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Mathematical Challenges Of Zero Range Physics
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Book Synopsis Mathematical Challenges of Zero-Range Physics by : Alessandro Michelangeli
Download or read book Mathematical Challenges of Zero-Range Physics written by Alessandro Michelangeli and published by Springer Nature. This book was released on 2021-02-04 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since long over the decades there has been a large transversal community of mathematicians grappling with the sophisticated challenges of the rigorous modelling and the spectral and scattering analysis of quantum systems of particles subject to an interaction so much localised to be considered with zero range. Such a community is experiencing fruitful and inspiring exchanges with experimental and theoretical physicists. This volume reflects such spirit, with a diverse range of original contributions by experts, presenting an up-to-date collection of most relevant results and challenging open problems. It has been conceived with the deliberate two-fold purpose of serving as an updated reference for recent results, mathematical tools, and the vast related literature on the one hand, and as a bridge towards several key open problems that will surely form the forthcoming research agenda in this field.
Book Synopsis Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians by : Matteo Gallone
Download or read book Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians written by Matteo Gallone and published by Springer Nature. This book was released on 2023-04-04 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the reader’s convenience). Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels, unitary evolution and, more generally, a self-consistent theory. Physical heuristics often produce candidate Hamiltonians that are only symmetric: their extension to suitably larger domains of self-adjointness, when possible, amounts to declaring additional physical states the operator must act on in order to have a consistent physics, and distinct self-adjoint extensions describe different physics. Realising observables self-adjointly is the first fundamental problem of quantum-mechanical modelling. The discussed applications concern models of topical relevance in modern mathematical physics currently receiving new or renewed interest, in particular from the point of view of classifying self-adjoint realisations of certain Hamiltonians and studying their spectral and scattering properties. The analysis also addresses intermediate technical questions such as characterising the corresponding operator closures and adjoints. Applications include hydrogenoid Hamiltonians, Dirac–Coulomb Hamiltonians, models of geometric quantum confinement and transmission on degenerate Riemannian manifolds of Grushin type, and models of few-body quantum particles with zero-range interaction. Graduate students and non-expert readers will benefit from a preliminary mathematical chapter collecting all the necessary pre-requisites on symmetric and self-adjoint operators on Hilbert space (including the spectral theorem), and from a further appendix presenting the emergence from physical principles of the requirement of self-adjointness for observables in quantum mechanics.
Book Synopsis Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics by : Boldrighini, Carlo
Download or read book Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics written by Boldrighini, Carlo and published by Universitätsverlag Potsdam. This book was released on 2020 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here.
Book Synopsis Analysis as a Tool in Mathematical Physics by : Pavel Kurasov
Download or read book Analysis as a Tool in Mathematical Physics written by Pavel Kurasov and published by Springer Nature. This book was released on 2020-07-14 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boris Pavlov (1936-2016), to whom this volume is dedicated, was a prominent specialist in analysis, operator theory, and mathematical physics. As one of the most influential members of the St. Petersburg Mathematical School, he was one of the founders of the Leningrad School of Non-self-adjoint Operators. This volume collects research papers originating from two conferences that were organized in memory of Boris Pavlov: “Spectral Theory and Applications”, held in Stockholm, Sweden, in March 2016, and “Operator Theory, Analysis and Mathematical Physics – OTAMP2016” held at the Euler Institute in St. Petersburg, Russia, in August 2016. The volume also includes water-color paintings by Boris Pavlov, some personal photographs, as well as tributes from friends and colleagues.
Book Synopsis Quantum and Stochastic Mathematical Physics by : Astrid Hilbert
Download or read book Quantum and Stochastic Mathematical Physics written by Astrid Hilbert and published by Springer Nature. This book was released on 2023-04-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sergio Albeverio gave important contributions to many fields ranging from Physics to Mathematics, while creating new research areas from their interplay. Some of them are presented in this Volume that grew out of the Random Transformations and Invariance in Stochastic Dynamics Workshop held in Verona in 2019. To understand the theory of thermo- and fluid-dynamics, statistical mechanics, quantum mechanics and quantum field theory, Albeverio and his collaborators developed stochastic theories having strong interplays with operator theory and functional analysis. His contribution to the theory of (non Gaussian)-SPDEs, the related theory of (pseudo-)differential operators, and ergodic theory had several impacts to solve problems related, among other topics, to thermo- and fluid dynamics. His scientific works in the theory of interacting particles and its extension to configuration spaces lead, e.g., to the solution of open problems in statistical mechanics and quantum field theory. Together with Raphael Hoegh Krohn he introduced the theory of infinite dimensional Dirichlet forms, which nowadays is used in many different contexts, and new methods in the theory of Feynman path integration. He did not fear to further develop different methods in Mathematics, like, e.g., the theory of non-standard analysis and p-adic numbers.
