Download or read book Semiclassical Analysis Witten Laplacians and Statistical Mechanics written by Bernard Helffer and published by World Scientific. This book was released on 2002 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform Log-Sobolev inequality.
Download or read book Mathematical Physics of Quantum Mechanics written by Joachim Asch and published by Springer. This book was released on 2006-09-09 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This selection of outstanding articles – an outgrowth of the QMath9 meeting for young scientists – covers new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and more. The book’s pedagogical style makes it a useful introduction to the research literature for postgraduate students. For more expert researchers it will serve as a concise source of modern reference.
Download or read book Spectral Theory and its Applications written by Bernard Helffer and published by Cambridge University Press. This book was released on 2013-01-17 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non self-adjoint operator theory with an emphasis on the role of the pseudospectra. The author's focus on applications, along with exercises and examples, enables readers to connect theory with practice so that they develop a good understanding of how the abstract spectral theory can be applied. The final chapter provides various problems that have been the subject of active research in recent years and will challenge the reader's understanding of the material covered.
Download or read book Complex Analysis written by Friedrich Haslinger and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-11-20 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy‘s integral theorem general versions of Runge‘s approximation theorem and Mittag-Leffler‘s theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. Contents Complex numbers and functions Cauchy’s Theorem and Cauchy’s formula Analytic continuation Construction and approximation of holomorphic functions Harmonic functions Several complex variables Bergman spaces The canonical solution operator to Nuclear Fréchet spaces of holomorphic functions The -complex The twisted -complex and Schrödinger operators
Download or read book Analysis and Geometry of Markov Diffusion Operators written by Dominique Bakry and published by Springer Science & Business Media. This book was released on 2013-11-18 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.
Download or read book The d bar Neumann Problem and Schr dinger Operators written by Friedrich Haslinger and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-08-20 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. It begins with results on the canonical solution operator to restricted to Bergman spaces of holomorphic d-bar functions in one and several complex variables.These operators are Hankel operators of special type. In the following the general complex is investigated on d-bar spaces over bounded pseudoconvex domains and on weighted d-bar spaces. The main part is devoted to the spectral analysis of the complex Laplacian and to compactness of the Neumann operator. The last part contains a detailed account of the application of the methods to Schrödinger operators, Pauli and Dirac operators and to Witten-Laplacians. It is assumed that the reader has a basic knowledge of complex analysis, functional analysis and topology. With minimal prerequisites required, this book provides a systematic introduction to an active area of research for both students at a bachelor level and mathematicians.
Download or read book Hypoelliptic Estimates and Spectral Theory for Fokker Planck Operators and Witten Laplacians written by Francis Nier and published by Springer. This book was released on 2005-01-17 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations, and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction, this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart, the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes, and the Morse inequalities.
Download or read book MATHEMATICAL CONCEPTS OF QUANTUM MECHANICS written by STEPHEN J. GUSTAFSON and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.
Download or read book Spectral Methods in Surface Superconductivity written by Søren Fournais and published by Springer Science & Business Media. This book was released on 2010-06-15 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines in detail the nonlinear Ginzburg–Landau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large Ginzburg–Landau parameter kappa. Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate-level understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semi-classical techniques in spectral theory that are involved in the nonlinear study of superconductivity.
Download or read book Advances in Partial Differential Equations and Control written by Kaïs Ammari and published by Springer Nature. This book was released on with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Order Structure and Topological Methods in Nonlinear Partial Differential Equations written by Yihong Du and published by World Scientific. This book was released on 2006 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems.The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time.
Download or read book Order Structure And Topological Methods In Nonlinear Partial Differential Equations Vol 1 Maximum Principles And Applications written by Yihong Du and published by World Scientific. This book was released on 2006-01-12 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems.The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time.
Download or read book Seminaire de Probabilites XXXV written by J. Azema and published by Springer. This book was released on 2004-10-21 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation. Researchers and graduate students in the theory of stochastic processes will find in this 35th volume some thirty articles on martingale theory, martingales and finance, analytical inequalities and semigroups, stochastic differential equations, functionals of Brownian motion and of Lévy processes. Ledoux's article contains a self-contained introduction to the use of semigroups in spectral gaps and logarithmic Sobolev inequalities; the contribution by Emery and Schachermayer includes an exposition for probabilists of Vershik's theory of backward discrete filtrations.
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multiple Time Scale Dynamics written by Christian Kuehn and published by Springer. This book was released on 2015-02-25 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Download or read book M moire written by and published by . This book was released on 2006 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Partial Differential Equations and Mathematical Physics written by Lars Hörmander and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: On March 17-19 and May 19-21,1995, analysis seminars were organized jointly at the universities of Copenhagen and Lund, under the heading "Danish-Swedish Analysis Seminar". The main topic was partial differen tial equations and related problems of mathematical physics. The lectures given are presented in this volume, some as short abstracts and some as quite complete expositions or survey papers. They span over a large vari ety of topics. The most frequently occurring theme is the use of microlocal analysis which is now important also in the study of non-linear differential equations although it originated entirely within the linear theory. Perhaps it is less surprising that microlocal analysis has proved to be useful in the study of mathematical problems of classical quantum mechanics, for it re ceived a substantial input of ideas from that field. The scientific committee for the invitation of speakers consisted of Gerd Grubb in Copenhagen, Lars Hormander and Anders MeHn in Lund, and Jo hannes Sjostrand in Paris. Lars Hormander and Anders Melin have edited the proceedings. They were hosts of the seminar days in Lund while Gerd Grubb was the host in Copenhagen. Financial support was obtained from the mathematics departments in Copenhagen and Lund, CNRS in France, the Danish and Swedish Na tional Research Councils, Gustaf Sigurd Magnuson's foundation at the Royal Swedish Academy of Sciences, and the Wenner-Gren foundation in Stockholm. We want to thank all these organisations for their support
