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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
$\sigma$-algebra      3
Abraham — Lorentz equation      587 610
Acceleration time      590
Additive process      46
Adiabatic elimination of fast variables      208
Adiabatic theorem      256
ALICE      558
Annihilation operator      392
Anticommutator function      572
Approximation, Born      131 136 441 445 465 468
Approximation, Born — Markov      132 136 146 174 176
Approximation, Markov      131 136 141 470
Approximation, mean-field      203
Approximation, rotating wave      132 139 144 172 586
Approximation, singular coupling      169
Approximation, weak-coupling      131 206
Autocorrelation function      189 487
Back-action      220 322
Back-action, evasion condition      104 270 275
Backward propagator      446
Bare frequency      476
Basin of attraction      426
Bath      116
Bayes’s theorem      5 88
Bell inequalities      564
Bell states      561
Bell-state operator      548 553 560
Bethe formula      588
Black-body radiation      575
Bloch equation      154
Bloch vector      148 170 288 491
Bob      558
Bochner theorem      136
Boltzmann distribution      138 161 493
Boltzmann equation      201
Borel set      6
Brownian motion      30 460 607
Brownian motion, free      181 186 199
Brownian motion, quadratic potential      185
Caldeira — Leggett model      172 263 607
Cauchy process      57
Causality principle      517 539
Causality principle, local density matrix      546
Causality principle, measurement of entangled eigenstates      545
Causality principle, measurement of projections      544
Causality principle, state verification measurements      540
Chapman — Kolmogorov equation      16 117
Chapman — Kolmogorov equation, differential      17
Characteristic function      10
Characteristic function, Levy process      46
Characteristic function, observable      72
Characteristic function, Wigner      74 228
Chebyshev inequality      10
Classical communication channel      559
Closed system      110
Coherence length      613
Coherent population trapping      420
Coherent state      162 242
Coherent state representation      162
Coherent subspace      224 231
Commutator function      570
Complete absorber theory      585
Complete positivity      88 123
Composite quantum system      74
Compton wavelength      590
Concavity      80
Conditional probability      5
Conditional transition probability      15
Conditional transition probability, PDP in Hilbert space      306
Conditional transition probability, short-time behaviour      322 323
Continuity condition      28
Convergence, strong      369
Convergence, weak      369
Convex linear combination      68
Convexity      81
Cooling temperature      428
Correlation coefficient      10
Correlation coefficient, EPR correlations      522
Correlation function, bath      174
Correlation function, electric field      574
Correlation function, equilibrium      453
Correlation function, multi-time      125 316
Correlation function, multi-time, stochastic representation      319
Correlation function, Poisson process      26
Correlation function, reservoir      134
Correlation function, Wiener process      31
Coulomb gauge      391 569
Counter-term      173 184 193
Counting probability      313
Covariance matrix      10
Covariant state vector history      514
CPU time      377 379 380
CPU time, scaling behaviour      381
Creation operator      392
Cross-section      240
Cumulant expansion      451 464 580
Cumulative distribution function      7
Current density      23 393 576
Current super-operator      578 582
Cutoff frequency      483 487
Damping kernel      184
Dark state      404 410
de Broglie wavelength      234 241 591
Decay rate      122 472 474
Decay rate, time-dependent      463 472
Decoherence      166 220
Decoherence function      222
Decoherence function, Caldeira — Leggett model      264
Decoherence function, damped harmonic oscillator      249
Decoherence function, free Brownian motion      265
Decoherence function, short-time behaviour      225
Decoherence function, strongly overdamped      269
Decoherence function, system-size dependence      231
Decoherence function, thermal part      229
Decoherence function, vacuum optical      243
Decoherence function, vacuum part      229
Decoherence functional      588 593
Decoherence rate      233
Decoherence rate, Brownian motion      234
Decoherence rate, internal transitions      237
Decoherence rate, scattering      241
Decoherence time      222 233
Decoherence, bremsstrahlung      568 588
Decoherence, Brownian motion      234
Decoherence, electromagnetic field states      251
Decoherence, internal transitions      235
Decoherence, many-particle states      614
Decoherence, quantum measurement      269
Decoherence, scattering      237
Defect      35 308 364 366 406
Density matrix      66
Density matrix as covariance matrix      286 297 310
Density matrix, equilibrium      454
Density matrix, irrelevant part      441
Density matrix, QED      576
Density matrix, reduced      76 116 460
Density matrix, relevant part      441
Detailed balance      138
Deterministic drift      30
Deterministic process      19 304
Dicke states      214
Diffusion matrix      30
Diffusion process      28
Dissipation kernel      174 477
Dissipator      123 148 169 178 202 586
