Quantum trajectories and measurements in continuous time: the diffusive case
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u. a.
Springer
2009
|
| Series: | Lecture notes in physics
782 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 313 - 320 |
| Physical Description: | XIV, 325 S. graph. Darst. 24 cm |
| ISBN: | 9783642012976 |
Staff View
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Record in the Search Index
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| adam_text | TRANSFORMATIONS 41 CONTENTS 1 INTRODUCTION 1 1.1 QUANTUM OPEN SYSTEMS 1
1.2 APPROACHES TO CONTINUOUS MEASUREMENTS 2 1.3 CLASSICAL SDES IN
CONTINUOUS MEASUREMENT THEORY 3 1.4 THE PLAN OF THE BOOK 3 REFERENCES 4
PART I GENERAL THEORY 2 THE STOCHASTIC SCHROEDINGER EQUATION 11 2.1
INTRODUCTION 11 2.2 LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS 12 2.2.1 AN
HOMOGENEOUS LINEAR SDE IN HUBERT SPACE 13 2.2.2 THE STOCHASTIC EVOLUTION
OPERATOR 14 2.2.3 THE SQUARE NORM OF THE SOLUTION 17 2.3 THE LINEAR
STOCHASTIC SCHROEDINGER EQUATION 19 2.3.1 A KEY RESTRICTION 19 2.3.2 A
CHANGE OF PROBABILITY 21 2.4 THE PHYSICAL INTERPRETATION 21 2.4.1 THE
POM OF THE OUTPUT AND THE PHYSICAL PROBABILITIES .. 23 2.4.2 THE A
POSTERIORI STATES 25 2.4.3 INFINITE TIME HORIZON 26 2.4.4 THE
CONSERVATIVE CASE 27 2.5 THE STOCHASTIC SCHROEDINGER EQUATION 28 2.5.1
THE STOCHASTIC DIFFERENTIAL OF THE A POSTERIORI STATE 28 2.5.2 FOUR
STOCHASTIC SCHROEDINGER EQUATIONS 30 2.5.3 EXISTENCE AND UNIQUENESS OF
THE SOLUTION 33 2.5.4 THE STOCHASTIC SCHROEDINGER EQUATION AS A STARTING
POINT 38 2.6 THE LINEAR APPROACH VERSUS THE NONLINEAR ONE 40 2.7 TRICKS
TO SIMPLIFY THE EQUATIONS 41 2.7.1 TIME-DEPENDENT COEFFICIENTS AND
UNITARY BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/994282559
DIGITALISIERT DURCH CONTENTS 2.7.2 COMPLEX NOISE 42 2.8 SUMMARY: THE
STOCHASTIC SCHROEDINGER EQUATION 43 2.8.1 THE LINEAR STOCHASTIC
SCHROEDINGER EQUATION 43 2.8.2 THE NONLINEAR STOCHASTIC SCHROEDINGER
EQUATION 46 REFERENCES 47 THE STOCHASTIC MASTER EQUATION: PART 1 51 3.1
FROM HUBERT SPACE TO STATISTICAL FORMULATION 51 3.1.1 A MIXED INITIAL
STATE 51 3.1.2 THE LINEAR STOCHASTIC MASTER EQUATION -1 54 3.2 THE
MASTER EQUATION 54 3.2.1 THE MEAN STATISTICAL OPERATOR 54 3.2.2 THE MEAN
