Quantum dissipative systems:
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| Format: | Buch |
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World Scientific
2012
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| Ausgabe: | 4. ed. |
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| Beschreibung: | XX, 566 S. |
| ISBN: | 9789814374910 9814374911 |
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| 245 | 1 | 0 | |a Quantum dissipative systems |c Ulrich Weiss |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2012 | |
| 300 | |a XX, 566 S. | ||
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Datensatz im Suchindex
| _version_ | 1804149195427282944 |
|---|---|
| adam_text | Titel: Quantum dissipative systems
Autor: Weiss, Ulrich
Jahr: 2012
Contents
Preface
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
1 Introduction
1 GENERAL THEORY OF OPEN QUANTUM SYSTEMS 5
2 Diverse limited approaches: a brief survey 5
2.1 Langevin equation for a damped classical system............ 5
2.2 New schemes of quantization....................... 7
2.3 Traditional system-plus-reservoir methods ............... 8
2.3.1 Quantum-mechanical master equations for weak coupling ... 8
2.3.2 Lindblad theory.......................... 11
2.3.3 Operator Langevin equations for weak coupling........ 13
2.3.4 Generalized quantum Langevin equation............ 14
2.3.5 Generalized quasiclassical Langevin equation.......... 15
2.3.6 Phenomenological methods.................... 16
2.4 Stochastic dynamics in Hilbert space.................. 16
3 System-plus-reservoir models 19
3.1 Harmonic oscillator bath with linear coupling ............. 20
3.1.1 The Hainiltonian of the global system.............. 20
3.1.2 The road to generalized Langevin equations.......... 23
3.1.3 Phenomenological modeling of friction ............. 24
3.1.4 Quantum statistical properties of the stochastic force..... 26
3.1.5 Displacement correlation function................ 28
3.1.6 Thermal propagator and imaginary-time correlations..... 29
3.1.7 Ohmic and frequency-dependent damping ........... 30
3.1.8 Fractional Langevin equation .................. 33
3.1.9 Rubin model ........................... 34
3.1.10 Interaction of a charged particle with the radiation field . ... 36
CONTENTS
3.2 Ergodicity................................. 37
3.3 The spin-boson model .......................... 40
3.3.1 The model Hamiltonian ..................... 40
3.3.2 Flux and charge qubits: reduction to the spin-boson model . . 44
3.4 Microscopic models............................ 48
3.4.1 Acoustic polaron: one-phonon and two-phonon coupling .... 49
3.4.2 Optical polaron.......................... 51
3.4.3 Interaction with fermions (normal and superconducting) ... 53
3.4.4 Superconducting tunnel junction ................ 56
3.5 Charging and environmental effects in tunnel junctions........ 57
3.5.1 The global system for single electron tunneling......... 58
3.5.2 Resistor, inductor, and transmission lines............ 63
3.5.3 Charging effects in junctions................... 64
3.6 Nonlinear quantum environments.................... 65
Imaginary-time approach and equilibrium dynamics 68
4.1 General concepts............................. 68
4.1.1 Density matrix and reduced density matrix........... 68
4.1.2 Imaginary-time path integral................... 70
4.2 Effective action and equilibrium density matrix ............ 72
4.2.1 Open system with bilinear coupling to a harmonic reservoir . . 73
4.2.2 State-dependent memory friction................ 78
4.2.3 Spin-boson model......................... 78
4.2.4 Acoustic polaron and defect tunneling: one-phonon coupling . 80
4.2.5 Acoustic polaron: two-phonon coupling............. 85
4.2.6 Tunneling between surfaces: one-phonon coupling....... 87
4.2.7 Optical polaron.......................... 89
4.2.8 Heavy particle in a metal..................... 90
4.2.9 Heavy particle in a superconductor............... 96
4.2.10 Effective action of a junction................... 98
4.2.11 Electromagnetic environment .................. 105
4.3 Partition function of the open system.................. 106
4.3.1 General path integral expression................. 106
4.3.2 Semiclassical approximation................... 106
