Solvable One-Dimensional Multi-State Models for Statistical and Quantum Mechanics PDF Download
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Author: Rajendran Saravanan
Publisher: Springer Nature
ISBN: 9811666547
Category : Science
Languages : en
Pages : 186
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Book Description
This book highlights the need for studying multi-state models analytically for understanding the physics of molecular processes. An intuitive picture about recently solved models of statistical and quantum mechanics is drawn along with presenting the methods developed to solve them. The models are relevant in the context of molecular processes taking place in gaseous phases and condensed phases, emphasized in the introduction. Chapter 1 derives the arisal of multi-state models for molecular processes from the full Hamiltonian description. The model equations are introduced and the literature review presented in short. In Chapter 2, the time-domain methods to solve Smoluchowski-based reaction-diffusion systems with single-state and two-state descriptions are discussed. Their corresponding analytical results derive new equilibrium concepts in reversible reactions and studies the effect of system and molecular parameters in condensed-phase chemical dynamics. In Chapter 3, time-domain methods to solve quantum scattering problems are developed. Along side introducing a brand new solvable model in quantum scattering, it discusses transient features of quantum two-state models. In interest with electronic transitions, a new solvable two-state model with localized non-adiabatic coupling is also presented. The book concludes by proposing the future scope of the model, thereby inviting new research in this fundamentally important and rich applicable field.
Author: Rajendran Saravanan
Publisher: Springer Nature
ISBN: 9811666547
Category : Science
Languages : en
Pages : 186
Get Book Here
Book Description
This book highlights the need for studying multi-state models analytically for understanding the physics of molecular processes. An intuitive picture about recently solved models of statistical and quantum mechanics is drawn along with presenting the methods developed to solve them. The models are relevant in the context of molecular processes taking place in gaseous phases and condensed phases, emphasized in the introduction. Chapter 1 derives the arisal of multi-state models for molecular processes from the full Hamiltonian description. The model equations are introduced and the literature review presented in short. In Chapter 2, the time-domain methods to solve Smoluchowski-based reaction-diffusion systems with single-state and two-state descriptions are discussed. Their corresponding analytical results derive new equilibrium concepts in reversible reactions and studies the effect of system and molecular parameters in condensed-phase chemical dynamics. In Chapter 3, time-domain methods to solve quantum scattering problems are developed. Along side introducing a brand new solvable model in quantum scattering, it discusses transient features of quantum two-state models. In interest with electronic transitions, a new solvable two-state model with localized non-adiabatic coupling is also presented. The book concludes by proposing the future scope of the model, thereby inviting new research in this fundamentally important and rich applicable field.
Author: Sergio Albeverio
Publisher: American Mathematical Soc.
ISBN: 0821836242
Category : Science
Languages : en
Pages : 506
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Book Description
"This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations–where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution–are covered. The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different methods in disparate contexts are thus unified and a systematic control over approximations to the models, in which the point interactions are replaced by more regular ones, is provided. The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics, especially those connected to the Schrödinger equations. This second edition includes a new appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988."--Résumé de l'éditeur.
Author: Mo-lin Ge
Publisher: World Scientific
ISBN: 9814549754
Category :
Languages : en
Pages : 186
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Book Description
This volume covers the recent developments of the exact solvable models, Yangian symmetry, the long-ranged interaction models and high-dimensional integrable systems. The authors are all experts in their fields. The volume provides a systematic introduction to statistical and mathematical physics and contains review papers and other contributions.
Author: Bill Sutherland
Publisher: World Scientific Publishing Company
ISBN: 9813102144
Category : Science
Languages : en
Pages : 398
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Book Description
This invaluable book provides a broad introduction to the fascinating and beautiful subject of many-body quantum systems that can be solved exactly. The subject began with Bethe's famous solution of the one-dimensional Heisenberg magnet more than 70 years ago, soon after the invention of quantum mechanics. Since then, the diversity and scope of such systems have been steadily growing.Beautiful Models is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and even ambitious undergraduates in physics. It is also suitable for the non-experts in physics who wish to have an overview of some of the classic and fundamental models in the subject. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.