DYNAMICS 55 3.2.3 QUANTUM DYNAMICAL SEMIGROUPS 57 3.3 AN INCOMPLETE
OBSERVATION 58 3.4 THE STATISTICAL FORMULATION 61 3.4.1 THE LINEAR
STOCHASTIC MASTER EQUATION - II 61 3.4.2 THE PHYSICAL PROBABILITIES, THE
A POSTERIORI AND THE A PRIORI STATES 67 3.4.3 BACK TO THE HUBERT SPACE
FORMULATION 70 3.5 THE STOCHASTIC MASTER EQUATION 70 3.6 SUMMARY OF
LINEAR QUANTUM TRAJECTORIES 71 3.6.1 THE MASTER EQUATION 71 3.6.2
REFERENCE PROBABILITY SPACE AND FILTRATIONS 72 3.6.3 THE LINEAR
STOCHASTIC MASTER EQUATION FOR NON-NORMALISED STATES 73 3.6.4 THE
PHYSICAL PROBABILITY AND THE POMS 74 3.6.5 THE NONLINEAR STOCHASTIC
MASTER EQUATION FOR NORMALISED STATES 74 REFERENCES 74 CONTINUOUS
MEASUREMENTS AND INSTRUMENTS 77 4. 1 THE INSTRUMENTS 77 4.1.1 THE
CONSTRUCTION OF THE INSTRUMENTS 77 4.1. CONTENTS 4.4 CLASSICAL
POST-MEASUREMENT PROCESSING 94 4.4.1 TIME-LOCAL TRANSFORMATIONS 94 4.4.2
RESPONSE WITH TIME DELAY 99 4.5 AUTOCORRELATION AND SPECTRUM OF THE
OUTPUT PROCESS 100 4.5.1 THE SPECTRUM OF A STATIONARY PROCESS 100 4.5.2
THE SPECTRUM OF AN ASYMPTOTICALLY STATIONARY PROCESS .102 4.5.3 THE
SPECTRUM OF THE OUTPUT OF THE CONTINUOUS MEASUREMENT 104 4.6 SUMMARY 108
REFERENCES 109 5 THE STOCHASTIC MASTER EQUATION: PART II ILL 5.1 QUANTUM
TRAJECTORIES: THE NONLINEAR SDE FORMULATION ILL 5.1.1 THE NONLINEAR SDE
112 5.1.2 STOCHASTIC MASTER EQUATION, A POSTERIORI STATES AND OUTPUT 115
5.1.3 THE LINEAR SDE 115 5.1.4 CHARACTERISTIC FUNCTIONAL AND INSTRUMENTS
116 5.2 PURIFICATION OF THE A POSTERIORI STATES 118 5.2.1 PRESERVATION
OF PURE STATES 118 5.2.2 FROM MIXED TO PURE STATES 119 REFERENCES 123 6
MUTUAL ENTROPIES AND INFORMATION GAIN IN QUANTUM CONTINUOUS MEASUREMENTS
125 6.1 INTRODUCTION 125 6.2 STATES AND ENTROPIES IN THE DISCRETE CASE
126 6.2.1 ALGEBRAS AND STATES 126 6.2.2 ENTROPIES AND RELATIVE ENTROPIES
126 6.2.3 MUTUAL ENTROPY AND X -QUANTITIES 127 6.3 THE CONTINUOUS
MEASUREMENT AS A CHANNEL 129 6.3.1 VON NEUMANN ALGEBRAS AND NORMAL
STATES 129 6.3.2 ENTROPIES 130 6.3.3 CHANNELS 131 6.4 A CLASSICAL
CONTINUOUS INFORMATION GAIN 132 6.4. XII CONTENTS PART II PHYSICAL
APPLICATIONS 7 QUANTUM OPTICAL SYSTEMS 145 7.1 HOW TO CONSTRUCT PHYSICAL
MODELS 145 7.1.1 FROM THE FULL QUANTUM LEVEL TO THE REDUCED DESCRIPTION
BY SDES 145 7.1.2 OBSERVED AND UNOBSERVED CHANNELS * THE GENERATORS .
