Solvable One Dimensional Multi State Models For Statistical And Quantum Mechanics

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Solvable One Dimensional Multi State Models For Statistical And Quantum Mechanics

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Author : Rajendran Saravanan
language : en
Publisher: Springer Nature
Release Date : 2021-11-14

Solvable One Dimensional Multi State Models For Statistical And Quantum Mechanics written by Rajendran Saravanan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-14 with Science categories.

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.​

Solvable One Dimensional Multi State Models For Statistical And Quantum Mechanics

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Author : Rajendran Saravanan
language : en
Publisher:
Release Date : 2021

Solvable One Dimensional Multi State Models For Statistical And Quantum Mechanics written by Rajendran Saravanan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

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.

Exactly Solved Models In Statistical Mechanics

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Author : Rodney J. Baxter
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01

Exactly Solved Models In Statistical Mechanics written by Rodney J. Baxter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Science categories.

Exploration of two-dimensional lattice models examines basic statistical mechanics, Ising models, spherical models, ice-type models, corner transfer matrices, and elliptic functions. 1982 edition, with author's 2007 update on subsequent developments.

Exactly Soluble Models In Statistical Mechanics Historical Perspectives And Current Status

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Author : Christopher King
language : en
Publisher: World Scientific
Release Date : 1997-02-26

Exactly Soluble Models In Statistical Mechanics Historical Perspectives And Current Status written by Christopher King and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-26 with categories.

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).

Beautiful Models 70 Years Of Exactly Solved Quantum Many Body Problems

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Author : Bill Sutherland
language : en
Publisher: World Scientific Publishing Company
Release Date : 2004-06-21

Beautiful Models 70 Years Of Exactly Solved Quantum Many Body Problems written by Bill Sutherland and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-21 with Science categories.

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.

Quasi Exactly Solvable Models In Quantum Mechanics

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Author : A.G Ushveridze
language : en
Publisher: CRC Press
Release Date : 1994-01-01

Quasi Exactly Solvable Models In Quantum Mechanics written by A.G Ushveridze and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Science categories.

Exactly solvable models, that is, models with explicitly and completely diagonalizable Hamiltonians are too few in number and insufficiently diverse to meet the requirements of modern quantum physics. Quasi-exactly solvable (QES) models (whose Hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical way forward. Although QES models are a recent discovery, the results are already numerous. Collecting the results of QES models in a unified and accessible form, Quasi-Exactly Solvable Models in Quantum Mechanics provides an invaluable resource for physicists using quantum mechanics and applied mathematicians dealing with linear differential equations. By generalizing from one-dimensional QES models, the expert author constructs the general theory of QES problems in quantum mechanics. He describes the connections between QES models and completely integrable theories of magnetic chains, determines the spectra of QES Schrödinger equations using the Bethe-Iansatz solution of the Gaudin model, discusses hidden symmetry properties of QES Hamiltonians, and explains various Lie algebraic and analytic approaches to the problem of quasi-exact solubility in quantum mechanics. Because the applications of QES models are very wide, such as, for investigating non-perturbative phenomena or as a good approximation to exactly non-solvable problems, researchers in quantum mechanics-related fields cannot afford to be unaware of the possibilities of QES models.

Topics In Theoretical Physics Proceedings Of The Second Pacific Winter For Theoretical Physics

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Author : Yongmin Cho
language : en
Publisher: World Scientific
Release Date : 1997-04-01

Topics In Theoretical Physics Proceedings Of The Second Pacific Winter For Theoretical Physics written by Yongmin Cho and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-01 with categories.

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.

Exactly Solvable Models In Many Body Theory

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Author : Norman H March
language : en
Publisher: World Scientific
Release Date : 2016-05-27

Exactly Solvable Models In Many Body Theory written by Norman H March and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-27 with Science categories.

The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.

Journal Of Physics A

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Author :
language : en
Publisher:
Release Date : 2001

Journal Of Physics A written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematical physics categories.

Focuses on fundamental mathematical and computational methods underpinning physics. Relevant to statistical physics, chaotic and complex systems, classical and quantum mechanics, classical and quantum integrable systems and classical and quantum field theory.

Inequalities

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Author : Elliott H. Lieb
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Inequalities written by Elliott H. Lieb and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.