Download or read book Gibbs Semigroups written by Valentin A. Zagrebnov and published by Springer Nature. This book was released on 2019-11-17 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the theory of the Gibbs semigroups, which originated in the 1970s and was motivated by the study of strongly continuous operator semigroups with values in the trace-class ideal. The book offers an up-to-date, exhaustive overview of the advances achieved in this theory after half a century of development. It begins with a tutorial introduction to the necessary background material, before presenting the Gibbs semigroups and then providing detailed and systematic information on the Trotter-Kato product formulae in the trace-norm topology. In addition to reviewing the state-of-art concerning the Trotter-Kato product formulae, the book extends the scope of exposition from the trace-class ideal to other ideals. Here, special attention is paid to results on semigroups in symmetrically normed ideals and in the Dixmier ideal. By examining the progress made in Gibbs semigroup theory and in extensions of the Trotter-Kato product formulae to symmetrically normed and Dixmier ideals, the book shares timely and valuable insights for readers interested in pursuing these subjects further. As such, it will appeal to researchers, undergraduate and graduate students in mathematics and mathematical physics.
Download or read book Topics in the Theory of Gibbs Semigroups written by Valentin Zagrebnov and published by Leuven University Press. This book was released on 2003 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: One-parameter semigroup theory started to be an important branch of mathematics in the thirties when it was realized that the theory has direct applications to partial differential equations, random processes, infinite dimensional control theory, mathematical physics, etc. It is now generally accepted as an integral part of contemporary functional analysis. Compact strongly continuous semigroups have been an important research subject since a long time, as in almost all applications of partial differential equations with bounded domains the semigroups turn out to be compact. From this point of view, the present volume of the Leuven Notes in Mathematical and Theoretical Physics emphasizes a special subclass of these semigroups. In fact, the focus here is mainly on semigroups acting on a Hilbert space H with values in the trace class ideal C1(H) of bounded operators on H. Historically, this class of semigroups is closely related to quantum statistical mechanics.
Download or read book Trotter Kato Product Formul written by Valentin A. Zagrebnov and published by Springer Nature. This book was released on with total page 879 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semigroups of Linear Operators written by David Applebaum and published by Cambridge University Press. This book was released on 2019-08-15 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of semigroups of operators is one of the most important themes in modern analysis. Not only does it have great intellectual beauty, but also wide-ranging applications. In this book the author first presents the essential elements of the theory, introducing the notions of semigroup, generator and resolvent, and establishes the key theorems of Hille–Yosida and Lumer–Phillips that give conditions for a linear operator to generate a semigroup. He then presents a mixture of applications and further developments of the theory. This includes a description of how semigroups are used to solve parabolic partial differential equations, applications to Levy and Feller–Markov processes, Koopmanism in relation to dynamical systems, quantum dynamical semigroups, and applications to generalisations of the Riemann–Liouville fractional integral. Along the way the reader encounters several important ideas in modern analysis including Sobolev spaces, pseudo-differential operators and the Nash inequality.
Download or read book Mathematical Analysis and Applications written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2019-12-12 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.
Download or read book Mathematical Analysis in Interdisciplinary Research written by Ioannis N. Parasidis and published by Springer Nature. This book was released on 2022-03-10 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.
Download or read book Xivth International Congress On Mathematical Physics written by Jean-claude Zambrini and published by World Scientific. This book was released on 2006-03-07 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2003 the XIV International Congress on Mathematical Physics (ICMP) was held in Lisbon with more than 500 participants. Twelve plenary talks were given in various fields of Mathematical Physics: E Carlen «On the relation between the Master equation and the Boltzmann Equation in Kinetic Theory»; A Chenciner «Symmetries and “simple” solutions of the classical n-body problem»; M J Esteban «Relativistic models in atomic and molecular physics»; K Fredenhagen «Locally covariant quantum field theory»; K Gawedzki «Simple models of turbulent transport»; I Krichever «Algebraic versus Liouville integrability of the soliton systems»; R V Moody «Long-range order and diffraction in mathematical quasicrystals»; S Smirnov «Critical percolation and conformal invariance»; J P Solovej «The energy of charged matter»; V Schomerus «Strings through the microscope»; C Villani «Entropy production and convergence to equilibrium for the Boltzmann equation»; D Voiculescu «Aspects of free probability».The book collects as well carefully selected invited Session Talks in: Dynamical Systems, Integrable Systems and Random Matrix Theory, Condensed Matter Physics, Equilibrium Statistical Mechanics, Quantum Field Theory, Operator Algebras and Quantum Information, String and M Theory, Fluid Dynamics and Nonlinear PDE, General Relativity, Nonequilibrium Statistical Mechanics, Quantum Mechanics and Spectral Theory, Path Integrals and Stochastic Analysis.
