Quantum Dynamics For Classical Systems

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Quantum Dynamics for Classical Systems

Fabio Bagarello
Quantum Dynamics for Classical Systems Book PDF

Author : Fabio Bagarello
Publisher : John Wiley & Sons
Page : 186 pages
File Size : 50,5 Mb
Release : 2012-10-11
Category : Science
ISBN : 9781118400609

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Quantum Dynamics for Classical Systems by Fabio Bagarello Pdf

Introduces number operators with a focus on the relationship between quantum mechanics and social science Mathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum tools—the number operator in particular—can be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results. The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features in Quantum Dynamics for Classical Systems include: Applications across diverse fields including stock markets and population migration as well as a unique quantum perspective on these classes of models Illustrations of the use of creation and annihilation operators for classical problems Examples of the recent increase in research and literature on the many applications of quantum tools in applied mathematics Clarification on numerous misunderstandings and misnomers while shedding light on new approaches in the field Quantum Dynamics for Classical Systems is an ideal reference for researchers, professionals, and academics in applied mathematics, economics, physics, biology, and sociology. The book is also excellent for courses in dynamical systems, quantum mechanics, and mathematical models.

Classical Systems in Quantum Mechanics

Pavel Bóna
Classical Systems in Quantum Mechanics Book PDF

Author : Pavel Bóna
Publisher : Springer Nature
Page : 243 pages
File Size : 48,9 Mb
Release : 2020-06-23
Category : Science
ISBN : 9783030450700

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Classical Systems in Quantum Mechanics by Pavel Bóna Pdf

This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems – i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of “quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".

Classical and Quantum Dynamics of Constrained Hamiltonian Systems

Heinz J. Rothe,Klaus Dieter Rothe
Classical and Quantum Dynamics of Constrained Hamiltonian Systems Book PDF

Author : Heinz J. Rothe,Klaus Dieter Rothe
Publisher : World Scientific
Page : 317 pages
File Size : 55,9 Mb
Release : 2010
Category : Science
ISBN : 9789814299640

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Classical and Quantum Dynamics of Constrained Hamiltonian Systems by Heinz J. Rothe,Klaus Dieter Rothe Pdf

This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field?antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. All topics are well illustrated with examples emphasizing points of central interest. The book should enable graduate students to follow the literature on this subject without much problems, and to perform research in this field.

Quantum Dynamics for Classical Systems

Anonim
Quantum Dynamics for Classical Systems Book PDF

Author : Anonim
Publisher : Unknown
Page : 246 pages
File Size : 51,5 Mb
Release : 2012
Category : Electronic
ISBN : 6613977543

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Quantum Dynamics for Classical Systems by Anonim Pdf

With a focus on the relationship between quantum mechanics and social science, this book introduces the main ideas of number operators while avoiding excessive technicalities that aren't necessary in understanding the various mathematical applications. It discusses the use of mathematical tools related to quantum mechanics and features applications in finance, biology, and social science; systematically shows how to use creation and annihilation operators for classical problems; and addresses the recent increase in research and literature on the many applications of quantum tools in applied mathematics.

Quantum Dynamics

Eric R. Bittner
Quantum Dynamics Book PDF

Author : Eric R. Bittner
Publisher : CRC Press
Page : 334 pages
File Size : 40,9 Mb
Release : 2009-07-21
Category : Science
ISBN : 9781439882146

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Quantum Dynamics by Eric R. Bittner Pdf

Even though time-dependent spectroscopic techniques continue to push the frontier of chemical physics, they receive scant mention in introductory courses and are poorly covered in standard texts. Quantum Dynamics: Applications in Biological and Materials Systems bridges the gap between what is traditionally taught in a one-semester quantum chemistr

Dynamics, Information and Complexity in Quantum Systems

Fabio Benatti
Dynamics Information and Complexity in Quantum Systems Book PDF

Author : Fabio Benatti
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 44,9 Mb
Release : 2009-04-17
Category : Computers
ISBN : 9781402093067

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Dynamics, Information and Complexity in Quantum Systems by Fabio Benatti Pdf

This book offers a self-contained overview of the entropic approach to quantum dynamical systems. In it, complexity in quantum dynamics is addressed by comparison with the classical ergodic, information, and algorithmic complexity theories.

