Quantum Mechanics of Non-Hamiltonian and Dissipative Systems

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

Part I. Quantum Kinematics
1. Quantum Kinematics of Bounded Observables
2. Quantum Kinematics of Unbounded Observables
3. Mathematical Structures in Quantum Kinematics
4. Spaces of Quantum Observables
5. Algebras of Quantum Observables
6. Mathematical Structures on State Sets
7. Mathematical Structures in Classical Kinematics
8. Quantization in Kinematics
9. Spectral Representation of Observable

Part II. Quantum Dynamics
10. Superoperators and its Properties
11. Superoperator Algebras and Spaces
12. Superoperator Functions
13. Semi-groups of Superoperators
14. Differential Equations for Quantum Observables
15. Quantum Dynamical Semi-Groups
16. Classical Non-Hamiltonian Dynamics
17. Quantization of Dynamical Structure
18. Quantum Dynamics of States
19. Dynamical Deformation of Algebras of Observables
20. Fractional Quantum Dynamics
21. Stationary States of non-Hamiltoniam Systems
22. Quantum Dynamical Methods
23. Path Integral for non-Hamiltoniam Systems
24. Non-Hamiltonian Systems as a Quantum Computers