Mathematical and physical aspects of stochastic mechanics:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo
Springer
1987
|
| Series: | Lecture notes in physics
281 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 158 - 171 |
| Physical Description: | VIII, 171 S. graph. Darst. |
| ISBN: | 3540180362 0387180362 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mathematical and physical aspects of stochastic mechanics |c Ph. Blanchard ; Ph. Combe ; W. Zheng |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo |b Springer |c 1987 | |
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| adam_text |
CONTENTS
I. INTRODUCTION
1.1 SOME PROBABILISTIC ASPECTS IN CLASSICAL AND QUANTUM
PHYSICS .
1.1A BROWNIAN MOTION. MECHANICS OF PARTICLES SUBMITTED TO
RANDOM DISTURBATION .
1.1B FROM FEYNMAN PATH INTEGRAL TO PROBABILISTIC
FORMULATIONS OF QUANTUM PHYSICS .
1.2 PROBABILISTIC INTERPRETATION OF QUANTUM MECHANICS AND
PROBABILITY THEORY .
1.2A HISTORICAL REMARKS .
I.2B THE WIGNER APPROACH .
I.2C PROBABILISTIC DESCRIPTION OF COMMUTING OBSERVABLES .
1.3 JACOBI AND MADELUNG FLUID .
I. 3A THE HAMILTON-JACOBI-FLUID .
I. 3B THE MADELUNG FLUID .
II. KINEMATICS OF STOCHASTIC DIFFUSION PROCESSES
II. 1 BROWNIAN MOTION .
11.2 STOCHASTIC INTEGRATION .
11.3 DIFFUSION PROCESS .
11.4 KINEMATICS OF DIFFUSION PROCESSES .
11.5 THE TIME-REVERSED DIFFUSION PROCESS .
II.5A BROWNIAN MOTION WITH LEBESGUE MEASURE AS INITIAL
DISTRIBUTION .
II.DB TIME-REVERSED DIFFUSION PROCESS .
11.6 STOCHASTIC ACCELERATION .
11.7 SOME BASIC EXAMPLES .
II.7A THE WIENER PROCESS .
1
1
4
7
7
10
1
2
15
16
1 9
22
31
34
37
44
44
46
47
51
51
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/871067684
VI
II. 7B THE BROWNIAN BRIDGE . 51
II. 7C THE BESSEL PROCESS . 53
II.7D THE ORNSTEIN-UHLENBECK PROCESS . 55
III. NELSON STOCHASTIC DYNAMICS - NEWTONIAN PROCESSES
111.1 STOCHASTIC NEWTON LAW . 60
111.2 CONSERVATIVE NEWTONIAN DIFFUSION PROCESSES . 61
111.3 MECHANICS OF CONSERVATIVE NEWTONIAN PROCESS . 62
111.4 CONSERVATIVE NEWTONIAN PROCESSES WITH STATIONARY
DISTRIBUTION . 67
111.5 UNATTAINABILITY OF THE NODES FOR STATIONARY DIFFUSION
PROCESSES . 69
111.6 DIFFUSION IN AN EXTERNAL ELECTROMAGNETIC FIELD . 74
111.7 NEWTONIAN DIFFUSION ON RIEMANNIAN MANIFOLD . 75
IV. GLOBAL EXISTENCE FOR DIFFUSIONS WITH SINGULAR DRIFTS
IV. 1 INTRODUCTION . 82
IV.2 EXISTENCE OF NELSON'S DIFFUSION PROCESSES . 84
IV.2A HEURISTICS . 84
IV.2B UNATTAINABILITY OF THE NODES AND GLOBAL EXISTENCE . 85
IV.3 APPLICATION TO STOCHASTIC MECHANICS . 92
IV. 4 ALTERNATIVE METHODS TO CONSTRUCT SINGULAR DIFFUSIONS . 94
V. STOCHASTIC VARIATIONAL PRINCIPLES
V. O INTRODUCTION . 97
V.1 THE CLASSES S(P) AND S F
P,
F) . 97
V.2 STRONGLY CONVEX FUNCTIONALS . 100
V.3 THE YASUE ACTION . 101
V.4 CONSTRUCTION OF DIFFUSION PROCESSES BY A FORWARD
STOCHASTIC VARIATIONAL PRINCIPLE . 105
V.5 OTHER APPROACHES TO STOCHASTIC CALCULUS OF VARIATIONS. 110
VII
VI. TWO VIEWPOINTS CONCERNING QUANTUM AND STOCHASTIC MECHANICS
VI. 1 GENERAL REMARKS .
1
J
4
VI.2 INTERFERENCE .