146 7.2 HETERODYNE AND HOMODYNE DETECTION 148 7.2.1 THE MEASUREMENT
SCHEME 148 7.2.2 HOMODYNING VERSUS HETERODYNING 150 REFERENCES 150 8 A
TWO-LEVEL ATOM: GENERAL SETUP 151 8.1 A TWO-LEVEL ATOM STIMULATED BY A
LASER 151 8.1.1 THE PAULI MATRICES 151 8.1.2 THE BLOCH REPRESENTATION
152 8.1.3 THE SYSTEM OPERATORS 153 8.2 THE REDUCED DYNAMICS OF THE
TWO-LEVEL ATOM 157 8.2.1 THE REDUCED DYNAMICS AND THE ROTATING FRAME 158
8.2.2 THE BLOCH EQUATIONS 159 8.2.3 THE EVOLUTION IN THE GENERIC CASE
163 8.3 THE EQUILIBRIUM STATE R/ EQ 165 8.3.1 CONVERGENCE TO EQUILIBRIUM
165 8.3.2 THE EXPLICIT EXPRESSION OF IJ EQ 167 8.3.3 SOME PROPERTIES OF
^ E Q 168 8.4 THE SDES FOR THE TWO-LEVEL ATOM 172 8.4.1 THE SDES IN THE
HUBERT SPACE 172 8.4.2 THE STOCHASTIC MASTER EQUATION 175 8.4.3 LINEAR
ENTROPY AND ATOMIC SQUEEZING 177 8.4.4 THE INSTRUMENTS IN THE ROTATING
FRAME 179 8.5 SUMMARY 179 8.5.1 BLOCH REPRESENTATION OF STATES AND
TERMINOLOGY 179 8.5.2 THE MODEL AND THE PARAMETERS 180 REFERENCE
CONTENTS 9.3.2 HETERODYNE SPECTRAL DENSITY 214 9.3.3 HOMODYNE SPECTRAL
DENSITY 216 REFERENCES 219 10 FEEDBACK 221 10.1 INTRODUCTION 221 10.1.1
FEEDBACK AND CONTROL OF QUANTUM SYSTEMS 221 10.1.2 FEEDBACK CONTROL OF A
QUANTUM OPTICAL SYSTEM 222 10.2 THE FEEDBACK SCHEME OF WISEMAN AND
MILBURN 222 10.2.1 OBSERVATION WITHOUT FEEDBACK 223 10.2.2 INTRODUCTION
OF THE FEEDBACK 224 10.3 THE TWO-LEVEL ATOM WITH FEEDBACK 225 10.3.1 THE
MODEL 226 10.3.2 A PRIORI STATES 229 10.3.3 THE CASE OF MANY STATIONARY
STATES 233 10.3.4 EQUILIBRIUM 234 10.3.5 THE NONLINEAR STOCHASTIC MASTER
EQUATION 234 10.4 CONTROL OF THE ATOMIC STATE 235 10.5 CONTROL OF THE
SQUEEZING OF FLUORESCENCE LIGHT 239 10.5.1 THE SPECTRAL DENSITIES 240
10.5.2 CHANNEL 1 : THE IN-LOOP LIGHT 241 10.5.3 CHANNEL 2 243 10.5.4 THE
SPECTRUM OF THE CROSS-CORRELATIONS 245 10.5.5 GLOBAL SQUEEZING OF LIGHT
AND ATOMIC SQUEEZING 246 10.6 CONTROL AND LINE NARROWING 248 10.6.1 A
FIRST CASE OF LINE NARROWING 249 10.6.2 A SECOND CASE OF LINE NARROWING
256 10.7 SUMMARY 258 10.7.1 ATOMIC AND MEASUREMENT QUANTITIES 259 10.7.2
HOMODYNE SPECTRAL DENSITIES 259 10.7.3 IMPORTANT FEATURES OF THE
HOMODYNE SPECTRAL DENSITIES. 261 REFERENCES 261 ORDINARY SDES 263 A.I
PROBABILITY SPACES AND RANDOM VARIABLES 263 A.I. XIV CONTENTS A.2.6 THE
WIENER PROCESS 273 A.3 STOCHASTIC CALCULUS 274 A.3.1 CLASSES OF
INTEGRANDS 275 A.3.2 INTEGRALS ON TIME 275 A.3.3 STOCHASTIC INTEGRALS
276 A.3.4 ITO FORMULA 277 A.4 ORDINARY STOCHASTIC DIFFERENTIAL EQUATIONS
279 A.4.1 THE MAIN CLASS OF SDES 279 A.4.2 TYPES OF SOLUTIONS 279 A.4.3
SUFFICIENT CONDITIONS FOR EXISTENCE AND UNIQUENESS .... 280 A.4.4 L P
-ESTIMATES ON THE SOLUTION 281 A.5 CHANGE OF MEASURE AND GIRSANOV
TRANSFORMATION 282 A.5.1 A CHARACTERISATION OF THE WIENER PROCESS 282
A.5.2 EXPONENTIAL OF ITO PROCESSES 283 A.5.3 POSITIVE MARTINGALES AND
CHANGE OF MEASURE 285 A.5.4 GIRSANOV THEOREM 286 A.5.5 EXTENSION OF THE
LOCAL PROBABILITY MEASURES 289 REFERENCES 291 B SOME NOTIONS OF QUANTUM
MECHANICS 293 B.I NOTATIONS 293 B.I.I THE HUBERT SPACE K = C 293 B.1.2
OPERATORS 293 B.1.3 DIRAC NOTATIONS 295 B.2 THE HUBERT SPACE FORMULATION
