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Alicki R., Lendi K. — Quantum Dynamical Semigroups And Applications

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Название: Quantum Dynamical Semigroups And Applications

Авторы: Alicki R., Lendi K.

Аннотация:

Reinvigorated by advances and insights, in particular from the active fields of quantum information and computing, the quantum theory of irreversible processes has recently attracted growing attention.

This volume introduces the very basic concepts of semigroup dynamics of open quantum systems and reviews a variety of modern applications. The present book, originally published as Vol. 286 (1987) in Lecture in Physics, has been newly typeset, revised and corrected and also expanded to include a review on recent developments.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2007

Количество страниц: 129

Добавлена в каталог: 02.02.2010

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Предметный указатель

Absorbed power      98
Adiabatic generalizations      112
Algebra of observables      40
Alternating external field      64
Anisotropy      71
Anisotropy parameter      69
Annihilation and creation operators      30 33
Averaging procedure      13
Bacterial photosynthesis      114
Banach space      2 11 42
BBKGY hierarchy      35
Benatti      110
Bifurcation point      77
Binomial distribution      38
Bipartite four-level system      109
Birth and death process      31
Bloch equations      47 62 64 72 97
Bloch sphere      97 112
Bloch — Boltzmann equations      114
Bloch — Wangsness — Redfield theory      114
Bloch-like equations      48 79 113
Bloch-lineshape      67
Bloch-vector      61
Bochner’s theorem      44
Boltzmann equation      21
Born approximation      18
Bose — Einstein occupancy      87
Bosons      29 32
Bounded functional      42
Bounded operators      2 42
Bounded solutions      58
Brillouin-zone      87
Central state      56 90
Characteristic lifetime      96
Chronological product      20
Classical detailed balance condition      18
Closed operator      43
Coarse graining procedure      115
Coherence spectroscopy      74
Coherence vector      53 69 70 90 111
Coherent states      32
Collapse and revival dynamics      115
Collective dissipative processes      23
Collective noise      110
Complete Nakajima — Zwanzig integro-differential equation      117
Complete orthonormal matrix set      49
Complete positivity      3 4 80 109
Completely positive quantum dynamical semigroups      90
Completely positive quantum transition map      10
Complex Hamiltonian      35
Complex spectrum      56
Constant of motion      54
Continuous energy spectrum      111
Continuous spectrum      35
Contracting semigroup      36 41
Convex set      2
Correlation functions      13 19 81 82 84 87 114 116
Correspondence principles      10
Damped and pumped oscillator      31
Davies      12 13 78 81 112
Davies generator      81
Davies theory      116
Decay constant      40
Decay operator      35
Decay time      40
Decoherence      110 114
Decoherence-free subspaces      110
Deficiency index      60
Degree of mixture      57
Density matrix      2 10 14 19 34 76
Detailed balance condition      10
Detailed balance generator      17
Diagonal dominance      50 75
Diagonal standard form      8
Diagonalizable      58
Diimcke      12 14
Dilations of quantum dynamical semigroups      19
Dirac-distribution      88
Discrete quantum Boltzmann equation      22
Discrete spectrum      12
Dissipative Jaynes-Cummings model      113
Dual map      42
Dual one-parameter semigroup      43
Dual space      42
Dynamical emergence of entanglement      110
Dynamical map in the Heisenberg picture      3
Dynamical map in the Schrodinger picture      4
Effective Hamiltonian      20
Electric dipole approximation      24
Elementary particle physics      109
Elementary particles      29
Elementary transition maps      10
Emch model      116
Emission and absorption      29
Energy trapping      28
Entanglement      109
entropy      5 22
Entropy production      6 89 91 93 95 112
Equilibrium      17
Equilibrium states      44
Error correction      114
Essential self-adjointness      9
exchange interaction      86
Far from equilibrium      57
Far from thermodynamic equilibrium      89
Fault-tolerant quantum computation      114
Femtosecond laser pulse      113
Fermi Golden Rule      18 39
fermions      29 32
Fidelity      114
Finite-dimensional Hilbert space      7 48 110
Fixed point      58
Floquet theory      115
Floreanini      110
Fluctuation-dissipation relations      112
Fluorescence signal      77
Fock space      33 40 87
Four-level system      113
Fourier transform      44
Free Brownian particle      111
Free dynamics      10
Free induction decay      68 80 97
Frequency detuning      66
Frequency off-set      97
Friction force      30
Frobenius-norm      56
Fundamental matrix solution      65
Gauge transformation      37
Generalized Bloch-equations      66 73
Generalized forces      92
Generalized H-theorem      6
Generalized master equation      10 11
Generator of a semigroup      7
Genuinely relaxing      58
Genuinely relaxing semigroup      90
Geometrical picture      56
Geometry of state space      112
Gibbs state      16 22 25 27
Gorini      3 8
harmonic oscillator      30
Hartree — Fock Hamiltonian      35
Heat bath      16
Heavy-ion dissipative collisions      20
Heisenberg ferromagnet      86
Heisenberg generator      32
Hilbert space      2 33
Hilbert-transforms      82
Holstein — Primakoff      86
Ideal quantum gas      13
Imaginary probabilities      47