Doob’s theorem      31
Doppler energy      417
Dressed states      255 436
Dynamical map      118
Dynamical Phase      256
Dynamical semigroup      18
Effect      86
Ehrenfest equation      113 181
Eigenoperator      132 142 147 394
Einselection      225
Electron density      393
Elementary events      3
Ensemble      63
Ensemble of type $\mathcal{E}_P$      285 321
Ensemble of type $\mathcal{E}_{\rho}$      283
Entangled state      78 521
Entangled state, basis      560
Entangled state, maximally      78 223 273 539 552
Entangled state, preparation      554
Entangled state, QND verification      550
Entangled state, verification      538
entropy      552
Entropy, flux      129
Entropy, linear      82 223
Entropy, production rate      128
Entropy, quantum measurement      92
Entropy, relative      81 128
Entropy, Shannon      79
Entropy, von Neumann      79 129 203
Environment      115
EPR correlations      521
Erasing of local information      541 544
Ergodic system      453
Error, estimate      456
Error, relative      456 479 483 488
Estimator, expectation value      362
Estimator, statistical error      363
Euler scheme      370
Event      3
expectation value      9 297
Feynman propagator      581
Field modes      391
Field operators      391
Field vacuum      392
Field vacuum as quantum probe      325
Floquet states      430
Floquet theory      429
Fluctuation-dissipation theorem      190
Fock states      325
Fokker — Planck equation      29 164
Fokker — Planck equation, diffusion in Hilbert space      314
Foliation      506 511
Gaussian process      31
Gaussian state      450 481 580
Gauss’s law      392
Gauss’s theorem      504
Generating function      11
Generating function, cumulant      46
Gibbs state      129 137 443
Golden Rule      23 138 146 468
H-Theorem      203
Hamiltonian, atom-laser interaction      411
Hamiltonian, Caldeira — Leggett      172 475
Hamiltonian, density      502
Hamiltonian, electromagnetic field      392
Hamiltonian, Jaynes — Cummings      253
Hamiltonian, non-Hermitian      306
Hamiltonian, QED      576
Hamiltonian, Spin-Boson      225 490
harmonic oscillator      160 242 266 373 460 474 491
Hartree equation      203
Heisenberg equation of motion      112
Heisenberg equation of motion, Brownian motion      182
Heisenberg picture, closed system      112
Heisenberg picture, open system      124
Heisenberg picture, stochastic representation      316
Helmholtz equation      391
Heun scheme      370
High harmonic generation      433
Hilbert space      59
Hilbert space path integral      311
Hilbert space path integral, direct photodetection      332
Hilbert space path integral, photodetection on a field mode      351
Hilbert space, Dirac measure      291
Hilbert space, doubled      316 457
Hilbert space, extended      430
Hilbert space, functional derivatives      304
Hilbert space, functional integration      292
Hilbert space, projective      68
Hilbert space, volume element      292
Hilbert — Schmidt operator      76
Homogeneous process      16
Hypersurface      502 508
Hypersurface, unit normal vector      503
Hypersurface, variation      503
Increments, complex Wiener process      165
Increments, field of Poisson      43
Increments, independent      46
Increments, Poisson process      27 363 415
Increments, stationary      46
Increments, Wiener process      32 368
Infinitely divisible      47
Influence functional, Feynman — Vernon      192 193 475
Influence functional, path integral representation      195
Influence functional, QED      581 582
Influence functional, QED, path integral representation      608
Influence functional, super-operator representation      193
Influence super-operator      581
Infrared catastrophe      595
Initial condition, factorizing      446 477
Initial condition, non-factorizing      446 452 489
Initial jolts      188 487
Integrability condition      505 513
Interaction picture      113
Interference contrast      247
Invariant manifolds      416
Irreversibility      19
Isolated system      110
Ito calculus      41
Ito calculus, diffusion process      39
Ito calculus, PDP      42
Ito formula      41
Jaynes — Cummings model      460
Jaynes — Cummings model on resonance      470
Jaynes — Cummings model with detuning      471
Jaynes — Cummings model, photonic band gap      474
Joint probability distributions      12 70
Joint probability distributions, consistent hierarchy      521
Joint probability distributions, family of      13
Joint probability distributions, relativistically invariant      518
Jump process      21
Klein inequality      81
KMS condition      137
Kolmogorov axioms      4
Kolmogorov consistency conditions      13
Kolmogorov forward equation      311
Kolmogorov theorem      14
Lamb shift      136 145 148 151 468 474 477 586
Lamb shift, time-dependent      463 472
Larmor formula      610
Laser cooling      409
Laser cooling, momentum distributions      426
Laser cooling, sub-recoil      410
Laser equations      207
Levy measure      48
Levy measure, stable      53 410 423
Levy process      45
Levy process, characteristic exponent      46 54
Levy process, generator      47
Levy — Khinchine theorem      47
Lieb theorem      82 128
Lindblad operator      122
Lindblad theorem      122 473
Liouville equation      21 305
Liouville master equation      33
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