OF QUANTUM MECHANICS 296 B.2.1 OBSERVABLES 296 B.2.2 THE ABSTRACT
SCHROEDINGER EQUATION 298 B.3 THE STATISTICAL FORMULATION OF QUANTUM
MECHANICS 298 B.3.1 STATISTICAL OPERATORS 299 B.3.2 THE VON NEUMANN
EQUATION 300 B.3.3 MASTER EQUATION AND QUANTUM DYNAMICAL SEMIGROUPS .
301 B.4 INSTRUMENTS 302 B.4.1 OPERATIONS AND EVENTS 302 B.4.2
INSTRUMENTS AND OBSERVABLES 304 B.4.
|
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| id | DE-604.BV035802896 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:56Z |
| institution | BVB |
| isbn | 9783642012976 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018661989 |
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| physical | XIV, 325 S. graph. Darst. 24 cm |
| publishDate | 2009 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Barchielli, Alberto Verfasser aut Quantum trajectories and measurements in continuous time the diffusive case A. Barchielli ; M. Gregoratti Berlin u. a. Springer 2009 XIV, 325 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 782 Literaturverz. S. 313 - 320 Quantum trajectories Messprozess (DE-588)4169530-6 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenoptik (DE-588)4047990-0 gnd rswk-swf Quantenoptik (DE-588)4047990-0 s DE-604 Messprozess (DE-588)4169530-6 s Quantenmechanik (DE-588)4047989-4 s Gregoratti, Matteo Verfasser aut Lecture notes in physics 782 (DE-604)BV000003166 782 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018661989&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barchielli, Alberto Gregoratti, Matteo Quantum trajectories and measurements in continuous time the diffusive case Lecture notes in physics Quantum trajectories Messprozess (DE-588)4169530-6 gnd Quantenmechanik (DE-588)4047989-4 gnd Quantenoptik (DE-588)4047990-0 gnd |
| subject_GND | (DE-588)4169530-6 (DE-588)4047989-4 (DE-588)4047990-0 |
| title | Quantum trajectories and measurements in continuous time the diffusive case |
| title_auth | Quantum trajectories and measurements in continuous time the diffusive case |
| title_exact_search | Quantum trajectories and measurements in continuous time the diffusive case |
| title_full | Quantum trajectories and measurements in continuous time the diffusive case A. Barchielli ; M. Gregoratti |
| title_fullStr | Quantum trajectories and measurements in continuous time the diffusive case A. Barchielli ; M. Gregoratti |
| title_full_unstemmed | Quantum trajectories and measurements in continuous time the diffusive case A. Barchielli ; M. Gregoratti |
| title_short | Quantum trajectories and measurements in continuous time |
| title_sort | quantum trajectories and measurements in continuous time the diffusive case |
| title_sub | the diffusive case |
| topic | Quantum trajectories Messprozess (DE-588)4169530-6 gnd Quantenmechanik (DE-588)4047989-4 gnd Quantenoptik (DE-588)4047990-0 gnd |
| topic_facet | Quantum trajectories Messprozess Quantenmechanik Quantenoptik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018661989&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
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