Quantum Mechanics of Non-Hamiltonian and Dissipative Systems (Volume 7) (Monograph Series on Nonlinear Science and Complexity, Volume 7)

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 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 Very Few Preliminaries Pt. I. Quantum Kinematics Ch. 1. Quantum Kinematics of Bounded Observables Ch. 2. Quantum Kinematics of Unbounded Observables Ch. 3. Mathematical Structures in Quantum Kinematics Ch. 4. Spaces of Quantum Observables Ch. 5. Algebras of Quantum Observables Ch. 6. Mathematical Structures on State Sets Ch. 7. Mathematical Structures in Classical Kinematics Ch. 8. Quantization in Kinematics Ch. 9. Spectral Representation of Observable Pt. II. Quantum Dynamics Ch. 10. Superoperators and its Properties Ch. 11. Superoperator Algebras and Spaces Ch. 12. Superoperator Functions Ch. 13. Semi-Groups of Superoperators Ch. 14. Differential Equations for Quantum Observables Ch. 15. Quantum Dynamical Semi-Group Ch. 16. Classical Non-Hamiltonian Dynamics Ch. 17. Quantization of Dynamical Structure Ch. 18. Quantum Dynamics of States Ch. 19. Dynamical Deformation of Algebras of Observables Ch. 20. Fractional Quantum Dynamics Ch. 21. Stationary States of Non-Hamiltonian Systems Ch. 22. Quantum Dynamical Methods Ch. 23. Path Integral for Non-Hamiltonian Systems Ch. 24. Non-Hamiltonian Systems as Quantum Computers. 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 This work is self-contained and can be used by students without a previous course in modern mathematics and physics. It describes the modern structure of the theory and covers the fundamental results of the last 15 years.