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Breuer H.-P., Petruccione F. — The Theory of Open Quantum Systems
Breuer H.-P., Petruccione F. — The Theory of Open Quantum Systems



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Название: The Theory of Open Quantum Systems

Авторы: Breuer H.-P., Petruccione F.

Аннотация:

This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states.

The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented.

The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.


Язык: en

Рубрика: Физика/Квантовая механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 625

Добавлена в каталог: 01.08.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Liouville master equation, PDP in Hilbert space      306
Liouville operator      111 577
Liouville space      76
Liouville — Von Neumann equation      111
Lorentz equations      207
Macroscopic quantum coherence      496
Mandel Q parameter      334
Markov condition      14
Markov process      14
Markov process, quantum      117
Master equation      22 109
Master equation, adjoint      125 162 481
Master equation, Caldeira — Leggett      173 178 199 478
Master equation, Caldeira — Leggett, recoilless limit      200
Master equation, Floquet representation      433
Master equation, generalized      470
Master equation, Hu — Paz — Zhang      477
Master equation, Lindblad      122
Master equation, low-density      140
Master equation, Markovian      119
Master equation, mean-field      203
Master equation, non-linear      201
Master equation, Pauli      138 161
Master equation, quantum optical      145 585
Master equation, Redfield equation      132
Master equation, singular-coupling      139
Master equation, time-convolutionless      447 470 474 585
Master equation, unravelling      306
Master equation, unravelling, doubled Hilbert space      457 473
Master equation, weak-coupling      135
Matsubara frequencies      175
Memory kernel      444 469
Micro-reversibility      202
Microcausality      505
Microcausality, operation      512
Mixture, improper      76
Mixture, statistical      68
Moments      9
Monte Carlo method      361
Monte Carlo method, numerical efficiency      380
Monte Carlo wave function method      313
Morse oscillator      383
Multi-time exclusive probability      313
Multipole moment, electric      397
Multipole moment, magnetic      397
Nakajima — Zwanzig equation      444
Nelson Theorem      71
Noise kernel      174 264 477
Noise, additive      368
Noise, multiplicative      368
Non-Markovian dynamics      445 460
Normal ordering      163
Observable      60
Observable frequency      488
Observable, mean value      65
Observable, not self-averaging      381
Observable, self-averaging      381
Observable, strongly self-averaging      381
One-step process      24 161
Open system      115
Operation      86 168 322 453
Operation, direct photodetection      325
Operation, entangled probe state      527
Operation, homodyne photodetection      337
Operation, indirect measurement      322
Operation, laser cooling      413
Operation, multipole radiation      396
Operation, QED form      396
Operation, relativistic      510
Operation, representation theorem      89
Operation, state verification measurements      537
Orbital angular momentum density      393
Ordered cumulants      452 464
Ornstein — Uhlenbeck process      31
Ornstein — Uhlenbeck process, complex      165
Overdamped      157 266 488
Overdamped, strongly      268
P-representation      162
Parallel processing      388
Pauli operator      146
Phase flow      20
Phase space methods      162
Photocounting formula      351
Photocounting formula, coherent state      352
Photocounting formula, flourescence radiation      334
Photocounting formula, Fock state      352
Photocounting formula, QND measurement      356
Photocounting formula, Schroedinger cat      353
Photodetection      596
Photodetection, direct      324
Photodetection, field mode      350
Photodetection, heterodyne      342
Photodetection, homodyne      335 368
Photon antibunching      335
Physical frequency      477 478
Piecewise deterministic process      32
Piecewise deterministic process, continuous measurement      323
Piecewise deterministic process, density matrix      349 400
Piecewise deterministic process, direct photodetection      329
Piecewise deterministic process, doubled Hilbert space      457 473
Piecewise deterministic process, Floquet representation      432
Piecewise deterministic process, Hilbert space      305
Piecewise deterministic process, homodyne photodetection      339
Piecewise deterministic process, Kolmogorov forward equation      38
Piecewise deterministic process, laser cooling      415
Piecewise deterministic process, path integral representation      37
Piecewise deterministic process, sample paths      35
Piecewise deterministic process, state vector      399
Piecewise deterministic process, stochastic calculus      39
Planck distribution      152
Platen scheme      372
Poincare recurrence times      135
Pointer basis      270 274
Poisson process      23 49
Poisson process, non-homogeneous      25
Polarization vectors      411
Positive operator-valued measure      87
Pre-acceleration      611
Pre-measurement      274
Preferred basis      222
Preparation      83
Preparation time      590
Preparation, non-local states      554
Probability current density      29
Probability density functional, Hilbert space      291
Probability density functional, space of density matrices      299
probability distribution      6
Probability distribution, projective Hilbert space      286 295
Probability measure      4
Projection operator technique, Nakajima — Zwanzig      442
Projection operator technique, time-convolutionless      446 460
Projection postulate      83 502 509 532
Projection postulate, relativistic      511
Projection-valued measure      65
Propagator      15
Propagator function      193 608
Pure state      68
Quantization of radiation field      391
Quantum Boltzmann equation      202
Quantum channel      558 563
Quantum computer      226