Download or read book Analysis and Operator Theory written by Themistocles M. Rassias and published by Springer. This book was released on 2019-05-31 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to Tosio Kato’s 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics. Survey papers and in-depth technical papers emphasize linear and nonlinear analysis, operator theory, partial differential equations, and functional analysis including nonlinear evolution equations, the Korteweg–de Vries equation, the Navier–Stokes equation, and perturbation theory of linear operators. The Kato inequality, the Kato type matrix limit theorem, the Howland–Kato commutator problem, the Kato-class of potentials, and the Trotter–Kato product formulae are discussed and analyzed. Graduate students, research mathematicians, and applied scientists will find that this book provides comprehensive insight into the significance of Tosio Kato’s impact to research in analysis and operator theory.
Download or read book Quantum Probability Communications Volume X written by R L Hudson and published by World Scientific. This book was released on 1998-10-07 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much has changed in the world of quantum probability since the publication of the last volume in this series. Giants in the field, such as P-A Meyer, K R Parthasarathy and W von Waldenfels, have reached the age of retirement. Readers will, however, be pleased to see evidence in the present volume that Partha remains as creatively active as ever. The field itself, regarded at one time as the esoteric province of a small group of devotees, has come of age. It has attracted the enthusiastic commitment of an ever-growing army of young mathematicians and physicists, many of whom are represented here.
Download or read book Stochastic Spectral Theory for Selfadjoint Feller Operators written by Michael Demuth and published by Birkhäuser. This book was released on 2012-12-06 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, a beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. The unified approach provides a new viewpoint of and a deeper insight into the subject.
Download or read book Modern Analysis and Applications written by Vadim Adamyan and published by Springer Science & Business Media. This book was released on 2009-08-29 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.
Download or read book Mathematical Foundations of Quantum Statistical Mechanics written by D.Y. Petrina and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to quantum statistical mechanics. It can be regarded as a continuation of the book "Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems" (Gordon & Breach SP, 1989) written together with my colleagues V. I. Gerasimenko and P. V. Malyshev. Taken together, these books give a complete pre sentation of the statistical mechanics of continuous systems, both quantum and classical, from the common point of view. Both books have similar contents. They deal with the investigation of states of in finite systems, which are described by infinite sequences of statistical operators (reduced density matrices) or Green's functions in the quantum case and by infinite sequences of distribution functions in the classical case. The equations of state and their solutions are the main object of investigation in these books. For infinite systems, the solutions of the equations of state are constructed by using the thermodynamic limit procedure, accord ing to which we first find a solution for a system of finitely many particles and then let the number of particles and the volume of a region tend to infinity keeping the density of particles constant. However, the style of presentation in these books is quite different.
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.
Download or read book Mathematical Results in Quantum Mechanics written by Jaroslav Dittrich and published by Birkhäuser. This book was released on 2012-12-06 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the QMath 7 Conference on Mathematical Results in Quantum Mechanics held in Prague, Czech Republic in June, 1998. The volume addresses mathematicians and physicists interested in contemporary quantum physics and associated mathematical questions, presenting new results on Schrödinger and Pauli operators with regular, fractal or random potentials, scattering theory, adiabatic analysis, and interesting new physical systems such as photonic crystals, quantum dots and wires.
Download or read book Garden Of Quanta A Essays In Honor Of Hiroshi Ezawa written by Keiji Watanabe and published by World Scientific. This book was released on 2003-07-01 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of reviews and essays about the recent wide-ranging developments in the areas of quantum physics. The articles have mostly been written at the graduate level, but some are accessible to advanced undergraduates. They will serve as good introductions for beginning graduate students in quantum physics who are looking for directions. Aspects of mathematical physics, quantum field theories and statistical physics are emphasized.
Download or read book Mathematical Methods of Quantum Physics 2nd Jagna International Workshop written by C C Bernido and published by CRC Press. This book was released on 2020-12-17 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles are presented, covering a wide range of topics in the mathematical methods of quantum physics. These include infinite dimensional analysis based on white noise, operator algebra methods, Feynman path integrals, quantum mechanics on non-simply connected spaces, recent results in supersymmetric theories, stochastic and quantum dynamics, Yang-Baxter systems, statistical physics, thermo field dynamics, and quantum field theory. The essays are based on lectures contributed for the Second Jagna International Workshop held in honour of Prof. Hiroshi Ezawa, a distinguished physicist, educator, and former president of the Physical Society of Japan.
Download or read book Stochastic Analysis And Mathematical Physics Samp anestoc 2002 written by Rolando Rebolledo and published by World Scientific. This book was released on 2004-09-15 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book collects a series of papers centered on two main streams: Feynman path integral approach to Quantum Mechanics and statistical mechanics of quantum open systems. Key authors discuss the state-of-the-art within their fields of expertise. In addition, the volume includes a number of contributed papers with new results, which have been thoroughly refereed.The contributions in this volume highlight emergent research in the area of stochastic analysis and mathematical physics, focusing, in particular on Feynman functional integral approach and, on the other hand, in quantum probability. The book is addressed to an audience of mathematical physicists, as well as specialists in probability theory, stochastic analysis and operator algebras.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
