QUANTUM DISSIPATIVE SYS (3RD ED)

By: WEISS ULRICH

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Paperback | 19 March 2008 | Edition Number 3

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526 Pages

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Major advances in the quantum theory of macroscopic systems, in combination with stunning experimental achievements, have brightened the field and brought it to the attention of the general community in natural sciences. Today, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book - originally published in 1990 and republished in 1999 as an enlarged second edition - delves much deeper than ever before into the fundamental concepts, methods, and applications of quantum dissipative systems, including the most recent developments.In this third edition, 26 chapters from the second edition contain additional material and several chapters are completely rewritten. It deals with the phenomena and theory of decoherence, relaxation, and dissipation in quantum mechanics that arise from the interaction with the environment. In so doing, a general path integral description of equilibrium thermodynamics and nonequilibrium dynamics is developed.

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Non-Fiction Science Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory Materials & States of Matter Condensed Matter Physics including Liquid State & Solid State Physics Classical Mathematics Booktopia Publisher Services World Scientific Publishing

Introduction	p. 1
General Theory of Open Quantum Systems	p. 5
Diverse limited approaches: a brief survey	p. 5
Langevin equation for a damped classical system	p. 5
New schemes of quantization	p. 7
Traditional system-plus-reservoir methods	p. 8
Quantum-mechanical master equations for weak coupling	p. 8
Operator Langevin equations for weak coupling	p. 12
Quantum and quasiclassical Langevin equation	p. 13
Phenomenological methods	p. 14
Stochastic dynamics in Hilbert space	p. 15
System-plus-reservoir models	p. 18
Harmonic oscillator bath with linear coupling	p. 19
The Hamiltonian of the global system	p. 19
The road to the classical generalized Langevin equation	p. 21
Phenomenological modeling	p. 24
Quasiclassical Langevin equation	p. 25
Ohmic and frequency-dependent damping	p. 27
Rubin model	p. 30
The Spin-Boson model	p. 31
The model Hamiltonian	p. 31
Josephson two-state systems: flux and charge qubit	p. 35
Microscopic models	p. 38
Acoustic polaron: one-phonon and two-phonon coupling	p. 40
Optical polaron	p. 41
Interaction with fermions (normal and superconducting)	p. 43
Superconducting tunnel junction	p. 46
Charging and environmental effects in tunnel junctions	p. 47
The global system for single electron tunneling	p. 49
Resistor, inductor and transmission lines	p. 53
Charging effects in Josephson junctions	p. 54
Nonlinear quantum environments	p. 55
Imaginary-time path integrals	p. 57
The density matrix: general concepts	p. 58
Effective action and equilibrium density matrix	p. 62
Open system with bilinear coupling to a harmonic reservoir	p. 63
State-dependent memory-friction	p. 67
Spin-boson model	p. 68
Acoustic polaron and defect tunneling: one-phonon coupling	p. 69
Acoustic polaron: two-phonon coupling	p. 75
Tunneling between surfaces: one-phonon coupling	p. 77
Optical polaron	p. 79
Heavy particle in a metal	p. 80
Heavy particle in a superconductor	p. 86
Effective action for a Josephson junction	p. 88
Electromagnetic environment	p. 95
Partition function of the open system	p. 96
General path integral expression	p. 96
Semiclassical approximation	p. 97
Partition function of the damped harmonic oscillator	p. 98
Functional measure in Fourier space	p. 99
Partition function of the damped harmonic oscillator revisited	p. 100
Quantum statistical expectation values in phase space	p. 102
Generalized Weyl correspondence	p. 103
Generalized Wigner function and expectation values	p. 105
Real-time path integrals and dynamics	p. 106
Feynman-Vernon method for a product initial state	p. 108
Decoherence and friction	p. 112
General initial states and preparation function	p. 115
Complex-time path integral for the propagating function	p. 116
Real-time path integral for the propagating function	p. 120
Extremal paths	p. 123
Classical limit	p. 124
Semiclassical limit: quasiclassical Langevin equation	p. 125
Stochastic unraveling of influence functionals	p. 127
Brief summary and outlook	p. 130
Few Simple Applications	p. 131
Damped harmonic oscillator	p. 131
Fluctuation-dissipation theorem	p. 132
Stochastic modeling	p. 135
Susceptibility for Ohmic friction and Drude damping	p. 138
Strict Ohmic friction	p. 138
Drude damping	p. 138
The position autocorrelation function	p. 139
Ohmic damping	p. 140
Algebraic spectral density	p. 142
Partition function, internal energy and density of states	p. 143
Partition function and internal energy	p. 143
Spectral density of states	p. 146
