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Quantum Mechanics Of Non Hamiltonian And Dissipative Systems

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Quantum Mechanics of Non Hamiltonian and Dissipative Systems

Quantum Mechanics of Non Hamiltonian and Dissipative Systems Book
Author : Vasily Tarasov
Publisher : Elsevier
Release : 2008-06-06
ISBN : 9780080559711
Language : En, Es, Fr & De

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Book Description :

Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006. • Requires no preliminary knowledge of graduate and advanced mathematics • Discusses the fundamental results of last 15 years in this theory • Suitable for courses for undergraduate students as well as graduate students and specialists in physics mathematics and other sciences

Classical And Quantum Dissipative Systems Second Edition

Classical And Quantum Dissipative Systems  Second Edition  Book
Author : Razavy Mohsen
Publisher : World Scientific
Release : 2017-02-27
ISBN : 9813207930
Language : En, Es, Fr & De

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Book Description :

Dissipative forces play an important role in problems of classical as well as quantum mechanics. Since these forces are not among the basic forces of nature, it is essential to consider whether they should be treated as phenomenological interactions used in the equations of motion, or they should be derived from other conservative forces. In this book we discuss both approaches in detail starting with the Stoke's law of motion in a viscous fluid and ending with a rather detailed review of the recent attempts to understand the nature of the drag forces originating from the motion of a plane or a sphere in vacuum caused by the variations in the zero-point energy. In the classical formulation, mathematical techniques for construction of Lagrangian and Hamiltonian for the variational formulation of non-conservative systems are discussed at length. Various physical systems of interest including the problem of radiating electron, theory of natural line width, spin-boson problem, scattering and trapping of heavy ions and optical potential models of nuclear reactions are considered and solved.

Applications in Physics

Applications in Physics Book
Author : Vasily E. Tarasov
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2019-02-19
ISBN : 3110571722
Language : En, Es, Fr & De

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Book Description :

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fifth volume collects authoritative chapters covering several applications of fractional calculus in physics, including electrodynamics, statistical physics and physical kinetics, and quantum theory.

Symmetries in Science X

Symmetries in Science X Book
Author : Bruno Gruber,Michael Ramek
Publisher : Springer Science & Business Media
Release : 2013-06-29
ISBN : 1489915370
Language : En, Es, Fr & De

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Book Description :

Proceedings an International Symposium held in Bregenz, Austria, July 13-18, 1997

Lagrangian and Hamiltonian Methods for Nonlinear Control 2003

Lagrangian and Hamiltonian Methods for Nonlinear Control 2003 Book
Author : A Astolfi,Francisco Gordillo,A J Van Der Schaft
Publisher : Elsevier
Release : 2003-10-21
ISBN : 9780080442785
Language : En, Es, Fr & De

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Book Description :

This is the second of a series of IFAC Workshops initiated in 2000. The first one chaired and organized by Profs. N. Leonard and R. Ortega, was held in Princeton in March 2000. This proceedings volume looks at the role-played by Lagrangian and Hamiltonian methods in disciplines such as classical mechanics, quantum mechanics, fluid dynamics, electrodynamics, celestial mechanics and how such methods can be practically applied in the control community. *Presents and illustrates new approaches to nonlinear control that exploit the Lagrangian and Hamiltonian structure of the system to be controlled *Highlights the important role of Lagrangian and Hamiltonian Structures as design methods

Quantum Dissipative Systems

Quantum Dissipative Systems Book
Author : Ulrich Weiss
Publisher : World Scientific
Release : 1999
ISBN : 9789810240929
Language : En, Es, Fr & De

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Book Description :

Recent advances in the quantum theory of macroscopic systems have brightened up the field and brought it into the focus of a general community in natural sciences. The fundamental concepts, methods and applications including the most recent developments, previously covered for the most part only in the original literature, are presented here in a comprehensive treatment to an audience who is reasonably familiar with quantum-statistical mechanics and has had rudimentary contacts with the path integral formulation. This book deals with the phenomena and theory of decoherence and dissipation in quantum mechanics that arise from the interaction with the environment. A general path integral description of equilibrium thermodynamics and non-equilibrium dynamics is developed. The approach can deal with weak and strong dissipation, and with all kinds of memory effects. Applications to numerous phenomenological and microscopic systems are presented, where emphasis is put on condensed matter and chemical physics. The basic principles and methods of preparation functions, propagating functions, and time correlation functions are described. Special attention is focused on quantum tunneling and quantum coherence phenomena of macroscopic variables. Many illustrative realistic examples are discussed in some detail. The book attempts to provide a broad perspective and to open up this rapidly developing field to interested researchers normally working in different fields. In this enlarged second edition, the nineteen chapters of the first edition have been expanded by about one-third to better meet both the requests of newcomers to the field and of advanced readers, and seven new chapters have beenadded that review the most recent important developments.