Classical and Quantum Dynamics

Walter Dittrich,Martin Reuter
Classical and Quantum Dynamics Book PDF

Author : Walter Dittrich,Martin Reuter
Publisher : Springer
Page : 461 pages
File Size : 45,6 Mb
Release : 2015-10-08
Category : Science
ISBN : 9783319216775

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Classical and Quantum Dynamics by Walter Dittrich,Martin Reuter Pdf

Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name a few. Well-chosen and detailed examples illustrate the perturbation theory, canonical transformations, the action principle and demonstrate the usage of path integrals. This new edition has been revised and enlarged with chapters on quantum electrodynamics, high energy physics, Green’s functions and strong interaction. "This book is a brilliant exposition of dynamical systems covering the essential aspects and written in an elegant manner. The book is written in modern language of mathematics and will ideally cater to the requirements of graduate and first year Ph.D. students...a wonderful introduction to any student who wants to do research in any branch of theoretical Physics." (Indian Journal of Physics)

Geometry from Dynamics, Classical and Quantum

José F. Cariñena,Alberto Ibort,Giuseppe Marmo,Giuseppe Morandi
Geometry from Dynamics Classical and Quantum Book PDF

Author : José F. Cariñena,Alberto Ibort,Giuseppe Marmo,Giuseppe Morandi
Publisher : Springer
Page : 739 pages
File Size : 48,7 Mb
Release : 2014-09-23
Category : Science
ISBN : 9789401792202

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Geometry from Dynamics, Classical and Quantum by José F. Cariñena,Alberto Ibort,Giuseppe Marmo,Giuseppe Morandi Pdf

This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.

Chaos in Classical and Quantum Mechanics

Martin C. Gutzwiller
Chaos in Classical and Quantum Mechanics Book PDF

Author : Martin C. Gutzwiller
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 41,8 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461209836

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Chaos in Classical and Quantum Mechanics by Martin C. Gutzwiller Pdf

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.

Quantum Dynamics of Simple Systems

G.L Oppo,Stephen M. Barnett,E Riis,M Wilkinson
Quantum Dynamics of Simple Systems Book PDF

Author : G.L Oppo,Stephen M. Barnett,E Riis,M Wilkinson
Publisher : CRC Press
Page : 386 pages
File Size : 40,7 Mb
Release : 1997-01-01
Category : Science
ISBN : 0750304901

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Quantum Dynamics of Simple Systems by G.L Oppo,Stephen M. Barnett,E Riis,M Wilkinson Pdf

The present level of experimental sophistication in quantum physics allows physicists to explore domains unimaginable just a decade ago and to test the most fundamental laws of quantum mechanics. This has led to renewed interest in devising new tests, experiments, and devices where it is possible to observe the interaction and localization of just a few atoms or photons. These techniques have been used to reveal new nonclassical effects, to question the limit of the principle of correspondence, and to force quantum behavior in semiconductors. With contributions from leading experts in quantum systems, Quantum Dynamics of Simple Systems provides an overview of the present range of quantum dynamics, exploring their use and exotic behaviors. It covers specific subjects of quantum dynamics in a competent and detailed way with emphasis on simple systems where few atoms or electrons are involved. This volume will prove to be a useful tool for graduate students as well as experienced physicists.

The Transition to Chaos

Linda Reichl
The Transition to Chaos Book PDF

Author : Linda Reichl
Publisher : Springer Nature
Page : 555 pages
File Size : 41,7 Mb
Release : 2021-04-12
Category : Science
ISBN : 9783030635343

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The Transition to Chaos by Linda Reichl Pdf

Based on courses given at the universities of Texas and California, this book treats an active field of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature; while problems at the ends of chapters help students clarify their understanding. This new edition has an updated presentation throughout, and a new chapter on open quantum systems.

Classical and Quantum Dynamics of Constrained Hamiltonian Systems

Heinz J. Rothe,Klaus Dieter Rothe
Classical and Quantum Dynamics of Constrained Hamiltonian Systems Book PDF

Author : Heinz J. Rothe,Klaus Dieter Rothe
Publisher : World Scientific
Page : 317 pages
File Size : 42,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814299657

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Classical and Quantum Dynamics of Constrained Hamiltonian Systems by Heinz J. Rothe,Klaus Dieter Rothe Pdf

This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field-antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. The book is comprehensive and well-illustrated with examples, enables graduate students to follow the literature on this subject without much problems, and to perform research in this field.

Quantum Statistical Mechanics in Classical Phase Space

ATTARD
Quantum Statistical Mechanics in Classical Phase Space Book PDF

Author : ATTARD
Publisher : IOP Publishing Limited
Page : 300 pages
File Size : 55,7 Mb
Release : 2021-11-30
Category : Science
ISBN : 0750340533

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Quantum Statistical Mechanics in Classical Phase Space by ATTARD Pdf

Quantum and classical physics are presented as distinct and unrelated. Transformation to classical phase space gives researchers access to algorithms derived from classical statistical mechanics that promise results on much more favourable terms. This book offers a framework for understanding the quantum world and collective molecular behaviour.

