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E-raamat: Quantum Dynamical Systems [Oxford Scholarship Online e-raamatud]

(, Instituut voor Theoretische Fysica, K. U. Leuven, Belgium), (Institute of Theoretical Physics and Astrophysics, University of Gdansk, Poland)
  • Formaat: 296 pages
  • Ilmumisaeg: 12-Jul-2001
  • Kirjastus: Oxford University Press
  • ISBN-13: 9780198504009
  • Oxford Scholarship Online e-raamatud
  • Raamatu hind pole hetkel teada
  • Formaat: 296 pages
  • Ilmumisaeg: 12-Jul-2001
  • Kirjastus: Oxford University Press
  • ISBN-13: 9780198504009
Aimed at graduate students and researchers in physics and mathematics, this text presents a general framework for describing quantum dynamical systems. Numerous examples illustrate systems both finite and infinite, conservative and dissipative. Alicki (physics, U. of Gdansk, Poland) and Fannes (physics, K. U. Leuven, Belgium) place particular emphasis on the use of statistical and geometrical techniques such as correlation matrices and quantum dynamical entropy. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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.
Introduction
1(3)
Basic tools for quantum mechanics
4(50)
Hilbert spaces and operators
5(20)
Vector spaces
5(2)
Banach and Hilbert spaces
7(2)
Geometrical properties of Hilbert spaces
9(1)
Orthonormal bases
10(1)
Subspaces and Projectors
11(2)
Linear maps between Banach spaces
13(1)
Linear functionals and Dirac notation
14(4)
Adjoints of bounded operators
18(1)
Hermitian, unitary and normal operators
19(2)
Partial isometries and polar decomposition
21(1)
Spectra of operators
22(2)
Unbounded operators
24(1)
Measures
25(9)
Measures and integration
25(4)
Distributions
29(1)
Hilbert spaces of functions
30(1)
Spectral measures
31(3)
Probability in quantum mechanics
34(4)
Pure states
35(2)
Mixed states, density matrices
37(1)
Observables in quantum mechanics
38(6)
Compact operators
38(2)
Weyl quantization
40(4)
Composed systems
44(9)
Direct sums
45(1)
Tensor products
46(2)
Observables and states of composite systems
48(5)
Notes
53(1)
Deterministic dynamics
54(19)
Deterministic quantum dynamics
55(7)
Time-independent Hamiltonians
55(2)
Perturbations of Hamiltonians
57(1)
Time-dependent Hamiltonians
58(1)
Periodic perturbations and Floquet operators
59(2)
Kicked dynamics
61(1)
Classical limits
62(4)
Classical differentiable dynamics
66(4)
Self-adjoint Laplacians on compact manifolds
70(2)
Notes
72(1)
Spin chains
73(9)
Local observables
73(2)
States of a spin system
75(2)
Symmetries and dynamics
77(5)
Algebraic tools
82(21)
C*-algebras
82(5)
Examples
87(3)
States and representations
90(6)
Dynamical systems and von Neumann algebras
96(6)
Notes
102(1)
Fermionic dynamical systems
103(19)
Fermions in Fock space
103(10)
Fock space
103(2)
Creation and annihilation
105(3)
Second quantization
108(5)
The CAR-algebra
113(8)
Canonical anticommutation relations
113(1)
Quasi-free automorphisms
114(3)
Quasi-free states
117(4)
Notes
121(1)
Ergodic theory
122(24)
Ergodicity in classical systems
122(3)
Ergodicity in quantum systems
125(14)
Asymptotic Abelianness
125(7)
Multitime correlations
132(3)
Fluctuations around ergodic means
135(4)
Lyapunov exponents
139(5)
Classical dynamics
140(3)
Quantum dynamics
143(1)
Notes
144(2)
Quantum irreversibility
146(23)
Measurement theory
146(5)
Open quantum systems
151(2)
Complete positivity
153(7)
Quantum dynamical semigroups
160(4)
Quasi-free completely positive maps
164(3)
Notes
167(2)
Entropy
169(17)
von Neumann entropy
171(10)
Technical preliminaries
171(3)
Properties of von Neumann's entropy
174(2)
Mean entropy
176(2)
Entropy of quasi-free states
178(3)
Relative entropy
181(4)
Finite-dimensional case
181(1)
Maximum entropy principle
182(2)
Algebraic setting
184(1)
Notes
185(1)
Dynamical entropy
186(27)
Operational partitions
188(7)
Dynamical entropy
195(5)
Symbolic dynamics
195(2)
The entropy
197(3)
Some technical results
200(5)
Examples
205(6)
The quantum shift
205(2)
The free shift
207(1)
Infinite entropy
208(1)
Powers-Price shifts
209(2)
Notes
211(2)
Classical dynamical entropy
213(12)
The Kolmogorov-Sinai invariant
213(5)
H-density
218(7)
Finite quantum systems
225(15)
Quantum chaos
225(2)
Time scales
226(1)
Spectral statistics
226(1)
Semi-classical limits
227(1)
The kicked top
227(3)
The model
227(1)
The classical limit
228(1)
Kicked mean-field Heisenberg model
228(1)
Chaotic properties
229(1)
Gram matrices
230(5)
Entropy production
235(3)
Notes
238(2)
Model systems
240(17)
Entropy of the quantum cat map
240(3)
Ruelle's inequality
243(6)
Non-commutative Riemannian structures
244(2)
Non-commutative Lyapunov exponents
246(1)
Ruelle's inequality
247(1)
Examples
248(1)
Quasi-free Fermion dynamics
249(7)
Description of the model
250(1)
Main result
251(1)
Sketch of the proof
251(5)
Notes
256(1)
Epilogue
257(2)
References 259(10)
Index 269


Professor Robert Alicki, Institute of Theoretical Physics and Astrophysics, University of Gdansk, Poland. Professor Mark Fannes, Instituut voor Theoretische Fysica, K.U. Leuven, Belgium.