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Quantum Dynamics for Classical Systems

Quantum Dynamics for Classical Systems PDF Author: Fabio Bagarello
Publisher: John Wiley & Sons
ISBN: 1118400607
Category : Science
Languages : en
Pages : 248

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Book Description
Introduces number operators with a focus on the relationshipbetween quantum mechanics and social science Mathematics is increasingly applied to classical problems infinance, biology, economics, and elsewhere. Quantum Dynamics forClassical Systems describes how quantum tools—the numberoperator in particular—can be used to create dynamicalsystems in which the variables are operator-valued functions andwhose results explain the presented model. The book presentsmathematical results and their applications to concrete systems anddiscusses the methods used, results obtained, and techniquesdeveloped for the proofs of the results. The central ideas of number operators are illuminated whileavoiding excessive technicalities that are unnecessary forunderstanding and learning the various mathematical applications.The presented dynamical systems address a variety of contexts andoffer clear analyses and explanations of concluded results.Additional features in Quantum Dynamics for ClassicalSystems include: Applications across diverse fields including stock markets andpopulation migration as well as a unique quantum perspective onthese classes of models Illustrations of the use of creation and annihilation operatorsfor classical problems Examples of the recent increase in research and literature onthe many applications of quantum tools in applied mathematics Clarification on numerous misunderstandings and misnomers whileshedding light on new approaches in the field Quantum Dynamics for Classical Systems is an idealreference for researchers, professionals, and academics in appliedmathematics, economics, physics, biology, and sociology. The bookis also excellent for courses in dynamical systems, quantummechanics, and mathematical models.

Quantum Dynamics for Classical Systems

Quantum Dynamics for Classical Systems PDF Author: Fabio Bagarello
Publisher: John Wiley & Sons
ISBN: 1118400607
Category : Science
Languages : en
Pages : 248

View

Book Description
Introduces number operators with a focus on the relationshipbetween quantum mechanics and social science Mathematics is increasingly applied to classical problems infinance, biology, economics, and elsewhere. Quantum Dynamics forClassical Systems describes how quantum tools—the numberoperator in particular—can be used to create dynamicalsystems in which the variables are operator-valued functions andwhose results explain the presented model. The book presentsmathematical results and their applications to concrete systems anddiscusses the methods used, results obtained, and techniquesdeveloped for the proofs of the results. The central ideas of number operators are illuminated whileavoiding excessive technicalities that are unnecessary forunderstanding and learning the various mathematical applications.The presented dynamical systems address a variety of contexts andoffer clear analyses and explanations of concluded results.Additional features in Quantum Dynamics for ClassicalSystems include: Applications across diverse fields including stock markets andpopulation migration as well as a unique quantum perspective onthese classes of models Illustrations of the use of creation and annihilation operatorsfor classical problems Examples of the recent increase in research and literature onthe many applications of quantum tools in applied mathematics Clarification on numerous misunderstandings and misnomers whileshedding light on new approaches in the field Quantum Dynamics for Classical Systems is an idealreference for researchers, professionals, and academics in appliedmathematics, economics, physics, biology, and sociology. The bookis also excellent for courses in dynamical systems, quantummechanics, and mathematical models.

Classical and Quantum Dynamics

Classical and Quantum Dynamics PDF Author: Walter Dittrich
Publisher: Springer Science & Business Media
ISBN: 3642979211
Category : Science
Languages : en
Pages : 341

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Book Description
In the past 10 to 15 years, the quantum leap in understanding of nonlinear dynamics has radically changed the frame of reference of physicists contemplating such systems. This book treats classical and quantum mechanics using an approach as introduced by nonlinear Hamiltonian dynamics and path integral methods. It is written for graduate students who want to become familiar with the more advancedcomputational strategies in classical and quantum dynamics. Therefore, worked examples comprise a large part of the text. While the first half of the book lays the groundwork for a standard course, the second half, with its detailed treatment of the time-dependent oscillator, classical and quantum Chern-Simons mechanics, the Maslov anomaly and the Berry phase, willacquaint the reader with modern topological methods that have not as yet found their way into the textbook literature.

