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Author : Piergiulio Tempesta
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 48,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821833292
The volume is suitable for graduate students and research mathematicians interested in integrable systems.
Author : Piergiulio Tempesta
Publisher : Unknown
Page : 347 pages
File Size : 53,9 Mb
Release : 2004
Category : Differential equations, Partial
ISBN : 1470439514
Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This proceedings volume grew out of the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathématiques in Montréal (Quebec). The meeting brought together scientists working in the area of finite-dimensional integrable systems to discuss new developments in this active field of interest. Properties possessed by these systems are manifold. In classical mechanics, they.
Author : P. Tempesta, P. Winternitz, J. Harnad, W. Miller, Jr., G. Pogosyan, and M. Rodriguez
Publisher : American Mathematical Soc.
Page : 364 pages
File Size : 45,6 Mb
Release : 2024-06-27
Category : Differential equations, Partial
ISBN : 0821870327
Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).
Author : A.B. Shabat,A. González-López,M. Mañas,L. Martínez Alonso,M.A. Rodríguez
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400710238
Proceedings of the NATO Advanced Research Workshop, held in Cadiz, Spain, from 12 to 16 June 2002
Author : Martin C. Gutzwiller
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 47,5 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461209836
Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.
Author : A.B. Shabat,A. González-López,M. Mañas,L. Martínez Alonso,M.A. Rodríguez
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 43,8 Mb
Release : 2004-01-31
Category : Science
ISBN : 1402018363
Proceedings of the NATO Advanced Research Workshop, held in Cadiz, Spain, from 12 to 16 June 2002
Author : John P. Harnad,Gert Sabidussi,Pavel Winternitz
Publisher : American Mathematical Soc.
Page : 284 pages
File Size : 51,8 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 082187022X
This volume presents the papers based upon lectures given at the 1999 Séminaire de Mathémathiques Supérieurs held in Montreal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development throughout the past three decades, resulting in new motivation for study in r s3risingly different directions. Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number of other fields of current interest. These fields include theoretical physics and pure mathematics, for example the Seiberg-Witten approach to supersymmetric Yang-Mills theory, the spectral theory of random matrices, topological models of quantum gravity, conformal field theory, mirror symmetry, quantum cohomology, etc. This collection gives a nice cross-section of the current state of the work in the area of integrable systems which is presented by some of the leading active researchers in this field. The scope and quality of the articles in this volume make this a valuable resource for those interested in an up-to-date introduction and an overview of many of the main areas of study in the theory of integral systems.
Author : Şengül Kuru,Javier Negro,Luis M. Nieto
Publisher : Springer
Page : 434 pages
File Size : 50,6 Mb
Release : 2019-07-12
Category : Science
ISBN : 9783030200879
This volume shares and makes accessible new research lines and recent results in several branches of theoretical and mathematical physics, among them Quantum Optics, Coherent States, Integrable Systems, SUSY Quantum Mechanics, and Mathematical Methods in Physics. In addition to a selection of the contributions presented at the "6th International Workshop on New Challenges in Quantum Mechanics: Integrability and Supersymmetry", held in Valladolid, Spain, 27-30 June 2017, several high quality contributions from other authors are also included. The conference gathered 60 participants from many countries working in different fields of Theoretical Physics, and was dedicated to Prof. Véronique Hussin—an internationally recognized expert in many branches of Mathematical Physics who has been making remarkable contributions to this field since the 1980s. The reader will find interesting reviews on the main topics from internationally recognized experts in each field, as well as other original contributions, all of which deal with recent applications or discoveries in the aforementioned areas.
