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Author : Mehran Kardar
Publisher : Cambridge University Press
Page : 376 pages
File Size : 47,7 Mb
Release : 2007-06-07
Category : Science
ISBN : 052187341X
Textbook on statistical field theories for advanced graduate courses in statistical physics.
Author : Mehran Kardar
Publisher : Cambridge University Press
Page : 211 pages
File Size : 49,5 Mb
Release : 2007-06-07
Category : Science
ISBN : 9781139464871
Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.
Author : Mehran Kardar
Publisher : Unknown
Page : 370 pages
File Size : 46,5 Mb
Release : 2014-05-14
Category : SCIENCE
ISBN : 1139855735
Textbook on statistical field theories for advanced graduate courses in statistical physics.
Author : Bohdan I Lev,Anatoly G Zagorodny
Publisher : World Scientific
Page : 352 pages
File Size : 53,9 Mb
Release : 2021-02-18
Category : Science
ISBN : 9789811229992
This book formulates a unified approach to the description of many-particle systems combining the methods of statistical physics and quantum field theory. The benefits of such an approach are in the description of phase transitions during the formation of new spatially inhomogeneous phases, as well in describing quasi-equilibrium systems with spatially inhomogeneous particle distributions (for example, self-gravitating systems) and metastable states.The validity of the methods used in the statistical description of many-particle systems and models (theory of phase transitions included) is discussed and compared. The idea of using the quantum field theory approach and related topics (path integration, saddle-point and stationary-phase methods, Hubbard-Stratonovich transformation, mean-field theory, and functional integrals) is described in detail to facilitate further understanding and explore more applications.To some extent, the book could be treated as a brief encyclopedia of methods applicable to the statistical description of spatially inhomogeneous equilibrium and metastable particle distributions. Additionally, the general approach is not only formulated, but also applied to solve various practically important problems (gravitating gas, Coulomb-like systems, dusty plasmas, thermodynamics of cellular structures, non-uniform dynamics of gravitating systems, etc.).
Author : Andreas Wipf
Publisher : Springer Nature
Page : 568 pages
File Size : 41,7 Mb
Release : 2021-10-25
Category : Science
ISBN : 9783030832636
This new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.
Author : Dr. Gérard G. Emch
Publisher : Courier Corporation
Page : 352 pages
File Size : 54,7 Mb
Release : 2014-08-04
Category : Science
ISBN : 9780486151717
This systematic algebraic approach offers a careful formulation of the problems' physical motivations as well as self-contained descriptions of the mathematical methods for arriving at solutions. 1972 edition.
Author : James Glimm,Arthur Jaffe
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461251583
This volume contains a selection of expository articles on quantum field theory and statistical mechanics by James Glimm and Arthur Jaffe. They include a solution of the original interacting quantum field equations and a description of the physics which these equations contain. Quantum fields were proposed in the late 1920s as the natural framework which combines quantum theory with relativ ity. They have survived ever since. The mathematical description for quantum theory starts with a Hilbert space H of state vectors. Quantum fields are linear operators on this space, which satisfy nonlinear wave equations of fundamental physics, including coupled Dirac, Max well and Yang-Mills equations. The field operators are restricted to satisfy a "locality" requirement that they commute (or anti-commute in the case of fer mions) at space-like separated points. This condition is compatible with finite propagation speed, and hence with special relativity. Asymptotically, these fields converge for large time to linear fields describing free particles. Using these ideas a scattering theory had been developed, based on the existence of local quantum fields.
Author : Giorgio Parisi
Publisher : Addison Wesley Publishing Company
Page : 378 pages
File Size : 42,9 Mb
Release : 1988-01-21
Category : Science
ISBN : UVA:X001401643
A comprehensive text book covering the field of statistical physics.
Author : Sacha Friedli,Yvan Velenik
Publisher : Cambridge University Press
Page : 643 pages
File Size : 49,9 Mb
Release : 2017-11-23
Category : Mathematics
ISBN : 9781107184824
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Author : Barry M McCoy
Publisher : Oxford University Press
Page : 641 pages
File Size : 47,7 Mb
Release : 2010
Category : Computers
ISBN : 9780199556632
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.
Author : G. Mussardo
Publisher : Oxford University Press
Page : 778 pages
File Size : 48,6 Mb
Release : 2010
Category : Science
ISBN : 9780199547586
A thorough and pedagogical introduction to phase transitions and exactly solved models in statistical physics and quantum field theory.
Author : Alekseĭ Alekseevich Abrikosov
Publisher : Unknown
Page : 376 pages
File Size : 51,8 Mb
Release : 1963
Category : Low temperature research
ISBN : UOM:39015001329716
Author : R K Pathria
Publisher : Elsevier
Page : 342 pages
File Size : 40,7 Mb
Release : 2017-02-21
Category : Science
ISBN : 9781483186887
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.
Author : Moritz Helias,David Dahmen
Publisher : Springer Nature
Page : 203 pages
File Size : 42,7 Mb
Release : 2020-08-20
Category : Science
ISBN : 9783030464448
This book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to pressing open problems in theoretical neuroscience and also machine learning. They enable a systematic and quantitative understanding of the dynamics in recurrent and stochastic neuronal networks. This book is intended for physicists, mathematicians, and computer scientists and it is designed for self-study by researchers who want to enter the field or as the main text for a one semester course at advanced undergraduate or graduate level. The theoretical concepts presented in this book are systematically developed from the very beginning, which only requires basic knowledge of analysis and linear algebra.
Author : Mehran Kardar
Publisher : Cambridge University Press
Page : 376 pages
File Size : 55,6 Mb
Release : 2007-06-07
Category : Science
ISBN : 9781139855884
While many scientists are familiar with fractals, fewer are familiar with scale-invariance and universality which underlie the ubiquity of their shapes. These properties may emerge from the collective behaviour of simple fundamental constituents, and are studied using statistical field theories. Initial chapters connect the particulate perspective developed in the companion volume, to the coarse grained statistical fields studied here. Based on lectures taught by Professor Kardar at MIT, this textbook demonstrates how such theories are formulated and studied. Perturbation theory, exact solutions, renormalization groups, and other tools are employed to demonstrate the emergence of scale invariance and universality, and the non-equilibrium dynamics of interfaces and directed paths in random media are discussed. Ideal for advanced graduate courses in statistical physics, it contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set available to lecturers at www.cambridge.org/9780521873413.