4.3.3 Partition function of the damped harmonic oscillator..... 108
4.3.4 Functional measure in Fourier space............... 109
4.3.5 Partition function of the damped harmonic oscillator revisited 109
4.4 Quantum statistical expectation values in phase space......... 112
4.4.1 Generalized Weyl correspondence................ 112
4.4.2 Generalized W igner function and expectation values...... 114
CONTENTS
Real-time path integrals and nonequilibrium dynamics 116
5.1 Statement of the problem and general concepts ............ 116
5.2 Feynman-Vernon method for a product initial state.......... 118
5.3 Decoherence and friction......................... 123
5.4 General initial states and preparation function............. 125
5.5 Complex-time path integral for the propagating function....... 126
5.6 Real-time path integral for the propagating function.......... 128
5.7 Closed time contour representation................... 130
5.7.1 Complex-time path........................ 131
5.7.2 Real-time path.......................... 133
5.8 Semiclassical regime ........................... 133
5.8.1 Extremal paths.......................... 133
5.8.2 Quasiclassical Langevin equation................ 134
5.9 Stochastic unraveling of influence functional.............. 137
5.10 Non-Markovian dissipative dynamics in the semiclassical limit .... 140
5.10.1 Van Vleck and Herman-Kluk propagator............ 140
5.10.2 Semiclassical dissipative dynamics................ 141
5.11 Brief summary and outlook ....................... 142
II MISCELLANEOUS APPLICATIONS 143
6 Damped linear quantum mechanical oscillator 143
6.1 Fluctuation-dissipation theorem..................... 144
6.2 Stochastic modeling............................ 148
6.3 Susceptibility............................... 150
6.3.1 Ohmic friction........................... 150
6.3.2 Ohmic friction with Drude cutoff................ 151
6.3.3 Radiation damping........................ 152
6.4 The position autocorrelation function.................. 153
6.4.1 Ohmic friction........................... 154
6.4.2 Non-Ohmic spectral density................... 156
6.4.3 Shiba relation........................... 158
6.5 Partition function and implications................... 158
6.5.1 Partition function......................... 158
6.5.2 Internal energy, free energy, and entropy............ 159
6.5.3 Specific heat and Wilson ratio.................. 162
6.5.4 Spectral density of states..................... 163
6.6 Mean square of position and momentum................ 165
6.6.1 General expressions for colored noise.............. 165
6.6.2 Ohmic friction........................... 167
6.6.3 Ohmic friction with Drude cutoff................ 168
6.7 Equilibrium density matrix........................ 170
CONTENTS
6.7.1 Derivation of the action ..................... 170
6.7.2 Purity............................... 172
6.8 Quantum master equations for the reduced density matrix...... 174
6.8.1 Thermal initial condition..................... 175
6.8.2 Product initial state ....................... 176
6.8.3 Approximate time-independent Liouville operators....... 177
6.8.4 Connection with Lindblad theory................ 178
7 Quantum Brownian free motion 178
7.1 Spectral density, damping function and mass renormalization..... 179
7.2 Displacement correlation and response function............ 181
7.3 Ohmic friction............................... 182
7.3.1 Response function......................... 182
7.3.2 Mean square displacement.................... 183
7.3.3 Momentum spread........................ 184
7.4 Frequency-dependent friction ...................... 185
7.4.1 Response function and mobility................. 185
7.4.2 Mean square displacement.................... 187
7.5 Partition function and thermodynamic properties........... 190
7.5.1 Partition function......................... 190
7.5.2 Internal and free energy..................... 190
7.5.3 Specific heat...... ...................... 192
7.5.4 Spectral density of states..................... 194
8 The thermodynamic variational approach 195
8.1 Centroid and the effective classical potential.............. 195
8.1.1 Centroid.............................. 195
8.1.2 The effective classical potential................. 196