Book Synopsis Inverse Linear Problems on Hilbert Space and their Krylov Solvability by : Noè Angelo Caruso
Download or read book Inverse Linear Problems on Hilbert Space and their Krylov Solvability written by Noè Angelo Caruso and published by Springer Nature. This book was released on 2022-02-10 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector f in a Hilbert space H, a linear operator A acting on H, and a vector g in H satisfying Af=g, one is interested in approximating f by finite linear combinations of g, Ag, A2g, A3g, ... The closed subspace generated by the latter vectors is called the Krylov subspace of H generated by g and A. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text. After giving a broad introduction to the subject, examples and counterexamples of Krylov-solvable and non-solvable inverse problems are provided, together with results on uniqueness of solutions, classes of operators inducing Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix collects material on weaker convergence phenomena in general projection methods. This subject of this book lies at the boundary of functional analysis/operator theory and numerical analysis/approximation theory and will be of interest to graduate students and researchers in any of these fields.
Book Synopsis From Complex Analysis to Operator Theory: A Panorama by : Malcolm Brown
Download or read book From Complex Analysis to Operator Theory: A Panorama written by Malcolm Brown and published by Springer Nature. This book was released on 2023-09-21 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.
Book Synopsis Qualitative Properties of Dispersive PDEs by : Vladimir Georgiev
Download or read book Qualitative Properties of Dispersive PDEs written by Vladimir Georgiev and published by Springer Nature. This book was released on 2022-12-02 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant latest developments and future challenges in the field of dispersive partial differential equations. The material covers four major lines: (1) Long time behaviour of NLS-type equations, (2) probabilistic and nonstandard methods in the study of NLS equation, (3) dispersive properties for heat-, Schrödinger-, and Dirac-type flows, (4) wave and KdV-type equations. Across a variety of applications an amount of crucial mathematical tools are discussed, whose applicability and versatility goes beyond the specific models presented here. Furthermore, all contributions include updated and comparative literature.
Book Synopsis Oswaal NCERT Exemplar (Problems - Solutions) Class 11 Physics, Chemistry and Mathematics (Set of 3 Books) For 2024 Exam by : Oswaal Editorial Board
Download or read book Oswaal NCERT Exemplar (Problems - Solutions) Class 11 Physics, Chemistry and Mathematics (Set of 3 Books) For 2024 Exam written by Oswaal Editorial Board and published by Oswaal Books. This book was released on 2023-10-28 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: Description of the product • Chapter-wise and Topic-wise presentation • Chapter-wise Objectives: A sneak peek into the chapter • Mind Map: A single page snapshot of the entire chapter • Revision Notes: Concept based study materials • Tips & Tricks: Useful guidelines for attempting each question perfectly • Some Commonly Made Errors: Most common and unidentified errors are focused • Expert Advice: Oswaal Expert Advice on how to score more • Oswaal QR Codes: For Quick Revision on your Mobile Phones and Tablets
Book Synopsis Problems & Solutions in Theoretical & Mathematical Physics: Introductory level by : W.-H. Steeb
Download or read book Problems & Solutions in Theoretical & Mathematical Physics: Introductory level written by W.-H. Steeb and published by World Scientific. This book was released on 2003 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of problems with detailed solutions which will prove valuable to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers will find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been tested in the author's lectures given around the world. The book is divided into two volumes. Volume I presents the introductory problems, for undergraduate and advanced undergraduate students. In Volume II, the more advanced problems, together with detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics, such as Lax representation, Backlund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painleve test, the Bethe ansatz, the Yang -- Baxter relation, chaos, fractals, complexity, etc.
Book Synopsis Mathematical Problems in Theoretical Physics by : Robert Schrader
Download or read book Mathematical Problems in Theoretical Physics written by Robert Schrader and published by . This book was released on 1982 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Dressing Method in Mathematical Physics by : Evgeny V. Doktorov
Download or read book A Dressing Method in Mathematical Physics written by Evgeny V. Doktorov and published by Springer Science & Business Media. This book was released on 2007-05-19 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. Throughout, the text exploits the "linear experience" of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions.