Author : Ruth E Kastner,Jasmina Jeknić-Dugić,George Jaroszkiewicz
Publisher : World Scientific
Page : 500 pages
File Size : 45,6 Mb
Release : 2016-11-10
Category : Science
ISBN : 9781786341426
The structural aspects of composite quantum systems in the foundation, interpretation and application of quantum theory is an increasingly prominent topic of physics research. As an emerging field, it seeks to understand the origins of the classical world of experience from the quantum level. Quantum Structural Studies presents conceptual fundamentals and mathematical methods for investigating the structuring of quantum systems into subsystems. Split into four sections, the topics covered include the historical and philosophical aspects of quantum structures, specific interpretive approaches and ontologies, and alternative methodological approaches to quantum mechanics. Questions addressed are: Can the classically relevant degrees of freedom (such as the center of mass) be considered physically realistic, and if so, in what sense?In what sense might various emergent structures be relevant for the transition from the quantum description to the classical?Do suggested new approaches describe phenomenology and proposals for new experiments? Specialists, graduate students and researchers seeking an introduction to the field of emergent structures and new directions for research and experimentation can use this book to find up-to-date representative texts and reviews.
Author : Maciej Błaszak
Publisher : Springer
Page : 460 pages
File Size : 48,5 Mb
Release : 2019-06-11
Category : Science
ISBN : 9783030183790
This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories.In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.
Author : Andreas Knauf,Yakov G. Sinai
Publisher : Birkhäuser
Page : 104 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034889322
Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schr6dinger equation. Scatter ing by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close.
Author : M. B. Paranjape,Richard MacKenzie,Zora Thomova,Pavel Winternitz,William Witczak-Krempa
Publisher : Springer Nature
Page : 670 pages
File Size : 40,5 Mb
Release : 2021
Category : Electronic books
ISBN : 9783030557775
This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montreal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-perturbative Quantum Field Theory, Particle Physics, Quantum Computing and Quantum Information Theory, and String/ADS-CFT. There was also a special session in honour of Decio Levi. The volume is divided into sections corresponding to the sessions held during the symposium, allowing the reader to appreciate both the homogeneity and the diversity of mathematical tools that have been applied in these subject areas. Several of the plenary speakers, who are internationally recognized experts in their fields, have contributed reviews of the main topics to complement the original contributions. .
Author : G.S Pogosyan,L.E Vincent,K.B Wolf
Publisher : CRC Press
Page : 300 pages
File Size : 46,5 Mb
Release : 2005-05-01
Category : Mathematics
ISBN : 9781482269185
Symmetry is permeating our understanding of nature: Group theoretical methods of intrinsic interest to mathematics have expanded their applications from physics to chemistry and biology. The ICGTMP Colloquia maintain the communication among the many branches into which this endeavor has bloomed. Lie group and representation theory, special function
Author : Giuseppe Gaeta,Raffaele Vitolo,Sebastian Walcher
Publisher : World Scientific
Page : 311 pages
File Size : 44,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812776174
This proceedings volume is devoted to the interplay of symmetry and perturbation theory, as well as to cognate fields such as integrable systems, normal forms, n-body dynamics and choreographies, geometry and symmetry of differential equations, and finite and infinite dimensional dynamical systems. The papers collected here provide an up-to-date overview of the research in the field, and have many leading scientists in the field among their authors, including: D Alekseevsky, S Benenti, H Broer, A Degasperis, M E Fels, T Gramchev, H Hanssmann, J Krashil''shchik, B Kruglikov, D Krupka, O Krupkova, S Lombardo, P Morando, O Morozov, N N Nekhoroshev, F Oliveri, P J Olver, J A Sanders, M A Teixeira, S Terracini, F Verhulst, P Winternitz, B Zhilinskii. Sample Chapter(s). Foreword (101 KB). Chapter 1: Homogeneous Bi-Lagrangian Manifolds and Invariant Monge-Ampere Equations (415 KB). Contents: On Darboux Integrability (I M Anderson et al.); Computing Curvature without Christoffel Symbols (S Benenti); Natural Variational Principles (D Krupka); Fuzzy Fractional Monodromy (N N Nekhoroshev); Emergence of Slow Manifolds in Nonlinear Wave Equations (F Verhulst); Complete Symmetry Groups and Lie Remarkability (K Andriopoulos); Geodesically Equivalent Flat Bi-Cofactor Systems (K Marciniak); On the Dihedral N-Body Problem (A Portaluri); Towards Global Classifications: A Diophantine Approach (P van der Kamp); and other papers. Readership: Researchers and students (graduate/advanced undergraduates) in mathematics, applied mathematics, physics and nonlinear science.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 53,7 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 9789814472470