Mean square of position and momentum	p. 147
General expressions for coloured noise	p. 147
Strict Ohmic case	p. 149
Ohmic friction with Drude regularization	p. 150
Equilibrium density matrix	p. 152
Purity	p. 154
Quantum Brownian free motion	p. 156
Spectral density, damping function and mass renormalization	p. 157
Displacement correlation and response function	p. 159
Ohmic damping	p. 160
Frequency-dependent damping	p. 163
Response function and mobility	p. 163
Mean square displacement	p. 165
The thermodynamic variational approach	p. 167
Centroid and the effective classical potential	p. 167
Centroid	p. 167
The effective classical potential	p. 169
Variational method	p. 170
Variational method for the free energy	p. 170
Variational method for the effective classical potential	p. 171
Variational perturbation theory	p. 174
Expectation values in coordinate and phase space	p. 176
Suppression of quantum coherence	p. 178
Nondynamical versus dynamical environment	p. 179
Suppression of transversal and longitudinal interferences	p. 180
Localized bath modes and universal decoherence	p. 182
A model with localized bath modes	p. 182
Statistical average of paths	p. 184
Ballistic motion	p. 185
Diffusive motion	p. 186
Quantum Statistical Decay	p. 189
Introduction	p. 189
Classical rate theory: a brief overview	p. 192
Classical transition state theory	p. 192
Moderate-to-strong-damping regime	p. 193
Strong damping regime	p. 195
Weak-damping regime	p. 197
Quantum rate theory: basic methods	p. 199
Formal rate expressions in terms of flux operators	p. 200
Quantum transition state theory	p. 202
Semiclassical limit	p. 203
Quantum tunneling regime	p. 205
Free energy method	p. 207
Centroid method	p. 211
Multidimensional quantum rate theory	p. 212
Crossover from thermal to quantum decay	p. 216
Normal mode analysis at the barrier top	p. 216
Turnover theory for activated rate processes	p. 218
The crossover temperature	p. 222
Thermally activated decay	p. 223
Rate formula above the crossover regime	p. 224
Quantum corrections in the preexponential factor	p. 227
The quantum Smoluchowski equation approach	p. 228
Multidimensional quantum transition state theory	p. 230
The crossover region	p. 233
Beyond steepest descent above T[subscript 0]	p. 235
Beyond steepest descent below T[subscript 0]	p. 236
The scaling region	p. 239
Dissipative quantum tunneling	p. 242
The quantum rate formula	p. 242
Thermal enhancement of macroscopic quantum tunneling	p. 245
Quantum decay in a cubic potential for Ohmic friction	p. 246
Bounce action and quantum prefactor	p. 247
Analytic results for strong Ohmic dissipation	p. 248
Quantum decay in a tilted cosine washboard potential	p. 250
Concluding remarks	p. 257
The Dissipative Two-State System	p. 259
Introduction	p. 259
Truncation of the double-well to the two-state system	p. 261
Shifted oscillators and orthogonality catastrophe	p. 261
Adiabatic renormalization	p. 263
Renormalized tunnel matrix element	p. 264
Polaron transformation	p. 269
Pair interaction in the charge picture	p. 269
Analytic expression for any s and arbitrary cutoff [omega subscript c]	p. 269
Ohmic dissipation and universality limit	p. 271
Thermodynamics	p. 272
Partition function and specific heat	p. 272
Exact formal expression for the partition function	p. 272
Static susceptibility and specific heat	p. 274
The self-energy method	p. 275
The limit of high temperatures	p. 277
Noninteracting-kink-pair approximation	p. 277
Weak-damping limit	p. 279
The self-energy method revisited: partial resummation	p. 280
Ohmic dissipation	p. 281
General results	p. 282
The special case K = 1/2	p. 283
Non-Ohmic spectral densities	p. 288
The sub-Ohmic case	p. 288
The super-Ohmic case	p. 289
Relation between the Ohmic TSS and the Kondo model	p. 290
Anisotropic Kondo model	p. 290
Resonance level model	p. 292
Equivalence of the Ohmic TSS with the 1/r[superscript 2] Ising model	p. 293
Electron transfer and incoherent tunneling	p. 294
Electron transfer	p. 295
Adiabatic bath	p. 296
Marcus theory for electron transfer	p. 298
Incoherent tunneling in the nonadiabatic regime	p. 302
General expressions for the nonadiabatic rate	p. 302
Probability for energy exchange: general results	p. 304
The spectral probability density for absorption at T = 0	p. 307
Crossover from quantum-mechanical to classical behaviour	p. 308
The Ohmic case	p. 312
Exact nonadiabatic rates for K = 1/2 and K = 1	p. 314
The sub-Ohmic case (0 < s < 1)	p. 315
The super-Ohmic case (s > 1)	p. 317
Incoherent defect tunneling in metals	p. 319
Single charge tunneling	p. 322
Weak-tunneling regime	p. 322
The current-voltage characteristics	p. 326
Weak tunneling of 1D interacting electrons	p. 328
Tunneling of Cooper pairs	p. 330
Tunneling of quasiparticles	p. 331
Two-state dynamics	p. 333
Initial preparation, expectation values, and correlations	p. 333
Product initial state	p. 333
Thermal initial state	p. 336
Exact formal expressions for the system dynamics	p. 340
Sojourns and blips	p. 340