Quantum dynamical semigroup      119 304 473 486
Quantum dynamical semigroup, contracting      123
Quantum dynamical semigroup, first standard form      121 136 139 153 178
Quantum dynamical semigroup, generator      119
Quantum dynamical semigroup, Heisenberg picture      122
Quantum dynamical semigroup, irreversibility      128
Quantum dynamical semigroup, Lindblad generator      122 137 139 141 145 152 178 463 470 473 477
Quantum dynamical semigroup, parametric Lindblad generator      201
Quantum dynamical semigroup, relaxation to equilibrium      137
Quantum efficiency      351
Quantum Jump      308
Quantum jump, selection algorithms      367
Quantum measurement, approximate      93 537
Quantum measurement, Bell-state operator      548
Quantum measurement, continuous      166 321 391 523
Quantum measurement, dynamical model      275
Quantum measurement, entropy      92
Quantum measurement, exchange      556
Quantum measurement, generalized      85
Quantum measurement, ideal      85 166 270
Quantum measurement, incomplete      398
Quantum measurement, indirect      96 168 508
Quantum measurement, local      508
Quantum measurement, non-ideal      167
Quantum measurement, non-local      526
Quantum measurement, non-local observables      530
Quantum measurement, non-selective      84 168 321 533 537
Quantum measurement, on ensembles of type $\mathcal{E}_P$      301
Quantum measurement, QND      102 532 544
Quantum measurement, QND state verification      536
Quantum measurement, quantum measurement, non-local, modular sums      535
Quantum measurement, selective      84 301
Quantum measurement, state verification      536 539
Quantum object      96
Quantum probe      96 508
Quantum probe, entangled      526
Quantum regression theorem      127 158 486
Quantum teleportation      557
Quantum trajectories      313
Quasi-energy      430
Qubit      226 231
Rabi frequency      154 171 254
Radiation damping      609 612
Radiation, dipole      398
Radiation, multipole      397
Random variable      5 63
Random variable, Hilbert space      286
Random variable, multivariate      8
Ray      68
Rayleigh scattering      160
Realization      6 12 362
Recoil energy      409 416
Recoil temperature      410
Reduced system      115
Reference state      443
Relative states      272
Renormalization transformation      425
Renormalized frequency      476 477
Reservoir      116 130
Reservoir correlation time      467
Response function      189
Runaway solutions      611
Runge — Kutta scheme      371
S-matrix      238
Sample      362
Sample path      12
Sample space      3
Sample, average      362
Scalability      388
Scale invariance      52
Scaling exponent      54
Scattering amplitude      239
Schmidt decomposition      77 538 551
Schmidt number      78
Schroedinger cat      242 251 353
Schroedinger equation      110
Schroedinger equation, non-linear      209 210 214 307
Schroedinger equation, stochastic      315
Schroedinger equation, stochastic, continuous spontaneous localization      345
Schroedinger equation, stochastic, heterodyne detection      344
Schroedinger equation, stochastic, homodyne detection      342
Schroedinger equation, stochastic, quantum state diffusion      347
Schwinger — Tomonaga equation      503
Self-adjoint operator      60
Single-step error      369
Singular value decomposition      78
Spectral correlation tensor      143 150
Spectral decomposition      61
Spectral density      174 228 264 463
Spectral density, Jaynes — Cummings model      467 471
Spectral density, Lorentz — Drude      175 191 491
Spectral density, Ohmic      175 185 186 191 265 476
Spectral density, photonic band gap      474
Spectral density, QED      607
Spectral density, super-Ohmic      607
Spectral family      60
Spectral measure      64
Spectrum, equilibrium fluctuations      189
Spectrum, resonance fluorescence      158 437
Spectrum, self-adjoint operator      61
Speed-up      388
Spin density      393
Spin-boson model      226 460 490
Squeezed vacuum      134 149
Stable distribution      52
Stable process      52
standard error of the mean      363
Stark shift      145 148 151 586
Stationary process      16
Statistical independence      5
Statistical operator      66
Stefan — Boltzmann law      575
Stern — Gerlach experiment      288
Stochastic collapse model      345
Stochastic differential equation      39 181
Stochastic differential equation, density matrix      348
Stochastic differential equation, diffusion process      41
Stochastic differential equation, PDP      42
Stochastic differential equation, PDP in Hilbert space      309
Stochastic process      11
Stochastic process, continuity condition      28
Stochastic process, generator      18
Stochastic process, multivariate      12
Stochastic process, non-Markovian      527
Stochastic process, relativistic      513 518
Stochastic simulation method      361 470 474
Stochastic simulation method, algorithm for PDPs      364
Stochastic simulation method, algorithm for SSEs      367
Stochastic simulation method, linear search      367
Stochastic simulation method, numerical efficiency      380
Stochastic simulation method, rejection method      367
Strong coupling regime      470
Sub-ensemble      68
Subadditivity      80
Subadditivity, strong      82
Super-operator      111
Super-radiance      210
Superselection rule      225
Superselection sector      224
T-matrix      239
TCL generator      447 461 486 491
TCL generator, perturbation expansion      447 451
TCL inhomogeneity      447 486 488 495
TCL inhomogeneity, perturbation expansion      453
Teleportation rate      560
Tensor product      75
Thermal correlation time      229 573
Time inversion      18
Time ordering, antichronological      446
Time ordering, chronological      444
Time-evolution operator      110
Transition rate      21
Transverse delta function      391
Trapping state      34 404
Trapping time      422
tunnelling      490
Two-level system      169 377 461 467
Ultraviolet cutoff      607
Ultraweak continuity      123
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