Statistical Mechanics Of Quantum Lattice Systemsa Path Integral Approach PDF Download
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Author | : |
Publisher | : European Mathematical Society |
Total Pages | : 402 |
Release | : 2009 |
Genre | : Science |
ISBN | : 9783037190708 |
Download The Statistical Mechanics of Quantum Lattice Systems Book in PDF, ePub and Kindle
Quantum statistical mechanics plays a major role in many fields such as thermodynamics, plasma physics, solid-state physics, and the study of stellar structure. While the theory of quantum harmonic oscillators is relatively simple, the case of anharmonic oscillators, a mathematical model of a localized quantum particle, is more complex and challenging. Moreover, infinite systems of interacting quantum anharmonic oscillators possess interesting ordering properties with respect to quantum stabilization. This book presents a rigorous approach to the statistical mechanics of such systems, in particular with respect to their actions on a crystal lattice. The text is addressed to both mathematicians and physicists, especially those who are concerned with the rigorous mathematical background of their results and the kind of problems that arise in quantum statistical mechanics. The reader will find here a concise collection of facts, concepts, and tools relevant for the application of path integrals and other methods based on measure and integration theory to problems of quantum physics, in particular the latest results in the mathematical theory of quantum anharmonic crystals. The methods developed in the book are also applicable to other problems involving infinitely many variables, for example, in biology and economics.
Author | : SERGIO ALBEVERIO; YURI KONDRATIEV; YURI KOZITSKY. |
Publisher | : |
Total Pages | : |
Release | : |
Genre | : |
ISBN | : 9783037195703 |
Download STATISTICAL MECHANICS OF QUANTUM LATTICE SYSTEMS;A PATH INTEGRAL APPROACH. Book in PDF, ePub and Kindle
Author | : M Chaichian |
Publisher | : CRC Press |
Total Pages | : 359 |
Release | : 2018-10-08 |
Genre | : Science |
ISBN | : 1482268914 |
Download Path Integrals in Physics Book in PDF, ePub and Kindle
The path integral approach has proved extremely useful for the understanding of the most complex problems in quantum field theory, cosmology, and condensed matter physics. Path Integrals in Physics: Volume II, Quantum Field Theory, Statistical Physics and other Modern Applications covers the fundamentals of path integrals, both the Wiener and Feynman types, and their many applications in physics. The book deals with systems that have an infinite number of degrees of freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. Each chapter is self-contained and can be considered as an independent textbook. It provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.
Author | : Gert Roepstorff |
Publisher | : Springer Science & Business Media |
Total Pages | : 387 |
Release | : 1994 |
Genre | : Integrals, Path |
ISBN | : 9783540552130 |
Download Path Integral Approach to Quantum Physics Book in PDF, ePub and Kindle
Apart from giving a broad introduction to the theory of the random walk and stochastic processes in general, the author emphasizes the close relationship between Brownian motion and the path integral formulation of quantum mechanics due to R. Feynman and M. Kac. Various recent advances in statistical mechanics and quantum field theory are included; they are presented in such a way as to make this a textbook suitable teaching purposes. This new edition also contains notes, exercises, and an updated list of references which will help the student to acquire a deeper grasp of the subject and to acquaint himself with the current research activity in this field. The greatly enlarged English edition has been completely rewritten by the author; the German original was first published in 1991.
Author | : Andreas Wipf |
Publisher | : Springer Nature |
Total Pages | : 568 |
Release | : 2021-10-25 |
Genre | : Science |
ISBN | : 3030832635 |
Download Statistical Approach to Quantum Field Theory Book in PDF, ePub and Kindle
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 | : Hagen Kleinert |
Publisher | : World Scientific |
Total Pages | : 1512 |
Release | : 2004 |
Genre | : Science |
ISBN | : 9789812381071 |
Download Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets Book in PDF, ePub and Kindle
This is the third, significantly expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions. The powerful Feynman -- Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals. Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbationexpansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders. Special attention is devoted to path integrals with topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chem-Simons theory of particles with fractional statistics (anyohs) is introduced and applied to explain the fractional quantum Hall effect. The relevance of path integrals to financial markets is discussed, and improvements of the famous Black -- Scholes formula for option prices are given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions.
Author | : George J. Papadopoulos |
Publisher | : Springer Science & Business Media |
Total Pages | : 516 |
Release | : 2013-11-11 |
Genre | : Science |
ISBN | : 1468491407 |
Download Path Integrals Book in PDF, ePub and Kindle
The Advanced Study Institute on "Path Integrals and Their Applications in Quantum, Statistical, and Solid State Physics" was held at the University of Antwerpen (R.U.C.A.), July 17-30, 1977. The Institute was sponsored by NATO. Co-sponsors were: A.C.E.C. (Belgium), Agfa-Gevaert (Belgium), l'Air Li~uide BeIge (Belgium), Be1gonucleaire (Belgium), Bell Telephone Mfg. Co. (Belgium), Boelwerf (Belgium), Generale BankmaatschappiJ (Belgium), I.B.M. (Belgium), Kredietbank (Belgium), National Science Foundation (U.S.A.), Siemens (Belgium). A total of 100 lecturers and partici pants attended the Institute. The development of path (or functional) integrals in relation to problems of stochastic nature dates back to the early 20's. At that time, Wiener succeeded in obtaining the fundamental solution of the diffusion e~uation using Einstein's joint probability of finding a Brownian particle in a succession of space intervals during a corresponding succession of time intervals. Dirac in the early 30's sowed the seeds of the path integral formulation of ~uantum mecha nics. However, the major and decisive step in this direction was taken with Feynman's works in ~uantum and statistical physics, and quantum electrodynamicso The applications now extend to areas such as continuous mechanics, and recently functional integration methods have been employed by Edwards for the study of polymerized matter
Author | : Mark S. Swanson |
Publisher | : Academic Press |
Total Pages | : 457 |
Release | : 2012-12-02 |
Genre | : Science |
ISBN | : 0323138160 |
Download Path Integrals and Quantum Processes Book in PDF, ePub and Kindle
In a clearly written and systematic presentation, Path Integrals and Quantum Processes covers all concepts necessary to understand the path integral approach to calculating transition elements, partition functions, and source functionals. The book, which assumes only a familiarity with quantum mechanics, is ideal for use as a supplemental textbook in quantum mechanics and quantum field theory courses. Graduate and post-graduate students who are unfamiliar with the path integral will also benefit from this contemporary text. Exercise sets are interspersed throughout the text to facilitate self-study. Explicates the relationship between the operator and path integral formulations of quantum mechanics and quantum field theory Provides a systematic and detailed presentation of Grassmann variables Covers Dirac's method of constraints and the relationship of ghosts, gauge invariance, and gauge conditions in gauge field theory Includes applications to statistical mechanics, the effective action and potential, and anomaly analysis
Author | : Randall Wayne Hall |
Publisher | : |
Total Pages | : 244 |
Release | : 1984 |
Genre | : Quantum theory |
ISBN | : |
Download Path Integral Approaches to Quantum Statistical Mechanics Book in PDF, ePub and Kindle
Author | : Ashok Das |
Publisher | : World Scientific Publishing Company |
Total Pages | : 384 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : |
Download Field Theory Book in PDF, ePub and Kindle
Latest Edition: Field Theory (3rd Edition)This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas.Adding new material keenly requested by readers, this second edition is an important expansion of the popular first edition. Two extra chapters cover path integral quantization of gauge theories and anomalies, and a new section extends the supersymmetry chapter, where singular potentials in supersymmetric systems are described.