8.2 Variational method............................ 197
8.2.1 Variational method for the free energy............. 198
8.2.2 Variational method for the effective classical potential..... 198
8.2.3 Variational perturbation theory................. 202
8.2.4 Expectation values in coordinate and phase space....... 204
9 Suppression of quantum coherence 206
9.1 Xondynaniical versus dynamical environment.............. 207
9.2 Suppression of transversal and longitudinal interferences ....... 208
9.3 Deeoherenee in the semiclassical picture ................ 210
9.3.1 A model with localized bath modes............... 210
9.3.2 Dephasing rate formula...................... 211
9.3.3 Statistical average of paths.................... 213
9.3.4 Ballistic motion.......................... 213
9.3.5 Diffusive motion.......................... 215
CONTENTS xv
9.4 Decoherence of electrons......................... 216
III QUANTUM STATISTICAL DECAY 221
10 Introduction 221
11 Classical rate theory: a brief overview 224
11.1 Classical transition state theory..................... 224
11.2 Moderate-to-strong-damping regime................... 225
11.3 Strong damping regime.......................... 227
11.4 Weak-damping regime.......................... 229
12 Quantum rate theory: basic methods 231
12.1 Formal rate expressions in terms of flux operators........... 232
12.2 Quantum transition state theory..................... 233
12.3 Semiclassical limit............................. 234
12.4 Quantum tunneling regime........................ 237
12.5 Free energy method............................ 240
12.6 Centroid method............................. 245
13 Multidimensional quantum rate theory 246
13.1 The global metastable potential..................... 246
13.2 Periodic orbit and bounce........................ 247
14 Crossover from thermal to quantum decay 250
14.1 Normal mode analysis at the barrier top................ 250
14.2 Turnover theory for activated rate processes.............. 252
14.3 The crossover temperature........................ 256
15 Thermally activated decay 258
15.1 Rate formula above the crossover regime................ 258
15.2 Quantum corrections in the pre-exponential factor........... 260
15.3 The quantum Smoluchowski equation approach ............ 262
15.4 Multidimensional quantum transition state theory........... 264
16 The crossover region 267
16.1 Beyond steepest descent above T0.................... 268
16.2 Beyond steepest descent below T0.................... 270
16.3 The scaling region............................. 273
CONTENTS
17 Dissipative quantum tunneling 275
17.1 The quantum rate formula........................ 275
17.2 Thermal enhancement of macroscopic quantum tunneling....... 278
17.3 Quantum decay in a cubic potential for Ohmic friction........ 279
17.3.1 Bounce action and quantum mechanical prefactor....... 280
17.3.2 Analytic results for strong Ohmic dissipation.......... 281
17.4 Quantum decay in a tilted cosine potential............... 283
17.4.1 The case of weak bias....................... 288
17.5 Concluding remarks............................ 290
IV THE DISSIPATIVE TWO-STATE SYSTEM 293
18 Introduction 293
18.1 Truncation of the double-well to the two-state system......... 295
18.1.1 Shifted oscillators and orthogonality catastrophe........ 295
18.1.2 Adiabatic renormalization.................... 297
18.1.3 Instanton in a double parabolic well............... 299
18.1.4 Renormalized tunneling matrix element............. 301
18.1.5 Polaron transformation...................... 303
18.2 Pair interaction in the charge picture.................. 304
18.2.1 Analytic expression for spectral density with any power s . . 304
18.2.2 Ohmic dissipation and universality limit............ 305
19 Thermodynamics 306
19.1 Partition function and specific heat................... 306
19.1.1 Exact formal expression for the partition function....... 306
19.1.2 Static susceptibility and specific heat.............. 308
19.1.3 The self-energy method...................... 309
19.1.4 The limit of high temperatures ................. 311
19.1.5 Noninteracting-kink-pair approximation............ 312
19.1.6 Weak-damping limit ....................... 313