Quantum Dynamics for Classical Systems

Quantum Dynamics for Classical Systems PDF Author:
Publisher:
ISBN: 9786613977540
Category :
Languages : en
Pages : 246

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Book Description
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.

Classical Systems in Quantum Mechanics

Classical Systems in Quantum Mechanics PDF Author: Pavel Bóna
Publisher: Springer Nature
ISBN: 3030450708
Category : Science
Languages : en
Pages : 234

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Book Description
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 in Condensed Phase Simulations

Classical and Quantum Dynamics in Condensed Phase Simulations PDF Author: Bruce J Berne
Publisher: World Scientific
ISBN: 9814496057
Category : Science
Languages : en
Pages : 880

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Book Description
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

The Transition to Chaos

The Transition to Chaos PDF Author: Linda Reichl
Publisher: Springer Science & Business Media
ISBN: 1475743505
Category : Science
Languages : en
Pages : 675

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Book Description
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.

Geometry from Dynamics, Classical and Quantum

Geometry from Dynamics, Classical and Quantum PDF Author: José F. Cariñena
Publisher: Springer
ISBN: 9401792208
Category : Science
Languages : en
Pages : 719

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Book Description
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.

Classical and Quantum Physics

Classical and Quantum Physics PDF Author: G. Marmo
Publisher: Springer Nature
ISBN: 3030247481
Category : Science
Languages : en
Pages : 374

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Book Description
This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas.Most of Albertos’s scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics.Let us mention some of the fields of expertise of Alberto Ibort:Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others.In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic.His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed.

Energy Transfer Dynamics in Biomaterial Systems

Energy Transfer Dynamics in Biomaterial Systems PDF Author: Irene Burghardt
Publisher: Springer Science & Business Media
ISBN: 3642023061
Category : Science
Languages : en
Pages : 476

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Book Description
The role of quantum coherence in promoting the e ciency of the initial stages of photosynthesis is an open and intriguing question. Lee, Cheng, and Fleming, Science 316, 1462 (2007) The understanding and design of functional biomaterials is one of today’s grand challenge areas that has sparked an intense exchange between biology, materials sciences, electronics, and various other disciplines. Many new - velopments are underway in organic photovoltaics, molecular electronics, and biomimetic research involving, e. g. , arti cal light-harvesting systems inspired by photosynthesis, along with a host of other concepts and device applications. In fact, materials scientists may well be advised to take advantage of Nature’s 3. 8 billion year head-start in designing new materials for light-harvesting and electro-optical applications. Since many of these developments reach into the molecular domain, the - derstanding of nano-structured functional materials equally necessitates f- damental aspects of molecular physics, chemistry, and biology. The elementary energy and charge transfer processes bear much similarity to the molecular phenomena that have been revealed in unprecedented detail by ultrafast op- cal spectroscopies. Indeed, these spectroscopies, which were initially developed and applied for the study of small molecular species, have already evolved into an invaluable tool to monitor ultrafast dynamics in complex biological and materials systems. The molecular-level phenomena in question are often of intrinsically quantum mechanical character, and involve tunneling, non-Born- Oppenheimer e ects, and quantum-mechanical phase coherence.

Quantum Dynamics and Information

Quantum Dynamics and Information PDF Author: Robert Olkiewicz
Publisher: World Scientific
ISBN: 9814317438
Category : Science
Languages : en
Pages : 229

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Book Description
The central theme of this lecture collection is quantum dynamics, regarded mostly as the dynamics of entanglement and that of decoherence phenomena. Both these concepts appear to refer to the behavior of surprisingly fragile features of quantum systems supposed to model quantum memories and to implement quantum date processing routines. This collection may serve as an essential resource for those interested in both theoretical description and practical applications of fundamentals of quantum mechanics.