Stochastic processes in quantum physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2000
|
| Schriftenreihe: | Monographs in mathematics
94 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 573 - 589 |
| Beschreibung: | VII, 598 S. graph. Darst. |
| ISBN: | 3764362081 |
Internformat
MARC
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| 100 | 1 | |a Nagasawa, Masao |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stochastic processes in quantum physics |c Masao Nagasawa |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2000 | |
| 300 | |a VII, 598 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Monographs in mathematics |v 94 | |
| 500 | |a Literaturverz. S. 573 - 589 | ||
| 650 | 4 | |a Quantenmechanik - Markov-Prozess | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Quantum theory |x Mathematics | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Quantenmechanik |0 (DE-588)4047989-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quantenmechanik |0 (DE-588)4047989-4 |D s |
| 689 | 0 | 1 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Monographs in mathematics |v 94 |w (DE-604)BV000008284 |9 94 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008771121 | ||
Datensatz im Suchindex
| _version_ | 1804127571787382784 |
|---|---|
| adam_text | Contents
Preface
Chapter I
Markov Processes
1.1 Classical Mechanics 1
1.2 Movement of a Particle with Noise 3
1.3 Transition Probability and the Markov Property 7
1.4 Diffusion Equations 12
1.5 Brownian Motions 16
1.6 The Ito formula 23
Appendix. Monotone Lemmas 26
Chapter II
Time Reversal and Duality
2.1 Time Reversal of Markov Processes and Duality 27
2.2 Space Time Markov Processes and Space Time Duality 37
2.3 Time Reversal and Schrodinger s Representation 44
Chapter III
Non Relativistic Quantum Theory
3.1 Non Relativistic Equation of Motion 53
3.2 Stationary States and Eigenvalue Problem 58
3.3 Time Reversal of Diffusion Processes 62
3.4 Duality Relation of Diffusion Processes 64
3.5 Equation of Motion in General Cases 69
3.6 Principle of Superposition of Markov Processes 74
3.7 Non Relativistic Schrodinger Equation 81
3.8 State Preparations and Measurements 85
3.9 Diffusion or Schrodinger Equations ? 93
3.10 The First Technical Convention 96
Chapter IV
Stationary Schrodinger Processes
4.1 Stationary States 105
4.2 One Dimensional Harmonic Oscillator 106
4.3 An Example in Two Dimension 109
4.4 Superposition of Eigenfunctions 113
4.5 Further Excited States 118
4.6 Hydrogen Atom 122
Chapter V
Construction of the Schrodinger Processes
5.1 The Feynman Kac Formula 139
5.2 Solving the Equation of Motion 143
5.3 Transformation by Multiplicative Functionals 153
5.4 Renormalization 159
5.5 A Variational Method 162
5.6 The Maruyama Girsanov Formula 168
5.7 A Lagrangian Formulation 175
5.8 The Second Technical Convention 179
Chapter VI
Markov Processes with Jumps
6.1 Poisson and Compound Poisson Processes 185
6.2 Poisson Random measures and Point Processes 191
6.3 Stochastic Integrals with Poisson Point Processes 194
6.4 Levy Processes 201
6.5 Stable Processes 210
6.6 Bochner s Subordination 212
6.7 Duality of Subordinate Semi Groups 221
6.8 Harmonic Transformation of Subordinate Semi Groups 225
6.9 Duality of Fractional Powers of Time Dependent Operators 228
Chapter VII
Relativistic Quantum Particles
7.1 A Relativistic Schrodinger Equation for a Spinless Paticle 231
7.2 Equation of Motion for Relativistic Quantum Particles 234
7.3 Stationary States of the Relativistic Schrodinger Equation 247
7.4 Stochastic Processes for Relativistic Spinless Particles 251
7.5 Non Relativistic Limit 257
7.6 A Diffusion Approximation 260
Chapter VIII
Stochastic Differential Equations of Pure Jumps
8.1 Markov Processes with the Generators of Fractional Power 263
8.2 Stochastic Differential Equations of Pure Jumps 265
8.3 The Case with no Potential Term 270
8.4 To Solve the Stochastic Differential Equations of Pure Jumps 276
8.5 To Construct Pure Jump Markov Processes 281
8.6 A Remark on the Integrability Condition 284
Chapter IX
Variational Principle
for Relativistic Quantum Particles
9.1 Absolute Continuity 287
9.2 Pure Jump Markov Processes 289
9.3 A Multiplicative Functional 294
9.4 Renormalization and Variational Principle 307
Chapter X
Time Dependent Subordination and
Markov Processes with Jumps
10.1 Time Inhomogeneous Subordination 315
10.2 Lemmas 319