19.1.7 The self-energy method revisited: partial resummation .... 315
19.2 Ohmic dissipation............................. 316
19.2.1 Specific heat and Wilson ratio.................. 316
19.2.2 The special case K= ...................... 318
19.3 Non-Ohmic spectral densities ...................... 322
19.3.1 The sub-Ohmic case ....................... 322
19.3.2 The super-Ohmic case...................... 323
19.4 Relation between the Ohmic TSS and the Kondo model........ 324
19.4.1 Anisotropic Kondo model .................... 324
19.4.2 Resonance level model...................... 326
19.5 Equivalence of the Ohmic TSS with the 1/r2 Ising model....... 327
CONTENTS
20 Electron transfer and incoherent tunneling 329
20.1 Electron transfer............................. 329
20.1.1 Adiabatic bath.......................... 330
20.1.2 Marcus theory for electron transfer............... 333
20.2 Incoherent tunneling in the nonadiabatic regime............ 336
20.2.1 General expressions for the nonadiabatic rate ......... 337
20.2.2 Probability for energy exchange: general results........ 338
20.2.3 The spectral probability density for absorption at T = 0 ... 341
20.2.4 Crossover from quantum-mechanical to classical behavior . . . 343
20.2.5 The Ohmic case.......................... 346
20.2.6 Exact nonadiabatic rates for K = | and K = 1 ........ 349
20.2.7 The sub-Ohmic case (0 s 1)................. 350
20.2.8 The super-Ohmic case (s 1).................. 351
20.2.9 Incoherent defect tunneling in metals.............. 354
20.3 Single charge tunneling.......................... 356
20.3.1 Weak-tunneling regime...................... 357
20.3.2 The current-volt age characteristics ............... 361
20.3.3 Weak tunneling of ID interacting electrons........... 363
20.3.4 Tunneling of Cooper pairs.................... 364
20.3.5 Tunneling of quasiparticles.................... 366
21 Two-state dynamics: basics and methods 367
21.1 Initial preparation, expectation values, and correlations........ 368
21.1.1 Product initial state....................... 368
21.1.2 Thermal initial state....................... 371
21.2 Exact formal expressions for the system dynamics........... 374
21.2.1 Sojourns and blips........................ 374
21.2.2 Conditional propagating functions................ 377
21.2.3 The expectation values ( 7-)t (J = x, y, z) ........... 378
21.2 A Correlation and response function of the populations..... 380
21.2.5 Correlation and response function of the coherences...... 382
21.2.6 Generalized exact master equation and integral relations . . . 383
21.3 The noninteracting-blip approximation (NIBA) ............ 386
21.3.1 Assumptions............................ 386
21.3.2 Limitations............................ 388
21.4 The interacting-blip chain approximation (IBCA)........... 389
22 Two-state dynamics: sundry topics 392
22.1 Symmetric TSS in the NIBA....................... 392
22.1.1 Ohmic scaling limit........................ 392
22.1.2 The super-Ohmic case...................... 396
22.2 White-noise regime............................ 399
22.2.1 Power spectrum of the stochastic force............. 399
CONTENTS
22.2.2 Symmetric Ohmic TSS at moderate-to-high temperature . . . 400
22.2.3 Biased Ohmic TSS at moderate-to-high temperature ..... 402
22.3 Weak quantum noise in the biased TSS................. 406
22.3.1 The one-boson self-energy.................... 407
22.3.2 Populations and coherences (super-Ohmic and Ohmic) .... 409
22.4 Pure dephasing.............................. 411
22.5 1// noise and decoherence........................ 414
22.5.1 1// noise from fluctuating background charges......... 414
22.5.2 1// noise from coherent two-level systems ........... 415
22.5.3 Decoherence from 1// noise................... 416
22.6 The Ohmic TSS at and close to the Toulouse point.......... 417
22.6.1 Grand-canonical sums of collapsed blips and sojourns..... 417
22.6.2 The expectation value {az)t for K = ............. 419
22.6.3 The case K = | - k; coherent-incoherent crossover ...... 420
22.6.4 Equilibrium az autocorrelation function............. 421
22.6.5 Equilibrium ax autocorrelation function ............ 426
22.6.6 Correlation functions in the Toulouse model.......... 428
