The theory of open quantum systems:
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| Format: | Book |
| Language: | English |
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Oxford [u.a.]
Oxford Univ. Press
2010
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| Edition: | Repr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 613 S. Ill., graph. Dast. |
| ISBN: | 9780199213900 9780198520634 |
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| 245 | 1 | 0 | |a The theory of open quantum systems |c Heinz-Peter Breuer ; Francesco Petruccione |
| 250 | |a Repr. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2010 | |
| 300 | |a XXI, 613 S. |b Ill., graph. Dast. | ||
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Record in the Search Index
| _version_ | 1804143421317709824 |
|---|---|
| adam_text | CONTENTS
I PROBABILITY IN CLASSICAL AND QUANTUM PHYSICS
Classical probability theory and stochastic processes
3
1.1
The probability space
3
1.1.1
The
σ-
algebra of events
3
1.1.2
Probability measures and Kolmogorov axioms
4
1.1.3
Conditional probabilities and independence
5
1.2
Random variables
5
1.2.1
Definition of random variables
5
1.2.2
Transformation of random variables
8
1.2.3
Expectation values and characteristic function
9
1.3
Stochastic processes
11
1.3.1
Formal definition of a stochastic process
11
1.3.2
The hierarchy of joint probability distributions
12
1.4
Markov processes
13
1.4.1
The Chapman-Kolmogorov equation
14
1.4.2
Differential Chapman-Kolmogorov equation
17
1.4.3
Deterministic processes and Liouville equation
19
1.4.4
Jump processes and the master equation
20
1.4.5
Diffusion processes and Fokker-Planck equation
27
1.5
Piecewise deterministic processes
31
1.5.1
The Liouville master equation
32
1.5.2
Waiting time distribution and sample paths
33
1.5.3
Path integral representation of PDPs
36
1.5.4
Stochastic calculus for PDPs
38
1.6
Levy processes
44
1.6.1
Translation invariant processes
44
1.6.2
The
Lévy-Khintchine
formula
46
1.6.3
Stable Levy processes
50
References
55
Quantum probability
57
2.1
The statistical interpretation of quantum mechanics
57
2.1.1
Self-adjoint operators and the spectral theorem
57
2.1.2
Observables
and random variables
61
2.1.3
Pure states and statistical mixtures
63
2.1.4
Joint probabilities in quantum mechanics
68
2.2
Composite quantum systems
72
2.2.1
Tensor product
72
xv
CONTENTS
2.2.2 Schmidt
decomposition and entanglement
75
2.3
Quantum entropies
76
2.3.1 Von
Neumann entropy
76
2.3.2
Relative entropy
78
2.3.3
Linear entropy
80
2.4
The theory of quantum measurement
80
2.4.1
Ideal quantum measurements
81
2.4.2
Operations and effects
83
2.4.3
Representation theorem for quantum operations
85
2.4.4
Quantum measurement and entropy
89
2.4.5
Approximate measurements
90
2.4.6
Indirect quantum measurements
93
2.4.7
Quantum non-demolition measurements
99
References
101
II DENSITY MATRIX THEORY
Quantum master equations
105
3.1
Closed and open quantum systems
106
3.1.1
The Liouville-von Neumann equation
106
3.1.2 Heisenberg
and interaction picture
108
3.1.3
Dynamics of open systems
110
3.2
Quantum Markov processes
113
3.2.1
Quantum dynamical semigroups
113
3.2.2
The Markovian quantum master equation
115
3.2.3
The adjoint quantum master equation
120
3.2.4
Multi-
time correlation functions
121
3.2.5
Irreversibility and entropy production
123
3.3
Microscopic derivations
125
3.3.1
Weak-coupling limit
126
3.3.2
Relaxation to equilibrium
132
3.3.3
Singular-coupling limit
133
3.3.4
Low-density limit
134
3.4
The quantum optical master equation
136
3.4.1
Matter in quantized radiation fields
136
3.4.2
Decay of a two-level system
141
3.4.3
Decay into a squeezed field vacuum
144
3.4.4
More general reservoirs
147
3.4.5
Resonance fluorescence
148
3.4.6
The damped harmonic oscillator
155
3.5
Non-selective, continuous measurements
160
3.5.1
The quantum
Zeno
effect
161
3.5.2
Density matrix equation
162
3.6
Quantum Brownian motion
166
CONTENTS
3.6.1 The Caldeira-Leggett
model
167
3.6.2
High-temperature master equation
168
3.6.3
The exact
Heisenberg
equations of motion
176
3.6.4
The influence functional
186
3.7
Non-linear quantum master equations
195
3.7.1
Quantum Boltzmann equation
195
3.7.2
Mean field master equations
197
3.7.3
Mean field laser equations
199
3.7.4
Non-linear
Schrödinger
equation
202
3.7.5
Super-radiance
204
References
209
Decoherence
212
4.1
The decoherence function
213
4.2
An exactly solvable model
218
4.2.1
Time evolution of the total system
218
4.2.2
Decay of coherences and the decoherence factor
220
4.2.3
Coherent subspaces and system-size dependence
223
4.3
Markovian mechanisms of decoherence
225
4.3.1
The decoherence rate
225
4.3.2
Quantum Brownian motion
