Quantum Mechanics of Non-Hamiltonian and Dissipative Systems

Vasily E. Tarasov (Eds.)9780444530912, 0444530916

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

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Table of contents :
Content:
Series Editors
Page ii

Volume Editor
Page iii

Copyright page
Page iv

Preface
Pages v-vi
Vasily E. Tarasov

Contents
Pages vii-xiii

A Very Few Preliminaries Review Article
Pages 1-7
Vasily E. Tarasov

Chapter 1 Quantum Kinematics of Bounded Observables Review Article
Pages 11-26
Vasily E. Tarasov

Chapter 2 Quantum Kinematics of Unbounded Observables Review Article
Pages 27-45
Vasily E. Tarasov

Chapter 3 Mathematical Structures in Quantum Kinematics Review Article
Pages 47-68
Vasily E. Tarasov

Chapter 4 Spaces of Quantum Observables Review Article
Pages 69-93
Vasily E. Tarasov

Chapter 5 Algebras of Quantum Observables Review Article
Pages 95-113
Vasily E. Tarasov

Chapter 6 Mathematical Structures on State Sets Review Article
Pages 115-128
Vasily E. Tarasov

Chapter 7 Mathematical Structures in Classical Kinematics Review Article
Pages 129-138
Vasily E. Tarasov

Chapter 8 Quantization in Kinematics Review Article
Pages 139-179
Vasily E. Tarasov

Chapter 9 Spectral Representation of Observable Review Article
Pages 181-209
Vasily E. Tarasov

Chapter 10 Superoperators and its Properties Review Article
Pages 213-236
Vasily E. Tarasov

Chapter 11 Superoperator Algebras and Spaces Review Article
Pages 237-249
Vasily E. Tarasov

Chapter 12 Superoperator Functions Review Article
Pages 251-266
Vasily E. Tarasov

Chapter 13 Semi-Groups of Superoperators Review Article
Pages 267-284
Vasily E. Tarasov

Chapter 14 Differential Equations for Quantum Observables Review Article
Pages 285-303
Vasily E. Tarasov

Chapter 15 Quantum Dynamical Semi-Group Review Article
Pages 305-335
Vasily E. Tarasov

Chapter 16 Classical Non-Hamiltonian Dynamics Review Article
Pages 337-360
Vasily E. Tarasov

Chapter 17 Quantization of Dynamical Structure Review Article
Pages 361-380
Vasily E. Tarasov

Chapter 18 Quantum Dynamics of States Review Article
Pages 381-407
Vasily E. Tarasov

Chapter 19 Dynamical Deformation of Algebras of Observables Review Article
Pages 409-432
Vasily E. Tarasov

Chapter 20 Fractional Quantum Dynamics Review Article
Pages 433-451
Vasily E. Tarasov

Chapter 21 Stationary States of Non-Hamiltonian Systems Review Article
Pages 453-462
Vasily E. Tarasov

Chapter 22 Quantum Dynamical Methods Review Article
Pages 463-474
Vasily E. Tarasov

Chapter 23 Path Integral for Non-Hamiltonian Systems Review Article
Pages 475-485
Vasily E. Tarasov

Chapter 24 Non-Hamiltonian Systems as Quantum Computers Review Article
Pages 487-520
Vasily E. Tarasov

Bibliography Review Article
Pages 521-531
Vasily E. Tarasov

Subject Index
Pages 533-539