22.7 Long-time behavior at T = 0 for K 1: general discussion...... 429
22.7.1 The populations.......................... 430
22.7.2 The population correlations and Shiba relation......... 430
22.7.3 The coherence correlation function ............... 432
22.8 From weak to strong tunneling: relaxation and decoherence...... 433
22.8.1 Incoherent tunneling beyond the nonadiabatic limit...... 433
22.8.2 Decoherence at zero temperature: analytic results....... 436
22.9 Thermodynamics from dynamics .................... 438
23 The driven two-state system 440
23.1 Time-dependent external fields...................... 441
23.1.1 Diagonal and off-diagonal driving................ 441
23.1.2 Exact formal solution....................... 442
23.1.3 Linear response.......................... 444
23.1.4 The Ohmic case with Kondo parameter K = ^......... 444
23.2 Markovian regime............................. 445
23.3 High-frequency regime.......................... 446
23.4 Quantum stochastic resonance...................... 449
23.5 Driving-induced symmetry breaking................... 451
V THE DISSIPATIVE MULTI-STATE SYSTEM 453
24 Quantum Brownian particle in a washboard potential 453
24.1 Introduction................................ 453
24.2 Weak- and tight-binding representation................. 454
CONTENTS
25 Multi-state dynamics 456
25.1 Quantum transport and quantum-statistical fluctuations....... 456
25.1.1 Product initial state ....................... 456
25.1.2 Characteristic functions of moments and cumulants...... 456
25.1.3 Thermal initial state and correlation functions......... 457
25.2 Poissonian quantum transport...................... 459
25.2.1 Incoherent nearest-neighbor transitions (weak tunneling) . . . 459
25.2.2 The general case (strong tunneling)............... 460
25.3 Exact formal expressions for the system dynamics........... 462
25.3.1 Product initial state....................... 464
25.3.2 Thermal initial state....................... 466
25.4 Mobility and Diffusion.......................... 468
25.4.1 Exact formal series expressions for transport coefficients . . . 468
25.4.2 Einstein relation ......................... 470
25.5 The Ohmic case.............................. 471
25.5.1 Weak-tunneling regime...................... 472
25.5.2 Weak-damping limit ....................... 472
25.6 Exact solution in the Ohmic scaling limit at K = |.......... 474
25.6.1 Current and mobility....................... 475
25.6.2 Diffusion and skewness...................... 477
25.7 The effects of a thermal initial state................... 479
25.7.1 Mean position and variance................... 479
25.7.2 Linear response.......................... 480
25.7.3 The exactly solvable case K = ................. 482
26 Duality symmetry 483
26.1 Duality for general spectral density................... 483
26.1.1 The map between the TB and WB Hamiltonian........ 484
26.1.2 Frequency-dependent linear mobility.............. 487
26.1.3 Nonlinear static mobility .................... 488
26.2 Self-duality in the exactly solvable cases K = | and K = 2...... 490
26.2.1 Full counting statistics at K = ................ 490
26.2.2 Full counting statistics at K = 2................. 492
26.3 Duality and supercurrent in Josephson junctions............ 495
26.3.1 Charge-phase duality....................... 495
26.3.2 Supercurrent-voltage characteristics for p C 1......... 498
26.3.3 Supercurrent-voltage characteristics at p = |.......... 499
26.3.4 Supercurrent-voltage characteristics at p = 2.......... 499
26.4 Self-duality in the Ohmic scaling limit ................. 500
26.4.1 Linear mobility at finite T.................... 500
26.4.2 Nonlinear mobility at T = 0................... 502
26.5 Exact scaling function at T = 0 for arbitrary K............ 504
CONTENTS
26.5.1 Construction of the self-dual scaling solution.......... 504
26.5.2 Supercurrent-voltage characteristics at T = 0 for arbitrary p . 507
26.5.3 Connection with Seiberg-Witten theory............. 507
26.5.4 Special limits........................... 509
26.6 Full counting statistics at zero temperature............... 510
26.7 Low temperature behavior of the characteristic function........ 512
27 Twisted partition function and nonlinear mobility 514
