The theory of open quantum systems:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
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Oxford [u.a.]
Oxford Univ. Press
2003
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| Edition: | Reprinted |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 625 S. graph. Darst. |
| ISBN: | 0198520638 |
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| adam_text | THE THEORY OF OPEN QUANTUM SYSTEMS HEINZ-PETER BREUER AND FRANCESCO
PETRUCCIONE ALBERT-LUDWIGS-UNIVERSITDT FREIBURG, FAKULTDT FUR PHYSIK AND
ISTITUTO ITALIANO PER GLI STUDI FILOSOFICI OXFORD UNIVERSITY PRESS
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 CR-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 6 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 14 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 21 1.4.5 DIFFUSION
PROCESSES AND FOKKER-PLANCK EQUATION 28 1.5 PIECEWISE DETERMINISTIC
PROCESSES ;32 1.5.1 THE LIOUVILLE MASTER EQUATION 33 1.5.2 WAITING TIME
DISTRIBUTION AND SAMPLE PATHS 33 1.5.3 PATH INTEGRAL REPRESENTATION OF
PDPS 37 1.5.4 STOCHASTIC CALCULUS FOR PDPS 39 1.6 LEVY PROCESSES 45
1.6.1 TRANSLATION INVARIANT PROCESSES 46 1.6.2 THE LEVY-KHINTCHINE
FORMULA 47 1.6.3 STABLE LEVY PROCESSES 51 REFERENCES 57 QUANTUM
PROBABILITY 59 2.1 THE STATISTICAL INTERPRETATION OF QUANTUM MECHANICS 1
59 2.1.1 SELF-ADJOINT OPERATORS AND THE SPECTRAL THEOREM 59 2.1.2
OBSERVABLES AND RANDOM VARIABLES 63 2.1.3 PURE STATES AND STATISTICAL
MIXTURES 65 2.1.4 JOINT PROBABILITIES IN QUANTUM MECHANICS 70 2.2
COMPOSITE QUANTUM SYSTEMS 74 CONTENTS 2.2.1 TENSOR PRODUCT 75 2.2.2
SCHMIDT DECOMPOSITION AND ENTANGLEMENT 77 2.3 QUANTUM ENTROPIES ~ 79
2.3.1 VON NEUMANN ENTROPY 79 2.3.2 RELATIVE ENTROPY 81 2.3.3 LINEAR
ENTROPY 82 2.4 THE THEORY OF QUANTUM MEASUREMENT 83 2.4.1 IDEAL QUANTUM
MEASUREMENTS 83 2.4.2 OPERATIONS AND EFFECTS 85 2.4.3 REPRESENTATION
THEOREM FOR QUANTUM OPERATIONS 87 2.4.4 QUANTUM MEASUREMENT AND ENTROPY
92 2.4.5 APPROXIMATE MEASUREMENTS 93 2.4.6 INDIRECT QUANTUM MEASUREMENTS
96 2.4.7 QUANTUM NON-DEMOLITION MEASUREMENTS 102 REFERENCES 104 II
DENSITY MATRIX THEORY QUANTUM MASTER EQUATIONS 109 3.1 CLOSED AND OPEN
QUANTUM SYSTEMS 110 3.1.1 THE LIOUVILLE-VON NEUMANN EQUATION 110 3.1.2
HEISENBERG AND INTERACTION PICTURE 112 3.1.3 DYNAMICS OF OPEN SYSTEMS
115 3.2 QUANTUM MARKOV PROCESSES 117 3.2.1 QUANTUM DYNAMICAL SEMIGROUPS
117 3.2.2 THE MARKOVIAN QUANTUM MASTER EQUATION 119 3.2.3 THE ADJOINT
QUANTUM MASTER EQUATION 124 3.2.4 MULTI-TIME CORRELATION FUNCTIONS 125
3.2.5 IRREVERSIBILITY AND ENTROPY PRODUCTION 128 3.3 MICROSCOPIC
DERIVATIONS 130 3.3.1 WEAK-COUPLING LIMIT 130 3.3.2 RELAXATION TO
EQUILIBRIUM 137 3.3.3 SINGULAR-COUPLING LIMIT 138 3.3.4 LOW-DENSITY
LIMIT 139 3.4 THE QUANTUM OPTICAL MASTER EQUATION 141 3.4.1 MATTER IN
QUANTIZED RADIATION FIELDS 141 3.4.2 DECAY OF A TWO-LEVEL SYSTEM _ 146
3.4.3 DECAY INTO A SQUEEZED FIELD VACUUM 149 3.4.4 MORE GENERAL