Fractional Dynamics

Fractional Dynamics Book
Author : Vasily E. Tarasov
Publisher : Springer Science & Business Media
Release : 2011-01-04
ISBN : 3642140033
Language : En, Es, Fr & De

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Book Description :

"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.

Quantum Theory from a Nonlinear Perspective

Quantum Theory from a Nonlinear Perspective Book
Author : Dieter Schuch
Publisher : Springer
Release : 2018-01-20
ISBN : 3319655949
Language : En, Es, Fr & De

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Book Description :

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.

Quantum Probability and Infinite Dimensional Analysis

Quantum Probability and Infinite Dimensional Analysis Book
Author : Habib Ouerdiane
Publisher : World Scientific
Release : 2010
ISBN : 9814295434
Language : En, Es, Fr & De

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Book Description :

This is the proceedings of the 29th Conference on Quantum Probability and Infinite Dimensional Analysis, which was held in Hammamet, Tunisia.

Dynamics and Thermodynamics of Systems with Long Range Interactions

Dynamics and Thermodynamics of Systems with Long Range Interactions Book
Author : Thierry Dauxois,Stefano Ruffo,Ennio Arimondo,Martin Wilkens
Publisher : Springer Science & Business Media
Release : 2002-12-10
ISBN : 3540443150
Language : En, Es, Fr & De

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Book Description :

Properties of systems with long range interactions are still poorly understood despite being of importance in most areas of physics. The present volume introduces and reviews the effort of constructing a coherent thermodynamic treatment of such systems by combining tools from statistical mechanics with concepts and methods from dynamical systems. Analogies and differences between various systems are examined by considering a large range of applications, with emphasis on Bose--Einstein condensates. Written as a set of tutorial reviews, the book will be useful for both the experienced researcher as well as the nonexpert scientist or postgraduate student.

Instabilities and Chaos in Quantum Optics II

Instabilities and Chaos in Quantum Optics II Book
Author : N.B. Abraham,F.T. Arecchi,L.A. Lugiato
Publisher : Springer Science & Business Media
Release : 1988-09-01
ISBN : 9780306429149
Language : En, Es, Fr & De

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Book Description :

This volume contains tutorial papers from the lectures and seminars presented at the NATO Advanced Study Institute on "Instabilities and Chaos in Quantum Optics", held at the "Il Ciocco" Conference Center, Castelvecchio Pascoli, Lucca, Italy, June 28-July 7, 1987. The title of the volume is designated Instabilities and Chaos in Quantum Optics II, because of the nearly coincident publication of a collection of articles on research in this field edited by F.T. Arecchi and R.G. Harrison [Instabilities and Chaos in Quantum Optics, (Springer, Berlin, 1987) 1. That volume provides more detailed information about some of these topics. Together they will serve as a comprehensive and tutorial pair of companion volumes. This school was directed by Prof. Massimo Inguscio, of the Department of Physics, University of Naples, Naples, Italy to whom we express our gratitude on behalf of all lecturers and students. The Scientific Advisory Committee consisted of N.B. Abraham of Bryn Mawr College; F.T. Arecchi of the National Institute of Optics in Florence and the University of Florence, and L.A. Lugiato of the Politechnic Institute of Torino. The school continues the long tradition of Europhysics Summer Schools in Quantum Electronics which have provided instruction and training for young researchers and advanced students working in this field for almost twenty years.

Equilibrium and Non equilibrium Statistical Mechanics

Equilibrium and Non equilibrium Statistical Mechanics Book
Author : Carolyn M. Van Vliet
Publisher : World Scientific
Release : 2008
ISBN : 9812704779
Language : En, Es, Fr & De

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Book Description :

This book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round.

Nonlinear Dynamics in Classical and Quantum Systems

Nonlinear Dynamics in Classical and Quantum Systems Book
Author : Hans Cruz Prado
Publisher :
Release : 2020
ISBN :
Language : En, Es, Fr & De

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Book Description :

In this work a nonlinear evolution of pure states of a finite dimensional quantum system is introduced, in particular a Riccati evolution equation. It is shown how this class of dynamics is actually a Hamiltonian dynamics in the complex projective space. In this projective space it is shown that there is a nonlinear superposition rule, consistent with its linear counterpart in the Hilbert space. As an example, the developed nonlinear formalism is applied to the semiclassical Jaynes-Cummings model. Later, it is shown that there is an inherent nonlinear evolution in the dynamics of the so-called generalized coherent states. To show this, the fact that in quantum mechanics it is possible to immerse a ''classical'' manifold into the Hilbert space is employed, such that one may parametrize the time-dependence of the wave function through the variation of parameters in the classical manifold. The immersion allows to consider the so-called principle of analogy, i.e. using the procedures and structures available from the classical setting to employ them in the quantum setting. Finally, it is introduced the contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and it is showed that it is a natural candidate for a geometric description of non-dissipative and dissipative systems.