27.1 Solving the imaginary-time Coulomb gas with Jack polynomials . . . 514
27.2 Nonlinear mobility............................ 517
27.2.1 Strong barrier limit........................ 518
27.2.2 The case K 1.......................... 519
27.2.3 The limit T - 0 ......................... 520
28 Charge transport in quantum impurity systems 521
28.1 Generic models for transmission of charge through barriers...... 521
28.1.1 The Tomonaga-Luttinger liquid................. 522
28.1.2 Charge transport through a single weak barrier ........ 523
28.1.3 Charge transport through a single strong barrier........ 525
28.1.4 Coherent conductor in an Ohmic environment......... 526
28.1.5 Equivalence with quantum transport in a washboard potential 528
28.2 Self-duality between weak and strong tunneling ............ 529
28.3 Full counting statistics of charge transfer................ 530
28.3.1 Charge transport at low temperature for arbitrary g...... 530
28.3.2 Full counting statistics at g = and general temperature . . . 533
29 Quantum transport for sub- and super-Ohmic friction 533
29.1 Tight-binding representation....................... 534
29.1.1 Sub-Ohmic friction........................ 536
29.1.2 Super-Ohmic friction....................... 537
29.2 Weak-binding representation....................... 537
29.2.1 Super-Ohmic friction....................... 538
29.2.2 Sub-Ohmic friction........................ 538
Bibliography 539
Index 561
|
| any_adam_object | 1 |
| author | Weiss, Ulrich ca. 20. Jh |
| author_GND | (DE-588)1049309855 |
| author_facet | Weiss, Ulrich ca. 20. Jh |
| author_role | aut |
| author_sort | Weiss, Ulrich ca. 20. Jh |
| author_variant | u w uw |
| building | Verbundindex |
| bvnumber | BV040196070 |
| classification_rvk | UG 4000 UK 1000 |
| classification_tum | PHY 057f |
| ctrlnum | (OCoLC)796255608 (DE-599)BSZ355867028 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV040196070 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:19:10Z |
| institution | BVB |
| isbn | 9789814374910 9814374911 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025052548 |
| oclc_num | 796255608 |
| open_access_boolean | |
| owner | DE-20 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-703 DE-91G DE-BY-TUM DE-83 DE-29T |
| owner_facet | DE-20 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-703 DE-91G DE-BY-TUM DE-83 DE-29T |
| physical | XX, 566 S. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Weiss, Ulrich ca. 20. Jh. Verfasser (DE-588)1049309855 aut Quantum dissipative systems Ulrich Weiss 4. ed. Singapore [u.a.] World Scientific 2012 XX, 566 S. txt rdacontent n rdamedia nc rdacarrier Quantenstatistik (DE-588)4047991-2 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Dissipatives System (DE-588)4209641-8 gnd rswk-swf Quantum statistics Path integrals Quantenmechanisches System (DE-588)4300046-0 s DE-604 Dissipatives System (DE-588)4209641-8 s Quantenstatistik (DE-588)4047991-2 s Quantentheorie (DE-588)4047992-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025052548&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Weiss, Ulrich ca. 20. Jh Quantum dissipative systems Quantenstatistik (DE-588)4047991-2 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanisches System (DE-588)4300046-0 gnd Dissipatives System (DE-588)4209641-8 gnd |
| subject_GND | (DE-588)4047991-2 (DE-588)4047992-4 (DE-588)4300046-0 (DE-588)4209641-8 |
| title | Quantum dissipative systems |
| title_auth | Quantum dissipative systems |
| title_exact_search | Quantum dissipative systems |
| title_full | Quantum dissipative systems Ulrich Weiss |
| title_fullStr | Quantum dissipative systems Ulrich Weiss |
| title_full_unstemmed | Quantum dissipative systems Ulrich Weiss |
| title_short | Quantum dissipative systems |
| title_sort | quantum dissipative systems |
| topic | Quantenstatistik (DE-588)4047991-2 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanisches System (DE-588)4300046-0 gnd Dissipatives System (DE-588)4209641-8 gnd |
| topic_facet | Quantenstatistik Quantentheorie Quantenmechanisches System Dissipatives System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025052548&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT weissulrich quantumdissipativesystems |