RESERVOIRS 152 3.4.5 RESONANCE FLUORESCENCE L 154 3.4.6 THE DAMPED
HARMONIC OSCILLATOR 160 3.5 NON-SELECTIVE, CONTINUOUS MEASUREMENTS 166
3.5.1 THE QUANTUM ZENO EFFECT 166 3.5.2 DENSITY MATRIX EQUATION 167
CONTENTS 3.6 QUANTUM BROWNIAN MOTION 172 3.6.1 THE CALDEIRA-LEGGETT
MODEL 172 3.6.2 HIGH-TEMPERATURE MASTER EQUATION 173 3.6.3 THE EXACT
HEISENBERG EQUATIONS OF MOTION 182 3.6.4 THE INFLUENCE FUNCTIONAL 192
3.7 NON-LINEAR QUANTUM MASTER EQUATIONS 201 3.7.1 QUANTUM BOLTZMANN
EQUATION 201 3.7.2 MEAN FIELD MASTER EQUATIONS 203 3.7.3 MEAN FIELD
LASER EQUATIONS 205 3.7.4 NON-LINEAR SCHRODINGER EQUATION 208 3.7.5
SUPER-RADIANCE 210 REFERENCES 216 DECOHERENCE 219 4.1 THE DECOHERENCE
FUNCTION 220 4.2 AN EXACTLY SOLVABLE MODEL 225 4.2.1 TIME EVOLUTION OF
THE TOTAL SYSTEM 225 4.2.2 DECAY OF COHERENCES AND THE DECOHERENCE
FACTOR 227 4.2.3 COHERENT SUBSPACES AND SYSTEM-SIZE DEPENDENCE 231 4.3
MARKOVIAN MECHANISMS OF DECOHERENCE 232 4.3.1 THE DECOHERENCE RATE 233
4.3.2 QUANTUM BROWNIAN MOTION 234 4.3.3 INTERNAL DEGREES OF FREEDOM .
235 4.3.4 SCATTERING OF PARTICLES 237 4.4 THE DAMPED HARMONIC OSCILLATOR
242 4.4.1 VACUUM DECOHERENCE 242 4.4.2 THERMAL NOISE 246 4.5
ELECTROMAGNETIC FIELD STATES 251 4.5.1 ATOMS INTERACTING WITH A CAVITY
FIELD MODE 251 4.5.2 SCHRODINGER CAT STATES 257 4.6 CALDEIRA-LEGGETT
MODEL 262 4.6.1 GENERAL DECOHERENCE FORMULA 263 4.6.2 OHMIC ENVIRONMENTS
265 4.7 DECOHERENCE AND QUANTUM MEASUREMENT 269 4.7.1 DYNAMICAL
SELECTION OF A POINTER BASIS 270 4.7.2 DYNAMICAL MODEL FOR A QUANTUM
MEASUREMENT 275 REFERENCES 278 III STOCHASTIC PROCESSES IN HILBERT SPACE
PROBABILITY DISTRIBUTIONS ON HILBERT SPACE 283 5.1 THE STATE VECTOR AS A
RANDOM VARIABLE IN HILBERT SPACE 283 5.1.1 A NEW TYPE OF QUANTUM
MECHANICAL ENSEMBLE 283 5.1.2 STERN-GERLACH EXPERIMENT * 288 5.2
PROBABILITY DENSITY FUNCTIONAL ON HILBERT SPACE 291 CONTENTS 5.2.1
PROBABILITY MEASURES ON HILBERT SPACE 291 5.2.2 DISTRIBUTIONS ON
PROJECTIVE HILBERT SPACE 294 5.2.3 EXPECTATION VALUES - - -- 297 5.3
ENSEMBLES OF MIXTURES 299 5.3.1 PROBABILITY DENSITY FUNCTIONALS ON STATE
SPACE 299 5.3.2 DESCRIPTION OF SELECTIVE QUANTUM MEASUREMENTS 301
REFERENCES 302 6 STOCHASTIC DYNAMICS IN HILBERT SPACE 303 6.1 DYNAMICAL
SEMIGROUPS AND PDPS IN HILBERT SPACE 304 6.1.1 REDUCED SYSTEM DYNAMICS
AS A PDP 304 6.1.2 THE HILBERT SPACE PATH INTEGRAL 311 6.1.3 DIFFUSION
APPROXIMATION 314 6.1.4 MULTI-TIME CORRELATION FUNCTIONS 316 6.2
STOCHASTIC REPRESENTATION OF CONTINUOUS MEASUREMENTS 320 6.2.1
STOCHASTIC TIME EVOLUTION OF P-ENSEMBLES 321 6.2.2 SHORT-TIME BEHAVIOUR
OF THE PROPAGATOR 322 6.3 DIRECT PHOTODETECTION 324 6.3.1 DERIVATION OF
THE PDP 324 6.3.2 PATH INTEGRAL SOLUTION 330 6.4 HOMODYNE PHOTODETECTION
335 6.4.1 DERIVATION OF THE PDP FOR HOMODYNE DETECTION 336 6.4.2
STOCHASTIC SCHRODINGER EQUATION 340 6.5 HETERODYNE PHOTODETECTION 342
6.5.1 STOCHASTIC SCHRODINGER EQUATION 342 6.5.2 STOCHASTIC COLLAPSE
MODELS 345 6.6 STOCHASTIC DENSITY MATRIX EQUATIONS 348 6.7