Impurity spin      86
Inequalities      49
Infinite lattice systems      111
Infinite quantum systems      111
Infinitesimal generators of SU(N)      50
information      95
Information-theoretic interpretation      95
Inhomogeneity due to entangled initial states      116
Initial condition      60
Initial slip tricks      116
Initial transit time      115
Integral equation      11
Interaction picture      12
Involution      42
Irreversibility      5 115
Irreversible process      90 95
Irreversible time evolutions      3 5
Isometric      42
Isomorphic      42
Ito type (classical or commutative) stochastic differential equations      111
Jordan-block      58
Kadison inequality      5
KMS condition      44
Kossakowski      3 8 48 77 114
Kossakowski-generator      73 81 84 92 96
Kossakowski’s structure theorem      49
Kraus      3
Kraus quantum dynamical map      115
Kraus representation      116
Lamb      76
Lamb equation      35
Landau equation      21
Langevin equations      111
Langevin force      30
Laser theory      47
Lax-pair      54
Lee-type interaction Hamiltonians      38
Level shifts      83
Liapunov functions      116
Lidar      110 116
Lie algebra      51 55 92
Lindblad      3 6 8 52
Lindblad generator      113
Linear response theory      78
Lineshape function      67
Lineshapes      66
Localized spins      11
Long range quantum memory      114
Longitudinal and transverse relaxation times      62
Lorentz group      40
Lorentz invariant measure      41
Low density      14
Low density approximation      16 18
Magnetic neutron scattering      87
Magnetic resonance      61
Magnon frequency      87
Markov property      7
Markovian master equation      13
Massive spin zero particles      41
Maximum information      95
Mean-field      21 28 111
Mean-field limit      23
Measure of coherence      50
Measure of distance      95
Measure of irreversibility      94
Memory effects      11 114
Microreversibility      18 22
Minimal solution      110
Minkowski space      40
Moeller wave operators      14
Most general generator      8
Multi-exponential      64
Multi-time correlation functions      115
N-level systems      47
Naive Markovian approximation      11
Nakajima      10
Nakajima — Zwanzig      116
Neutron interferometry      109
Non — Markovian description      114
Non — Markovian dynamics      115
Non-diagonalizable      58
Non-ergodic behavior      27
Non-Markovian integro-differential equation      116
Non-negative      2
Non-phenomenological Kraus map      116
Non-trivial stationary state      56
Nonconservative dynamical map      19
Nonconservative quantum Markovian master equation      19
Nonconservative semigroups      20
Nonequilibrium      89 94
Nonequilibrium phase-transition      77
Nonlinear completely positive maps      111
Nonlinear dissipative Schrodinger equation      24
Nonlinear kinetic equations      21
Nonlinear maps      21
Nonlinear power-dependent relaxation      79
Nonlinear quantum dynamical semi-groups      21
Nonlinear quantum master equation      21
Nonlinear Schrodinger equation      28
Nonlocal structure of noise      114
Norm      42
Norm continuous      43
One-parameter contraction semigroup      7 43
One-parameter family of dynamical maps      7
One-parameter semigroup      42
One-parameter unitary group      44
One-sided Fourier transforms      85
Onsager theory      90 112
Open system      2 7 11 48 90
Operator-valued distributions      33
Operator-valued function      95
Operator-valued integral kernel      11
Optical Bloch equations      74
Optical masers      76
Optical potential      20
Oscillating terms      12 13
Pair-correlations      116
Partial trace      2
Partially relaxing      60
Pauli master equation      9 17
Pauli matrices      51
Phenomenological thermodynamics      6
Phonons      11
Poincare group      40
Poincare recurrences      13
Positive      2 42
Positive-definite integral kernel      9
Positive-definite matrix      8
Positive-semidefinite      2 49
Power broadening      67
Power-dependent relaxation times      80
probability distribution      14 37
Probability measure      6
Product state      23
Production operator      35
Projection      10 19
Proton-spin relaxation      113
Prototype of an irreversible process      94
Pure point spectrum      22
Quantum beats      77
Quantum computer      114
Quantum computing      109
Quantum detailed balance condition      16 27 31 111
Quantum dynamical Kraus maps      116
Quantum dynamical maps      6
Quantum dynamical semigroup      8 15 23 28 110
Quantum engines      112
Quantum fields      9 33
Quantum fluid      111
Quantum information      109

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