Conditional propagating functions	p. 343
The expectation values [left angle bracket sigma right angle bracket subscript t] (j = x, y, z)	p. 344
Correlation and response function of the populations	p. 346
Correlation and response function of the coherences	p. 348
Generalized exact master equation and integral relations	p. 349
The noninteracting-blip approximation (NIBA)	p. 352
Symmetric Ohmic system in the scaling limit	p. 355
Weak Ohmic damping and moderate-to-high temperature	p. 359
The super-Ohmic case	p. 365
Weak-coupling theory beyond the NIBA for a biased system	p. 368
The one-boson self-energy	p. 369
Populations and coherences (super-Ohmic and Ohmic)	p. 371
The interacting-blip chain approximation	p. 373
Ohmic dissipation with K at and near 1/2: exact results	p. 376
Grand-canonical sums of collapsed blips and sojourns	p. 376
The expectation value [left angle bracket sigma subscript z right angle bracket subscript t] for K = 1/2	p. 377
The case K = 1/2 - [kappa]; coherent-incoherent crossover	p. 379
Equilibrium [sigma subscript z] autocorrelation function	p. 380
Equilibrium [sigma subscript x] autocorrelation function	p. 385
Correlation functions in the Toulouse model	p. 387
Long-time behaviour at T = 0 for K < 1: general discussion	p. 388
The populations	p. 389
The population correlations and generalized Shiba relation	p. 389
The coherence correlation function	p. 391
From weak to strong tunneling: relaxation and decoherence	p. 392
Incoherent tunneling beyond the nonadiabatic limit	p. 392
Decoherence at zero temperature: analytic results	p. 395
Thermodynamics from dynamics	p. 396
The driven two-state system	p. 399
Time-dependent external fields	p. 399
Diagonal and off-diagonal driving	p. 399
Exact formal solution	p. 400
Linear response	p. 402
The Ohmic case with Kondo parameter K = 1/2	p. 403
Markovian regime	p. 403
High-frequency regime	p. 404
Quantum stochastic resonance	p. 407
Driving-induced symmetry breaking	p. 409
The Dissipative Multi-State System	p. 411
Quantum Brownian particle in a washboard potential	p. 411
Introduction	p. 411
Weak- and tight-binding representation	p. 412
Multi-state dynamics	p. 413
Quantum transport and quantum-statistical fluctuations	p. 413
Product initial state	p. 414
Characteristic function of moments and cumulants	p. 414
Thermal initial state and correlation functions	p. 415
Poissonian quantum transport	p. 416
Dynamics by incoherent nearest-neighbour tunneling moves	p. 416
The general case	p. 418
Exact formal expressions for the system dynamics	p. 419
Product initial state	p. 421
Thermal initial state	p. 423
Mobility and Diffusion	p. 426
Exact formal series expressions for transport coefficients	p. 426
Einstein relation	p. 427
The Ohmic case	p. 428
Weak-tunneling regime	p. 429
Weak-damping limit	p. 429
Exact solution in the Ohmic scaling limit at K = 1/2	p. 431
Current and mobility	p. 431
Diffusion and skewness	p. 434
The effects of a thermal initial state	p. 435
Mean position and variance	p. 435
Linear response	p. 436
The exactly solvable case K = 1/2	p. 439
Duality symmetry	p. 439
Duality for general spectral density	p. 440
The map between the TB and WB Hamiltonian	p. 440
Frequency-dependent linear mobility	p. 443
Nonlinear static mobility	p. 444
Self-duality in the exactly solvable cases K = 1/2 and K = 2	p. 446
Full counting statistics at K = 1/2	p. 446
Full counting statistics at K = 2	p. 448
Duality and supercurrent in Josephson junctions	p. 450
Charge-phase duality	p. 450
Supercurrent-voltage characteristics for [rho] [double less-than sign] 1	p. 453
Supercurrent-voltage characteristics at [rho] = 1/2	p. 454
Supercurrent-voltage characteristics at [rho] = 2	p. 454
Self-duality in the Ohmic scaling limit	p. 455
Linear mobility at finite T	p. 456
Nonlinear mobility at T = 0	p. 457
Exact scaling function at T = 0 for arbitrary K	p. 459
Construction of the self-dual scaling solution	p. 459
Supercurrent-voltage characteristics at T = 0 for arbitrary [rho]	p. 462
Connection with Seiberg-Witten theory	p. 462
Special limits	p. 463
Full counting statistics at zero temperature	p. 464
Low temperature behaviour of the characteristic function	p. 467
The sub- and super-Ohmic case	p. 468
Charge transport in quantum impurity systems	p. 470
Generic models for transmission of charge through barriers	p. 471
The Tomonaga-Luttinger liquid	p. 471
Transport through a single weak barrier	p. 472
Transport through a single strong barrier	p. 474
Coherent conductor in an Ohmic environment	p. 476
Equivalence with quantum transport in a washboard potential	p. 478
Self-duality between weak and strong tunneling	p. 478
Full counting statistics	p. 479
Charge transport at low T for arbitrary g	p. 479
Full counting statistics at g = 1/2 and general temperature	p. 482
Bibliography	p. 483
Index	p. 503
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QUANTUM DISSIPATIVE SYS (3RD ED)

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