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.
Contents
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.