PHOTODETECTION ON A FIELD MODE 350 6.7.1 THE PHOTOCOUNTING FORMULA 350
6.7.2 QND MEASUREMENT OF A FIELD MODE 354 REFERENCES 358 7 THE
STOCHASTIC SIMULATION METHOD 361 7.1 NUMERICAL SIMULATION ALGORITHMS FOR
PDPS 362 7.1.1 ESTIMATION OF EXPECTATION VALUES 362 7.1.2 GENERATION OF
REALIZATIONS OF THE PROCESS 363 7.1.3 DETERMINATION OF THE WAITING TIME
364 7.1.4 SELECTION OF THE JUMPS 367 7.2 ALGORITHMS FOR STOCHASTIC
SCHRODINGER EQUATIONS 367 7.2.1 GENERAL REMARKS ON CONVERGENCE 368 7.2.2
THE EULER SCHEME 370 7.2.3 THE HEUN SCHEME 370 7.2.4 THE FOURTH-ORDER
RUNGE-KUTTA SCHEME 370 7.2.5 A SECOND-ORDER WEAK SCHEME 372 7.3 EXAMPLES
373 CONTENTS 7.3.1 THE DAMPED HARMONIC OSCILLATOR 373 7.3.2 THE DRIVEN
TWO-LEVEL SYSTEM 377 7.4 A CASE STUDY ON NUMERICAL PERFORMANCE 380
7.4.1 NUMERICAL EFFICIENCY AND SCALING LAWS 381 7.4.2 THE DAMPED DRIVEN
MORSE OSCILLATOR 383 REFERENCES 389 8 APPLICATIONS TO QUANTUM OPTICAL
SYSTEMS 390 8.1 CONTINUOUS MEASUREMENTS IN QED 391 8.1.1 CONSTRUCTING
THE MICROSCOPIC HAMILTONIAN 391 8.1.2 DETERMINATION OF THE QED OPERATION
393 8.1.3 STOCHASTIC DYNAMICS OF MULTIPOLE RADIATION 396 8.1.4
REPRESENTATION OF INCOMPLETE MEASUREMENTS 398 8.2 DARK STATE RESONANCES
401 8.2.1 WAITING TIME DISTRIBUTION AND TRAPPING STATE 401 8.2.2
MEASUREMENT SCHEMES AND STOCHASTIC EVOLUTION 405 8.3 LASER COOLING AND
LEVY PROCESSES 409 8.3.1 DYNAMICS OF THE ATOMIC WAVE FUNCTION 410 8.3.2
COHERENT POPULATION TRAPPING 416 8.3.3 WAITING TIMES AND MOMENTUM
DISTRIBUTIONS 421 8.4 STRONG FIELD INTERACTION AND THE FLOQUET PICTURE
428 8.4.1 FLOQUET THEORY 429 8.4.2 STOCHASTIC DYNAMICS IN THE FLOQUET
PICTURE 431 8.4.3 SPECTRAL DETECTION AND THE DRESSED ATOM 434 REFERENCES
437 IV NON-MARKOVIAN QUANTUM PROCESSES 9 PROJECTION OPERATOR TECHNIQUES
. 441 9.1 THE NAKAJIMA-ZWANZIG PROJECTION OPERATOR TECHNIQUE 442 9.1.1
PROJECTION OPERATORS 442 9.1.2 THE NAKAJIMA-ZWANZIG EQUATION 443 9.2 THE
TIME-CONVOLUTIONLESS PROJECTION OPERATOR METHOD 445 9.2.1 THE TIME-LOCAL
MASTER EQUATION 446 9.2.2 PERTURBATION EXPANSION OF THE TCL GENERATOR
447 9.2.3 THE CUMULANT EXPANSION 451 9.2.4 PERTURBATION EXPANSION OF THE
INHOMOGENEITY 452 9.2.5 ERROR ANALYSIS 455 9.3 STOCHASTIC UNRAVELLING IN
THE DOUBLED HILBERT SPACE 456 REFERENCES 458 10 NON-MARKOVIAN DYNAMICS
IN PHYSICAL SYSTEMS 460 10.1 SPONTANEOUS DECAY OF A TWO-LEVEL SYSTEM 461
10.1.1 EXACT MASTER EQUATION AND TCL GENERATOR , 461 10.1.2
JAYNES-CUMMINGS MODEL ON RESONANCE 466 XX CONTENTS 10.1.3
JAYNES-CUMMINGS MODEL WITH DETUNING 471 10.1.4 SPONTANEOUS DECAY INTO A
PHOTONIC BAND GAP 474 10.2 THE DAMPED HARMONIC OSCILLATOR 474 10.2.1
THE MODEL AND FREQUENCY RENORMALIZATION 475 10.2.2 FACTORIZING INITIAL
CONDITIONS 477 10.2.3 THE STATIONARY STATE 481 10.2.4 NON-FACTORIZING
INITIAL CONDITIONS 483 10.2.5 DISREGARDING THE INHOMOGENEITY 488 10.3
THE SPIN-BOSON SYSTEM 490 10.3.1 MICROSCOPIC MODEL 490 10.3.2 RELAXATION
OF AN INITIALLY FACTORIZING STATE 491 10.3.3 EQUILIBRIUM CORRELATION
