal systems -- Interacting particles -- Diagrammatic and functional expansions -- Pair functions -- Functional and perturbation theory -- Inhomogeneous systems -- Coulomb systems -- Computer simulations.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
Author: Boyan Sirakov
Publisher: World Scientific
Total Pages: 5393
Release: 2019-02-27
Genre: Mathematics
ISBN: 9813272899

The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Statistical Mechanics

Statistical Mechanics
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.