Book Synopsis Methods for Solving Mathematical Physics Problems by : Valeriĭ Ivanovich Agoshkov
Download or read book Methods for Solving Mathematical Physics Problems written by Valeriĭ Ivanovich Agoshkov and published by Cambridge Int Science Publishing. This book was released on 2006 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to present to a wide range of readers (students, postgraduates, scientists, engineers, etc.) basic information on one of the directions of mathematics, methods for solving mathematical physics problems. The authors have tried to select for the book methods that have become classical and generally accepted. However, some of the current versions of these methods may be missing from the book because they require special knowledge. The book is of the handbook-teaching type. On the one hand, the book describes the main definitions, the concepts of the examined methods and approaches used in them, and also the results and claims obtained in every specific case. On the other hand, proofs of the majority of these results are not presented and they are given only in the simplest (methodological) cases. Another special feature of the book is the inclusion of many examples of application of the methods for solving specific mathematical physics problems of applied nature used in various areas of science and social activity, such as power engineering, environmental protection, hydrodynamics, elasticity theory, etc. This should provide additional information on possible applications of these methods. To provide complete information, the book includes a chapter dealing with the main problems of mathematical physics, together with the results obtained in functional analysis and boundary-value theory for equations with partial derivatives.
Book Synopsis A Collection of Problems on Mathematical Physics by : B. M. Budak
Download or read book A Collection of Problems on Mathematical Physics written by B. M. Budak and published by Elsevier. This book was released on 2013-10-22 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Collection of Problems on Mathematical Physics is a translation from the Russian and deals with problems and equations of mathematical physics. The book contains problems and solutions. The book discusses problems on the derivation of equations and boundary condition. These Problems are arranged on the type and reduction to canonical form of equations in two or more independent variables. The equations of hyperbolic type concerns derive from problems on vibrations of continuous media and on electromagnetic oscillations. The book considers the statement and solutions of boundary value problems pertaining to equations of parabolic types when the physical processes are described by functions of two, three or four independent variables such as spatial coordinates or time. The book then discusses dynamic problems pertaining to the mechanics of continuous media and problems on electrodynamics. The text also discusses hyperbolic and elliptic types of equations. The book is intended for students in advanced mathematics and physics, as well as, for engineers and workers in research institutions.
Book Synopsis Problems in Physics and Mathematics by : Sumit Kumar
Download or read book Problems in Physics and Mathematics written by Sumit Kumar and published by Blue Rose Publishers. This book was released on 2022-08-30 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems in Physics and Mathematics, is a basic academic Test-Bank intended to 10+2 students and aspirants of Engineering (B.Tech-Programme) like JEE (Advanced), JEE (Main) and Medical (MBBS-Programme) like NEET (UG) entrance examinations. But this book can be used for preparing competitions vis, UPSC, State Commissions, NTA, UGC-CSIR, NET-JRF, GATE, JEST, TIFR, BARC, ISRO, JAM, SAT, GRE, Olympiads, Universities Undergraduate or Postgraduate or Research Programmes at various levels where Physics and Mathematics predominates.
Book Synopsis Mathematical Problems of Statistical Mechanics by : IAkov Grigorevich Sinai
Download or read book Mathematical Problems of Statistical Mechanics written by IAkov Grigorevich Sinai and published by World Scientific. This book was released on 1991 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text consists of very high quality articles which not only give a very good account of the field of statistical mechanics in the Soviet Union, but also provide stimulating materials for researchers working on this topic.
Book Synopsis Mathematical Problems in Quantum Physics by : Federico Bonetto
Download or read book Mathematical Problems in Quantum Physics written by Federico Bonetto and published by American Mathematical Soc.. This book was released on 2018-10-24 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the QMATH13: Mathematical Results in Quantum Physics conference, held from October 8–11, 2016, at the Georgia Institute of Technology, Atlanta, Georgia. In recent years, a number of new frontiers have opened in mathematical physics, such as many-body localization and Schrödinger operators on graphs. There has been progress in developing mathematical techniques as well, notably in renormalization group methods and the use of Lieb–Robinson bounds in various quantum models. The aim of this volume is to provide an overview of some of these developments. Topics include random Schrödinger operators, many-body fermionic systems, atomic systems, effective equations, and applications to quantum field theory. A number of articles are devoted to the very active area of Schrödinger operators on graphs and general spectral theory of Schrödinger operators. Some of the articles are expository and can be read by an advanced graduate student.
