Quantum Dynamical Systems [Hardcover]

The present book provides a general framework for studying quantum and classical dynamical systems, both finite and infinite, conservative and dissipative. Special attention is paid to the use of statistical and geometrical techniques, such as multitime correlation functions, quantum dynamical entropy, and non-commutative Lyapunov exponents, for systems with a complex evolution. The material is presented in a concise but self-contained and mathematically friendly way with main ideas introduced and illustrated by numerous examples which are directly connected to the relevant physics.

Preface
1. Introduction
2. Basic tools for quantum mechanics
2.1. Hilbert spaces and operators
2.2. Measures
2.3. Probability in quantum mechanics
2.4. Observables in quantum mechanics
2.5. Composed systems
2.6. Notes
3. Deterministic dynamics
3.1. Deterministic quantum dynamics
3.2. Classical Limits
3.3. Classical differentiable dynamics
3.4. Self-adjoint Laplacians on compact manifolds
3.5. Notes
4. Spin chains
4.1. Local observables
4.2. States of a spin system
4.3. Symmetries and dynamics
5. Algebraic tools
5.1. C*-algebras
5.2. Examples
5.3. States and representations
5.4. Dynamical systems and von Neumann algebras
5.5. Notes
6. Fermionic dynamical systems
6.1. Fermions in Fock space
6.2. The CAR-algebra
6.3. Notes
7. Ergodic theory
7.1. Ergodicity in classical systems
7.2. Ergodicity in quantum systems
7.3. Lyapunov exponents
7.4. Notes
8. Quantum irreversibility
8.1. Measurement theory
8.2. Open quantum systems
8.3. Complete positivity
8.4. Quantum dynamical semigroups
8.5. Quasi-free completely positive maps
8.6. Notes
9. Entropy
9.1. von Neumann entropy
9.2. Relative entropy
9.3. Notes
10. Dynamical entropy
10.1. Operational partitions
10.2. Dynamical entropy
10.3. Some technical results
10.4. Examples
10.5. Notes
11. CllÓe