Classical and Quantum Dynamics in Condensed Phase Simulations

Bruce J Berne,Giovanni Ciccotti,David F Coker
Classical and Quantum Dynamics in Condensed Phase Simulations Book PDF

Author : Bruce J Berne,Giovanni Ciccotti,David F Coker
Publisher : World Scientific
Page : 880 pages
File Size : 44,7 Mb
Release : 1998-06-17
Category : Science
ISBN : 9789814496056

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Classical and Quantum Dynamics in Condensed Phase Simulations by Bruce J Berne,Giovanni Ciccotti,David F Coker Pdf

The school held at Villa Marigola, Lerici, Italy, in July 1997 was very much an educational experiment aimed not just at teaching a new generation of students the latest developments in computer simulation methods and theory, but also at bringing together researchers from the condensed matter computer simulation community, the biophysical chemistry community and the quantum dynamics community to confront the shared problem: the development of methods to treat the dynamics of quantum condensed phase systems. This volume collects the lectures delivered there. Due to the focus of the school, the contributions divide along natural lines into two broad groups: (1) the most sophisticated forms of the art of computer simulation, including biased phase space sampling schemes, methods which address the multiplicity of time scales in condensed phase problems, and static equilibrium methods for treating quantum systems; (2) the contributions on quantum dynamics, including methods for mixing quantum and classical dynamics in condensed phase simulations and methods capable of treating all degrees of freedom quantum-mechanically. Contents:Barrier Crossing: Classical Theory of Rare but Important Events (D Chandler)Monte Carlo Simulations (D Frenkel)Molecular Dynamics Methods for the Enhanced Sampling of Phase Space (B J Berne)Constrained and Nonequilibrium Molecular Dynamics (G Ciccotti & M Ferrario)From Erying to Kramers: Computation of Diffusive Barrier Crossing Rates (M J Ruiz-Montero)Monte Carlo Methods for Sampling of Rare Event States (W Janke)Proton Transfer in Ice (D Marx)Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions (H Jónsson et al.)RAW Quantum Transition State Theory (G Mills et al.)Dynamics of Peptide Folding (R Elber et al.)Theoretical Studies of Activated Processes in Biological Ion Channels (B Roux & S Crouzy)The Semiclassical Initial Value Representation for Including Quantum Effects in Molecular Dynamics Simulations (W H Miller)Tunneling in the Condensed Phase: Barrier Crossing and Dynamical Control (N Makri)Feynman Path Centroid Methods for Condensed Phase Quantum Dynamics (G A Voth)Quantum Molecular Dynamics Using Wigner Representation (V S Filinov et al.)Nonadiabatic Molecular Dynamics Methods for Diffusion (D Laria et al.)and other papers Readership: Computational and statistical physicists. Keywords:Quantum;Molecular Dynamics;DynamicsReviews: “… this volume is a useful introduction to currently popular, and widely-used techniques in chemical and statistical physics. The authors are well-respected researchers in the field and the level is appropriate to graduate students and researchers.” Journal of Statistical Physics

Quantum Dissipative Systems

Ulrich Weiss
Quantum Dissipative Systems Book PDF

Author : Ulrich Weiss
Publisher : World Scientific
Page : 527 pages
File Size : 41,8 Mb
Release : 2008
Category : Science
ISBN : 9789812791795

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Quantum Dissipative Systems by Ulrich Weiss Pdf

Major advances in the quantum theory of macroscopic systems, in combination with stunning experimental achievements, have brightened the field and brought it to the attention of the general community in natural sciences. Today, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book OCo originally published in 1990 and republished in 1999 as an enlarged second edition OCo delves much deeper than ever before into the fundamental concepts, methods, and applications of quantum dissipative systems, including the most recent developments. In this third edition, 26 chapters from the second edition contain additional material and several chapters are completely rewritten. It deals with the phenomena and theory of decoherence, relaxation, and dissipation in quantum mechanics that arise from the interaction with the environment. In so doing, a general path integral description of equilibrium thermodynamics and nonequilibrium dynamics is developed. Sample Chapter(s). Introduction (262 KB). Contents: General Theory of Open Quantum Systems; Few Sample Applications; Quantum Statistical Decay; The Dissipative Two-State System; The Dissipative Multi-State System. Readership: Advanced undergraduate and graduate students as well as researchers in quantum-statistical and condensed matter physics, quantum/classical mechanics, quantum information and computation, and quantum optics."