Author: Yongmin Cho
Publisher: World Scientific
ISBN: 9814546321
Category :
Languages : en
Pages : 278
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Book Description
Recently, exciting new notions have been emerging in theoretical physics. The quantum nature of gravitation revealed in the physics of black holes, exotic excitations obeying fractional statistics, and integrable structure such as Yangian symmetry in low-dimensional models are some of the subjects presented in this volume.The spectrum of the talks at the School, reflected in the proceedings, is a wide one ranging from the phenomenology of particle physics to that of condensed matter physics, to topics of a mathematical nature. This is an indication that there is a robust interplay of ideas from diverse disciplines of theoretical physics in the Asia-Pacific region.
Author: Tohru Eguchi
Publisher: World Scientific
ISBN: 9814549908
Category :
Languages : en
Pages : 546
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Book Description
The topics discussed in this volume are: Symmetry and Foundations in Classical and Quantum Mechanics; Geometry, Topology and Quantum Field Theory; Quantum Groups and Infinite-Dimensional Lie Algebras; Algebraic Approach to Nuclear Structure; Integrable Statistical Systems and Theory of Critical Phenomena Supersymmetry; Atomic and Molecular Physics; Condensed Matter Physics; Other Applications of Group Theory to Physics.
Author: Yupeng Wang
Publisher: Springer
ISBN: 3662467569
Category : Science
Languages : en
Pages : 303
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Book Description
This book serves as an introduction of the off-diagonal Bethe Ansatz method, an analytic theory for the eigenvalue problem of quantum integrable models. It also presents some fundamental knowledge about quantum integrability and the algebraic Bethe Ansatz method. Based on the intrinsic properties of R-matrix and K-matrices, the book introduces a systematic method to construct operator identities of transfer matrix. These identities allow one to establish the inhomogeneous T-Q relation formalism to obtain Bethe Ansatz equations and to retrieve corresponding eigenstates. Several longstanding models can thus be solved via this method since the lack of obvious reference states is made up. Both the exact results and the off-diagonal Bethe Ansatz method itself may have important applications in the fields of quantum field theory, low-dimensional condensed matter physics, statistical physics and cold atom systems.
Author: Rodney J. Baxter
Publisher: Elsevier
ISBN: 1483265943
Category : Science
Languages : en
Pages : 499
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Book Description
Exactly Solved Models in Statistical Mechanics
Author: Christopher King
Publisher: World Scientific
ISBN: 9814546593
Category :
Languages : en
Pages : 234
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Book Description
This volume contains the proceedings of the conference on 'Exactly Soluble Models in Statistical Mechanics: Historical Perspectives and Current Status', held at Northeastern University in March 1996 — the first ever conference to deal exclusively with this topic. Besides invited presentations by leading researchers in the field, the conference held a session of contributed papers by participants from throughout the world. The proceedings, which include both the invited and the contributed papers, reflect the broad range of interest in exactly soluble models as well as the diverse fields in physics and mathematics that they connect. Apart from providing concise and timely reviews, the papers in this volume give a snapshot of the current state of affairs. The topics covered range from a historical survey of the field (by E H Lieb) to the latest formulation of a star-star transformation of spin models (by R J Baxter).
Author: Leong-chuan Kwek
Publisher: World Scientific
ISBN: 9814460338
Category : Science
Languages : en
Pages : 238
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Book Description
This volume mainly summarizes the invited talks presented at the 5th Asia-Pacific Workshop on Quantum Information Science (APWQIS) in conjunction with a Festschrift in honor of Professor Vladimir Korepin's 60th birthday. In this Festschrift, we have assembled a medley of interesting articles from some of his friends, well-wishers and collaborators. Comprising both reviews of the state-of-the-art and the latest results, this book covers various aspects of quantum information science, including topics like quantum discord, quantum computing, quantum entanglement, etc.
