A measure theoretical approach to quantum stochastic processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2014
|
| Schriftenreihe: | Lecture Notes in Physics
878 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 228 S. |
| ISBN: | 9783642450822 9783642450815 |
Internformat
MARC
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| 245 | 1 | 0 | |a A measure theoretical approach to quantum stochastic processes |c Wilhelm von Waldenfels |
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| 300 | |a XVII, 228 S. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
1 WEYL ALGEBRAS 1
1.1 DEFINITION OF A WEYL ALGEBRA 1
1.2 THE ALGEBRAIC TENSOR PRODUCT 2
1.3 WICK S THEOREM 5
1.4 BASIS OF A WEYL ALGEBRA 8
1.5 GAUSSIAN FUNCTIONALS 10
1.6 MULTISETS 12
1.7 FINITE SETS OF CREATION AND ANNIHILATION OPERATORS 16
2 CONTINUOUS SETS OF CREATION AND ANNIHILATION OPERATORS 25
2.1 CREATION AND ANNIHILATION OPERATORS ON FOCK SPACE 25
2.2 THE SUM-INTEGRAL LEMMA FOR MEASURES 26
2.3 CREATION AND ANNIHILATION OPERATORS ON LOCALLY COMPACT SPACES 31
2.4 INTRODUCTION OF POINT MEASURES 34
3 ONE-PARAMETER GROUPS 39
3.1 RESOLVENT AND GENERATOR 39
3.2 THE SPECTRAL SCHWARTZ DISTRIBUTION 46
4 FOUR EXPLICITLY CALCULABLE ONE-EXCITATION PROCESSES 55
4.1 KREIN S FORMULA 55
4.2 A TWO-LEVEL ATOM COUPLED TO A HEAT BATH OF OSCILLATORS .... 57
4.2.1 DISCUSSION OF THE MODEL 57
4.2.2 SINGULAR COUPLING LIMIT 61
4.2.3 TIME EVOLUTION 66
4.2.4 REPLACING FREQUENCIES BY FORMAL TIMES 68
4.2.5 THE EIGENVALUE PROBLEM 70
4.3 A TWO-LEVEL ATOM INTERACTING WITH POLARIZED RADIATION 79
4.3.1 PHYSICAL CONSIDERATIONS 79
4.3.2 SINGULAR COUPLING 83
4.3.3 THE HAMILTONIAN AND THE EIGENVALUE PROBLEM 86
4.4 THE HEISENBERG EQUATION OF THE AMPLIFIED OSCILLATOR 88
XV
HTTP://D-NB.INFO/104364072X
XVI
CONTENTS
4.4.1 PHYSICAL CONSIDERATIONS 88
4.4.2 THE SINGULAR COUPLING LIMIT, ITS HAMILTONIAN
AND EIGENVALUE PROBLEM 90
4.5 THE PURE NUMBER PROCESS 94
5 WHITE NOISE CALCULUS 97
5.1 MULTIPLICATION OF DIFFUSIONS 97
5.2 MULTIPLICATION OF POINT MEASURES 99
5.3 WHITE NOISE OPERATORS 101
5.4 WICK S THEOREM 107
5.5 REPRESENTATION OF UNITY 109
5.6 DUALITY ILL
6 CIRCLED INTEGRALS 113
6.1 DEFINITION 113
6.2 A CIRCLED INTEGRAL EQUATION 114
6.3 FUNCTIONS OF CLASS ^ 117
7 WHITE NOISE INTEGRATION 123
7.1 INTEGRATION OF NORMAL ORDERED MONOMIALS 123
7.2 MEYER S FORMULA 127
7.3 QUANTUM STOCHASTIC PROCESSES OF CLASS ^
1
: DEFINITION
AND FUNDAMENTAL PROPERTIES 129
7.4 ITO S THEOREM 131
8 THE HUDSON-PARTHASARATHY DIFFERENTIAL EQUATION 139
8.1 FORMULATION OF THE EQUATION 139
8.2 EXISTENCE AND UNIQUENESS OF THE SOLUTION 140
8.3 EXAMPLES 141
8.3.1 A TWO-LEVEL ATOM IN A HEATBATH OF OSCILLATORS 141
8.3.2 A TWO-LEVEL ATOM INTERACTING WITH POLARIZED RADIATION . 143
8.3.3 THE HEISENBERG EQUATION OF THE AMPLIFIED OSCILLATOR . . 144
8.3.4 A PURE NUMBER PROCESS 144
8.4 A PRIORI ESTIMATE AND CONTINUITY AT THE ORIGIN 145
8.5 CONSECUTIVE INTERVALS IN TIME 150
8.6 UNITARITY 152
8.7 ESTIMATION OF THE /VNORM 154
8.8 THE HAMILTONIAN 161
8.8.1 DEFINITION OF THE ONE-PARAMETER GROUP
W(T)
161
8.8.2 DEFINITION OF A, A
+