10.3 Stochastic Differential Equation with Jumps 327
10.4 A Formula of Feynman Kac Type 334
10.5 Markov Processes with Jumps 350
Appendix. Integration by Parts Formulae 353
Chapter XI
Concave Majorants of Levy Processes
and the Light Cone
14.1 The Vertex Process of a Levy Process 355
14.2 Propositions on Random walks 359
14.3 Proof of Propositions on Random Walks 361
14.4 Proof of the main Theorems 372
14.5 Examples 382
14.6 The light Cone 386
Chapter XII
The Locality in Quantum Physics
12.1 Historical Overview 389
12.2 Hidden Variable Theories 390
12.3 Locality of Hidden Variable Theories 399
12.4 Spin Correlation of Three Particles 408
12.5 Gudder s Hidden Variable Theory 417
12.6 Spin Correlations in Gudder s Theory 421
12.7 Some Remarks 252
Chapter XIII
Micro Statistical Theory
13.1 The Source of the Noise 437
13.2 Large Deviations of the Renormalized Processes 442
13.3 The Propagation of Chaos 444
13.4 Micro Statistical Mechanics 447
13.5 Propagation of Chaos of Pure Jump Processes 449
13.6 Superposition of Movements 451
12.7 A Remark on the Gibbs Distribution 455
Chapter XIV
Processes on Open Time Intervals
14.1 Diffusion Processes on Open Time Intervals 461
14.2 Time Reversed Schrodinger Processes 463
14.3 A Theorem of Jeulin Yor 470
14.4 Reflecting Brownian Motion 473
14.5 Two Sided Skorokhod Type Problem 477
14.6 Skorokhod Problem with Singular Drift 483
14.7 The Minimum and Maximum Solutions 487
14.8 The Uniqueness and Non Uniqueness of Solutions 489
14.9 An Application: The Origin of Universes 493
Chapter XV
Creation and Killing of Particles
15.1 Non Linear Differential Equations 501
15.2 Branching Markov Processes 505
15.3 The Expected Number of Particles 511
15.4 Killing 517
Chapter XVI
The ltd Calculus
16.1 The Ito Integral 521
16.2 Martingales 530
16.3 The Ito Integral with Local Martingales 546
16.4 Ito s formula 553
16.5 Stochastic Differential Equations 561
16.6 Stochastic Differential Calculus 567
References 573
Index 591
|
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| author | Nagasawa, Masao |
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| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV012884924 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:35:28Z |
| institution | BVB |
| isbn | 3764362081 |
| language | English |
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| physical | VII, 598 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Birkhäuser |
| record_format | marc |
| series | Monographs in mathematics |
| series2 | Monographs in mathematics |
| spelling | Nagasawa, Masao Verfasser aut Stochastic processes in quantum physics Masao Nagasawa Basel [u.a.] Birkhäuser 2000 VII, 598 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs in mathematics 94 Literaturverz. S. 573 - 589 Quantenmechanik - Markov-Prozess Mathematik Quantentheorie Quantum theory Mathematics Stochastic processes Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Monographs in mathematics 94 (DE-604)BV000008284 94 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008771121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nagasawa, Masao Stochastic processes in quantum physics Monographs in mathematics Quantenmechanik - Markov-Prozess Mathematik Quantentheorie Quantum theory Mathematics Stochastic processes Quantenmechanik (DE-588)4047989-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4057630-9 |
| title | Stochastic processes in quantum physics |
| title_auth | Stochastic processes in quantum physics |
| title_exact_search | Stochastic processes in quantum physics |
| title_full | Stochastic processes in quantum physics Masao Nagasawa |
| title_fullStr | Stochastic processes in quantum physics Masao Nagasawa |
| title_full_unstemmed | Stochastic processes in quantum physics Masao Nagasawa |
| title_short | Stochastic processes in quantum physics |
| title_sort | stochastic processes in quantum physics |
| topic | Quantenmechanik - Markov-Prozess Mathematik Quantentheorie Quantum theory Mathematics Stochastic processes Quantenmechanik (DE-588)4047989-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Quantenmechanik - Markov-Prozess Mathematik Quantentheorie Quantum theory Mathematics Stochastic processes Quantenmechanik Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008771121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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