226
4.3.3
Internal degrees of freedom
227
4.3.4
Scattering of particles
230
4.4
The damped harmonic oscillator
234
4.4.1
Vacuum decoherence
234
4.4.2
Thermal noise
238
4.5
Electromagnetic field states
242
4.5.1
Atoms interacting with a cavity field mode
243
4.5.2 Schrödinger
cat states
248
4.6
Caldeira-Leggett model
254
4.6.1
General decoherence formula
254
4.6.2
Ohmic environments
256
4.7
Decoherence and quantum measurement
261
4.7.1
Dynamical selection of a pointer basis
261
4.7.2
Dynamical model for a quantum measurement
267
References
270
HI STOCHASTIC PROCESSES IN HILBERT SPACE
Probability distributions on Hubert space
275
5.1
The state vector as a random variable in Hubert space
275
5.1.1
A new type of quantum mechanical ensemble
275
5.1.2
Stern-Gerlach experiment
280
5.2
Probability density functionals on Hubert space
283
5.2.1
Probability measures on Hubert space
283
CONTENTS
5.2.2
Distributions on
projective
Hubert space
286
5.2.3
Expectation values
289
5.3
Ensembles of mixtures
290
5.3.1
Probability density
funcţionale
on state space
291
5.3.2
Description of selective quantum measurements
292
References
293
Stochastic dynamics in Hubert space
295
6.1
Dynamical semigroups and PDPs in Hubert space
296
6.1.1
Reduced system dynamics as a PDP
296
6.1.2
The Hubert space path integral
303
6.1.3
Diffusion approximation
305
6.1.4
Multi-time correlation functions
307
6.2
Stochastic representation of continuous measurements
312
6.2.1
Stochastic time evolution of
E p-ensembles
313
6.2.2
Short-time behaviour of the propagator
313
6.3
Direct photodetection
316
6.3.1
Derivation of the PDP
316
6.3.2
Path integral solution
322
6.4
Homodyne
photodetection
326
6.4.1
Derivation of the PDP for
homodyne
detection
327
6.4.2
Stochastic
Schrödinger
equation
331
6.5
Heterodyne photodetection
333
6.5.1
Stochastic
Schrödinger
equation
333
6.5.2
Stochastic collapse models
336
6.6
Stochastic density matrix equations
339
6.7
Photodetection on a field mode
341
6.7.1
The photocounting formula
341
6.7.2
QND measurement of a field mode
345
References
349
The stochastic simulation method
352
7.1
Numerical simulation algorithms for PDPs
353
7.1.1
Estimation of expectation values
353
7.1.2
Generation of realizations of the process
354
7.1.3
Determination of the waiting time
355
7.1.4
Selection of the jumps
357
7.2
Algorithms for stochastic
Schrödinger
equations
358
7.2.1
General remarks on convergence
359
7.2.2
The
Euler
scheme
360
7.2.3
The Heun scheme
361
7.2.4
The fourth-order Runge-Kutta scheme
361
7.2.5
A second-order weak scheme
362
7.3
Examples
363
7.3.1
The damped harmonic oscillator
363
CONTENTS
7.3.2
The driven two-level system
366
7.4
A case study on numerical performance
371
7.4.1
Numerical efficiency and scaling laws
371
7.4.2
The damped driven Morse oscillator
373
References
379
8
Applications to quantum optical systems
381
8.1
Continuous measurements in QED
382
8.1.1
Constructing the microscopic Hamiltonian
382
8.1.2
Determination of the QED operation
384
8.1.3
Stochastic dynamics of multipole radiation
387
8.1.4
Representation of incomplete measurements
389
8.2
Dark state resonances
391
8.2.1
Waiting time distribution and trapping state
392
8.2.2
Measurement schemes and stochastic evolution
394
8.3
Laser cooling and Levy processes
399
8.3.1
Dynamics of the atomic wave function
401
8.3.2
Coherent population trapping
406
8.3.3
Waiting times and momentum distributions
411
8.4
Strong field interaction and the Floquet picture
418
8.4.1
Floquet theory
419
8.4.2
Stochastic dynamics in the Floquet picture
421
8.4.3
Spectral detection and the dressed atom
424
References
427
IV NON-MARKOVIAN QUANTUM PROCESSES
9
Projection operator techniques
431
9.1
The
N aka j
ima—
Zwanzig
projection operator technique
432
9.1.1
Projection operators
432
9.1.2
The Nakajima-Zwanzig equation
433
9.2
The time-convolutionless projection operator method
435
9.2.1
The time-local master equation
436
9.2.2
Perturbation expansion of the TCL generator
437
9.2.3
The
cumulant
expansion
441
9.2.4
Perturbation expansion of the inhomogeneity
442
9.2.5
Error analysis
445
9.3
Stochastic unravelling in the doubled Hubert space
446
References
448
10
Non-Markovian dynamics in physical systems
450
10.1
Spontaneous decay of a two-level system
451
10.1.1
Exact master equation and TCL generator
451
10.1.2
Jaynes-Cummmgs model on resonance
456
10.1.3
Jaynes-Cummmgs model with detuning
461
CONTENTS
10.1.4
Spontaneous decay into a photonic band gap
464
10.2
The damped harmonic oscillator
465
10.2.1
The model and frequency renormalization
465
10.2.2
Factorizing initial conditions
466
10.2.3
The stationary state
471
10.2.4
Non-factorizing initial conditions
475
10.2.5