FUNCTIONS 495 10.3.4 TRANSITION FROM COHERENT TO INCOHERENT MOTION 496
REFERENCES 497 V RELATIVISTIC QUANTUM PROCESSES 11 MEASUREMENTS IN
RELATIVISTIC QUANTUM MECHANICS 501 11.1 THE SCHWINGER-TOMONAGA EQUATION
502 11.1.1 STATES AS FUNCTIONALS OF SPACELIKE HYPERSURFACES 502 11.1.2
FOLIATIONS OF SPACE-TIME 506 11.2 THE MEASUREMENT OF LOCAL OBSERVABLES
507 11.2.1 THE OPERATION FOR A LOCAL MEASUREMENT , 508 11.2.2
RELATIVISTIC STATE REDUCTION 511 11.2.3 MULTIVALUED SPACE-TIME
AMPLITUDES 514 11.2.4 THE CONSISTENT HIERARCHY OF JOINT PROBABILITIES
517 11.2.5 EPR CORRELATIONS 521 11.2.6 CONTINUOUS MEASUREMENTS 523 11.3
NON-LOCAL MEASUREMENTS AND CAUSALITY 526 11.3.1 ENTANGLED QUANTUM PROBES
527 11.3.2 NON-LOCAL MEASUREMENT BY EPR PROBES 530 11.3.3 QUANTUM STATE
VERIFICATION 536 11.3.4 NON-LOCAL OPERATIONS AND THE CAUSALITY PRINCIPLE
538 11.3.5 RESTRICTIONS ON THE MEASURABILITY OF OPERATORS 544 11.3.6 QND
VERIFICATION OF NON-LOCAL STATES 550 11.3.7 PREPARATION OF NON-LOCAL
STATES 554 11.3.8 EXCHANGE MEASUREMENTS 555 11.4 QUANTUM TELEPORTATION
557 11.4.1 COHERENT TRANSFER OF QUANTUM STATES 557 11.4.2 TELEPORTATION
AND BELL-STATE MEASUREMENT 560 11.4.3 EXPERIMENTAL REALIZATION 562
REFERENCES 565 12 OPEN QUANTUM ELECTRODYNAMICS 56 8 12.1 DENSITY MATRIX
THEORY FOR QED 569 CONTENTS 12.1.1 FIELD EQUATIONS AND CORRELATION
FUNCTIONS 569 12.1.2 THE REDUCED DENSITY MATRIX 576 12.2 THE INFLUENCE
FUNCTIONAL OF QED 577 12.2.1 ELIMINATION OF THE RADIATION DEGREES OF
FREEDOM 577 12.2.2 VACUUM-TO-VACUUM AMPLITUDE 583 12.2.3 SECOND-ORDER
EQUATION OF MOTION 585 12.3 DECOHERENCE BY EMISSION OF BREMSSTRAHLUNG
588 12.3.1 INTRODUCING THE DECOHERENCE FUNCTIONAL 589 12.3.2 PHYSICAL
INTERPRETATION 593 12.3.3 EVALUATION OF THE DECOHERENCE FUNCTIONAL 596
12.3.4 PATH INTEGRAL APPROACH 607 12.4 DECOHERENCE OF MANY-PARTICLE
STATES 614 REFERENCES 617 INDEX 619
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:19:34Z |
| institution | BVB |
| isbn | 0198520638 |
| language | English |
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| spelling | Breuer, Heinz-Peter Verfasser aut The theory of open quantum systems Heinz-Peter Breuer and Francesco Petruccione Reprinted Oxford [u.a.] Oxford Univ. Press 2003 XXI, 625 S. graph. Darst. 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 Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010579424&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Breuer, Heinz-Peter Petruccione, Francesco 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 and Francesco Petruccione |
| title_fullStr | The theory of open quantum systems Heinz-Peter Breuer and Francesco Petruccione |
| title_full_unstemmed | The theory of open quantum systems Heinz-Peter Breuer and 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=010579424&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT breuerheinzpeter thetheoryofopenquantumsystems AT petruccionefrancesco thetheoryofopenquantumsystems |