AND 3 163
8.8.3 CHARACTERIZATION OF THE HAMILTONIAN 169
9 THE AMPLIFIED OSCILLATOR 179
9.1 THE QUANTUM STOCHASTIC DIFFERENTIAL EQUATION 179
9.2 CLOSED SOLUTION 180
9.3 THE UNITARY EVOLUTION 192
9.4 HEISENBERG EQUATION 196
9.5 THE HAMILTONIAN 203
CONTENTS XVII
9.6 AMPLIFICATION 207
9.7 THE CLASSICAL YULE-MARKOV PROCESS 208
10 APPROXIMATION BY COLOURED NOISE 213
10.1 DEFINITION OF THE SINGULAR COUPLING LIMIT 213
10.2 APPROXIMATION OF THE HUDSON-PARTHASARATHY EQUATION 215
REFERENCES 225
INDEX 227
|
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| discipline | Physik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:58:20Z |
| institution | BVB |
| isbn | 9783642450822 9783642450815 |
| language | English |
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| physical | XVII, 228 S. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| series | Lecture Notes in Physics |
| series2 | Lecture Notes in Physics |
| spelling | Waldenfels, Wilhelm von Verfasser aut A measure theoretical approach to quantum stochastic processes Wilhelm von Waldenfels Berlin [u.a.] Springer 2014 XVII, 228 S. txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Physics 878 Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 s Stochastische Differentialgleichung (DE-588)4057621-8 s Maßtheorie (DE-588)4074626-4 s DE-604 Erscheint auch als Online-Ausgabe Waldenfels, Wilhelm von a Measure Theoretical Approach to Quantum Stochastic Processes (DE-604)BV041463689 Lecture Notes in Physics 878 (DE-604)BV000003166 878 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026996400&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Waldenfels, Wilhelm von A measure theoretical approach to quantum stochastic processes Lecture Notes in Physics Stochastische Differentialgleichung (DE-588)4057621-8 gnd Maßtheorie (DE-588)4074626-4 gnd Quantenmechanisches System (DE-588)4300046-0 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4074626-4 (DE-588)4300046-0 |
| title | A measure theoretical approach to quantum stochastic processes |
| title_auth | A measure theoretical approach to quantum stochastic processes |
| title_exact_search | A measure theoretical approach to quantum stochastic processes |
| title_full | A measure theoretical approach to quantum stochastic processes Wilhelm von Waldenfels |
| title_fullStr | A measure theoretical approach to quantum stochastic processes Wilhelm von Waldenfels |
| title_full_unstemmed | A measure theoretical approach to quantum stochastic processes Wilhelm von Waldenfels |
| title_short | A measure theoretical approach to quantum stochastic processes |
| title_sort | a measure theoretical approach to quantum stochastic processes |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd Maßtheorie (DE-588)4074626-4 gnd Quantenmechanisches System (DE-588)4300046-0 gnd |
| topic_facet | Stochastische Differentialgleichung Maßtheorie Quantenmechanisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026996400&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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