Disregarding the inhomogeneity
479
10.3
The spin-boson system
480
10.3.1
Microscopic model
480
10.3.2
Relaxation of an initially factorizing state
481
10.3.3
Equilibrium correlation functions
485
10.3.4
Transition from coherent to incoherent motion
486
References
487
V RELATIVISTIC QUANTUM PROCESSES
11
Measurements in relativistic quantum mechanics
491
11.1
The Schwinger-Tomonaga equation
492
11.1.1
States as functionals of spacelike hypersurfaces
492
11.1.2
Foliations of space-time
496
11.2
The measurement of local
observables
497
11.2.1
The operation for a local measurement
498
11.2.2
Relativistic state reduction
500
11.2.3
Multivalued space-time amplitudes
504
11.2.4
The consistent hierarchy of joint probabilities
507
11.2.5
EPR correlations
511
11.2.6
Continuous measurements
512
11.3
Non-local measurements and causality
516
11.3.1
Entangled quantum probes
517
11.3.2
Non-local measurement by EPR probes
520
11.3.3
Quantum state verification
525
11.3.4
Non-local operations and the causality principle
528
11.3.5
Restrictions on the measurability of operators
534
11.3.6
QND verification of non-local states
539
11.3.7
Preparation of non-local states
543
11.3.8
Exchange measurements
544
11.4
Quantum
teleportation
546
11.4.1
Coherent transfer of quantum states
546
11.4.2
Teleportation
and Bell-state measurement
549
11.4.3
Experimental realization
551
References
555
12
Open quantum electrodynamics
557
12.1
Density matrix theory for QED
558
12.1.1
Field equations and correlation functions
558
CONTENTS
12.1.2
The reduced density matrix
565
12.2
The influence functional of QED
566
12.2.1
Elimination of the radiation degrees of freedom
566
12.2.2
Vacuum-to-vacuum amplitude
572
12.2.3
Second-order equation of motion
574
12.3
Decoherence by emission of bremsstrahlung
577
12.3.1
Introducing the decoherence functional
577
12.3.2
Physical interpretation
582
12.3.3
Evaluation of the decoherence functional
585
12.3.4
Path integral approach
595
12.4
Decoherence of many-particle states
602
References
605
Index
607
|
| any_adam_object | 1 |
| author | Breuer, Heinz-Peter 1961- Petruccione, Francesco 1961- |
| author_GND | (DE-588)1081452161 (DE-588)1111818347 |
| author_facet | Breuer, Heinz-Peter 1961- Petruccione, Francesco 1961- |
| author_role | aut aut |
| author_sort | Breuer, Heinz-Peter 1961- |
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| building | Verbundindex |
| bvnumber | BV036756030 |
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| id | DE-604.BV036756030 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:47:23Z |
| institution | BVB |
| isbn | 9780199213900 9780198520634 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020673197 |
| oclc_num | 705944917 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-83 DE-384 |
| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-83 DE-384 |
| physical | XXI, 613 S. Ill., graph. Dast. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Breuer, Heinz-Peter 1961- Verfasser (DE-588)1081452161 aut The theory of open quantum systems Heinz-Peter Breuer ; Francesco Petruccione Repr. Oxford [u.a.] Oxford Univ. Press 2010 XXI, 613 S. Ill., graph. Dast. txt rdacontent n rdamedia nc rdacarrier Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Dissipatives System (DE-588)4209641-8 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 s Dissipatives System (DE-588)4209641-8 s DE-604 Petruccione, Francesco 1961- Verfasser (DE-588)1111818347 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020673197&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Breuer, Heinz-Peter 1961- Petruccione, Francesco 1961- The theory of open quantum systems Quantenmechanisches System (DE-588)4300046-0 gnd Dissipatives System (DE-588)4209641-8 gnd |
| subject_GND | (DE-588)4300046-0 (DE-588)4209641-8 |
| title | The theory of open quantum systems |
| title_auth | The theory of open quantum systems |
| title_exact_search | The theory of open quantum systems |
| title_full | The theory of open quantum systems Heinz-Peter Breuer ; Francesco Petruccione |
| title_fullStr | The theory of open quantum systems Heinz-Peter Breuer ; Francesco Petruccione |
| title_full_unstemmed | The theory of open quantum systems Heinz-Peter Breuer ; Francesco Petruccione |
| title_short | The theory of open quantum systems |
| title_sort | the theory of open quantum systems |
| topic | Quantenmechanisches System (DE-588)4300046-0 gnd Dissipatives System (DE-588)4209641-8 gnd |
| topic_facet | Quantenmechanisches System Dissipatives System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020673197&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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