Semiclassical Analysis, Witten Laplacians, and Statistical Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Semiclassical Analysis, Witten Laplacians, and Statistical Mechanics write by Bernard Helffer. This book was released on 2002. Semiclassical Analysis, Witten Laplacians, and Statistical Mechanics available in PDF, EPUB and Kindle. 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.
Mathematical Physics of Quantum Mechanics
Mathematical Physics of Quantum Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematical Physics of Quantum Mechanics write by Joachim Asch. This book was released on 2006-09-09. Mathematical Physics of Quantum Mechanics available in PDF, EPUB and Kindle. 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.
Spectral Theory and its Applications
Spectral Theory and its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spectral Theory and its Applications write by Bernard Helffer. This book was released on 2013-01-17. Spectral Theory and its Applications available in PDF, EPUB and Kindle. 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.
Complex Analysis
Complex Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Complex Analysis write by Friedrich Haslinger. This book was released on 2017-11-20. Complex Analysis available in PDF, EPUB and Kindle. 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
Analysis and Geometry of Markov Diffusion Operators
Analysis and Geometry of Markov Diffusion Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analysis and Geometry of Markov Diffusion Operators write by Dominique Bakry. This book was released on 2013-11-18. Analysis and Geometry of Markov Diffusion Operators available in PDF, EPUB and Kindle. 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.