*115
VI.3 OBSERVABLES - MEASUREMENT .
116
VI. 3A OBSERVABLES .
115
VI.3B MOMENTUM PROCESS .
11
7
VI.3C REPEATED MEASUREMENTS: A CASE AGAINST STOCHASTIC
MECHANICS? .
11
9
VI.4 INDETERMINACY RELATIONS . 123
VI.5 LOCALITY . 126
VI
.6
SCATTERING THEORY . 127
VI.7 SPINNING PARTICLE . 129
VI
.8
PAULI-PRINCIPLE . 130
VI.9 THE CONNECTION BETWEEN STOCHASTIC MECHANICS AND
EUCLIDEAN QUANTUM MECHANICS .
131
VI. 10 THE SEMICLASSICAL LIMIT .
133
VI. 11 BOSE QUANTUM FIELD THEORY .
135
VII. A NON-QUANTAL LOOK AT STOCHASTIC MECHANICS
VII. 1 GENERAL REMARKS .
137
VII.2 TRAPPING PHENOMENA AND FORMATION OF SPATIAL PATTERNS . 140
VII.2A A MODEL OF THE FORMATION OF JET-STREAMS IN THE
PROTOSOLAR NEBULA . 140
VII.2B CLOUD COVERING OF THE PLANETS . 142
VII.2C THE VAN ALLEN RADIATION BELTS . 143
VII. 3 A MODEL FOR TRANSPORT IN A PLASMA . 145
APPENDIX
A1 . NOTATIONS AND CONVENTIONS . 147
A2. CONDITIONING . 148
A3. STOCHASTIC PROCESSES . 149
A4. MARTINGALES . 150
VIII
A5. WEAK CONVERGENCE AND MEASURES ON METRIC SPACES . 151
A
6
. STOCHASTIC ITO INTEGRALS . 153
A7. DEFINITION AND CHARACTERISTICS OF QUADRATIC
VARIATION . 156
BIBLIOGRAPHY . 157 |
| any_adam_object | 1 |
| author | Blanchard, Philippe Combe, Philippe Zheng, W. |
| author_facet | Blanchard, Philippe Combe, Philippe Zheng, W. |
| author_role | aut aut aut |
| author_sort | Blanchard, Philippe |
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| building | Verbundindex |
| bvnumber | BV025873128 |
| classification_rvk | SK 820 UD 8220 |
| ctrlnum | (OCoLC)263109405 (DE-599)BVBBV025873128 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV025873128 |
| illustrated | Illustrated |
| indexdate | 2024-10-09T12:05:28Z |
| institution | BVB |
| isbn | 3540180362 0387180362 |
| language | English |
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| physical | VIII, 171 S. graph. Darst. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Blanchard, Philippe Verfasser aut Mathematical and physical aspects of stochastic mechanics Ph. Blanchard ; Ph. Combe ; W. Zheng Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo Springer 1987 VIII, 171 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 281 Literaturverz. S. 158 - 171 Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Mechanik (DE-588)4038168-7 s Combe, Philippe Verfasser aut Zheng, W. Verfasser aut Lecture notes in physics 281 (DE-604)BV000003166 281 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019120336&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blanchard, Philippe Combe, Philippe Zheng, W. Mathematical and physical aspects of stochastic mechanics Lecture notes in physics Statistische Mechanik (DE-588)4056999-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4056999-8 (DE-588)4057630-9 (DE-588)4038168-7 |
| title | Mathematical and physical aspects of stochastic mechanics |
| title_auth | Mathematical and physical aspects of stochastic mechanics |
| title_exact_search | Mathematical and physical aspects of stochastic mechanics |
| title_full | Mathematical and physical aspects of stochastic mechanics Ph. Blanchard ; Ph. Combe ; W. Zheng |
| title_fullStr | Mathematical and physical aspects of stochastic mechanics Ph. Blanchard ; Ph. Combe ; W. Zheng |
| title_full_unstemmed | Mathematical and physical aspects of stochastic mechanics Ph. Blanchard ; Ph. Combe ; W. Zheng |
| title_short | Mathematical and physical aspects of stochastic mechanics |
| title_sort | mathematical and physical aspects of stochastic mechanics |
| topic | Statistische Mechanik (DE-588)4056999-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Statistische Mechanik Stochastischer Prozess Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019120336&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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