Scattering theory of classical and quantum N-particle systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1997
|
| Schriftenreihe: | Texts and monographs in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 444 S. graph. Darst. |
| ISBN: | 3540620664 |
Internformat
MARC
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| 100 | 1 | |a Dereziński, Jan |d 1957- |e Verfasser |0 (DE-588)11520816X |4 aut | |
| 245 | 1 | 0 | |a Scattering theory of classical and quantum N-particle systems |c Jan Dereziński ; Christian Gérard |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
| 300 | |a XII, 444 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Texts and monographs in physics | |
| 650 | 4 | |a Diffusion (Physique nucléaire) | |
| 650 | 7 | |a Diffusion (Physique) |2 ram | |
| 650 | 4 | |a Dispersion (Mathématiques) | |
| 650 | 7 | |a Dispersion (Mathématiques) |2 ram | |
| 650 | 4 | |a Physique mathématique - Théorie asymptotique | |
| 650 | 7 | |a Physique mathématique - Théorie asymptotique |2 ram | |
| 650 | 4 | |a Théorie quantique | |
| 650 | 7 | |a Théorie quantique |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Mathematical physics |x Asymptotic theory | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Scattering (Mathematics) | |
| 650 | 4 | |a Scattering (Physics) | |
| 650 | 0 | 7 | |a Vielteilchensystem |0 (DE-588)4063491-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Streutheorie |0 (DE-588)4183697-2 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Streutheorie |0 (DE-588)4183697-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Gérard, Christian |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-007509846 | ||
Datensatz im Suchindex
| _version_ | 1804125693488922624 |
|---|---|
| adam_text | Contents
0. Introduction 1
1. Classical Time Decaying Forces 5
1.0 Introduction 5
1.1 Basic Notation 11
1.2 Newton s Equation 13
1.3 Asymptotic Momentum 14
1.4 Fast Decaying Case 15
1.5 Slow Decaying Case I 20
1.6 Slow Decaying Case II 26
1.7 Boundary Conditions for Wave Transformations 31
1.8 Conservative Forces 33
1.9 Gauge Invariance of Wave Transformations 35
1.10 Smoothness of Trajectories 46
1.11 Comparison of Two Dynamics 50
1.12 More Examples of Modified Free Dynamics 53
2. Classical 2 Body Hamiltonians 57
2.0 Introduction 57
2.1 General Facts About Dynamical Systems 60
2.2 Upper Bounds on Trajectories 62
2.3 The Mourre Estimate and Scattering Trajectories 65
2.4 Non trapping Energies 69
2.5 Asymptotic Velocity 72
2.6 Short Range Case 74
2.7 Long Range Case 77
2.8 The Eikonal Equation 88
2.9 Smoothness of Trajectories 89
3. Quantum Time Decaying Hamiltonians 93
3.0 Introduction 93
3.1 Time Dependent Schrodinger Hamiltonians 97
3.2 Asymptotic Momentum 98
3.3 Fast Decaying Case 104
X Contents
3.4 Slow Decaying Case Hormander Potentials 106
3.5 Slow Decaying Case Smooth Potentials 115
3.6 Dollard Wave Operators 118
3.7 Isozaki Kitada Construction 120
3.8 Counterexamples to Asymptotic Completeness 124
3.8.1 Adiabatic Evolution 124
3.8.2 Counterexample Based on the Adiabatic Approximation . 125
3.8.3 A Sharper Counterexample 127
3.9 Smoothness of Wave Operators in the Fast Decaying Case .... 129
3.10 Smoothness of Wave Operators in the Slow Decaying Case . . . . 132
4. Quantum 2 Body Hamiltonians 135
4.0 Introduction 135
4.1 Schrodinger Hamiltonians 143
4.2 Weak Large Velocity Estimates 145
4.3 The Mourre Estimate and Its Consequences 148
4.4 Asymptotic Velocity 151
4.5 Joint Spectrum of P+ and H 161
4.6 Short Range Case 164
4.7 Long Range Case 167
4.8 Dollard Wave Operators 174
4.9 Isozaki Kitada Construction 176
4.10 Counterexamples to Asymptotic Completeness 181
4.10.1 The Born Oppenheimer Approximation
an Abstract Setting 181
4.10.2 The Born Oppenheimer Approximation
for Schrodinger Operators 183
4.10.3 Counterexample to Asymptotic Completeness 186
4.11 Strong Large Velocity Estimates 190
4.12 Strong Propagation Estimates for the Generator of Dilations . . 193
4.13 Strong Low Velocity Estimates 196
4.14 Schrodinger Operators as Pseudo differential Operators 198
4.15 Improved Isozaki Kitada Modifiers 199
4.16 Microlocal Propagation Estimates 203
4.17 Wave Operators with Outgoing Cutoffs 207
4.18 Wave Operators on Weighted Spaces 209
5. Classical TV Body Hamiltonians 215
5.0 Introduction 215
5.1 TV Body Systems 219
5.2 Some Special Observables 226
5.3 Bounded Trajectories and the Classical Mourre Estimate .... 236
5.4 Asymptotic Velocity 243
5.5 Joint Localization of the Energy and the Asymptotic Velocity . . 247
5.6 Regular a Trajectories 249
Contents XI
5.7 Upper Bound on the Size of Clusters 252
5.8 Free Region Scattering 255
5.8.1 Short Range Free Region Case 256
5.8.2 Long Range Free Region Case 257
5.9 Existence of the Asymptotic External Position 258
5.9.1 Asymptotic External Position in the Short Range Case . 259
5.9.2 Asymptotic External Position in the Long Range Case . . 259
5.9.3 External Position for Regular a Trajectories 262
5.10 Potentials of Super Exponential Decay 262
6. Quantum Af Body Hamiltonians 265
6.0 Introduction 265
6.1 Basic Definitions 274
6.2 HVZ Theorem 276
6.3 Weak Large Velocity Estimates 280
6.4 The Mourre Estimate 281
6.5 Exponential Decay of Eigenfunctions
and Absence of Positive Eigenvalues 289
6.6 Asymptotic Velocity 297
6.7 Asymptotic Completeness of Short Range Systems 306
6.8 Asymptotic Separation of the Dynamics I 309
6.9 Time Dependent iV Body Hamiltonians 315
6.10 Joint Spectrum of P+ and H 319
6.11 Asymptotic Clustering
and Asymptotic Absolute Continuity 326
6.12 Improved Propagation Estimates 328
6.13 Upper Bound on the Size of Clusters 333
6.14 Asymptotic Separation of the Dynamics II 345
6.15 Modified Wave Operators and Asymptotic Completeness
in the Long Range Case 347
A. Miscellaneous Results in Real Analysis 353
A.I Some Inequalities 353
A.2 The Fixed Point Theorem 356
A.3 The Hamilton Jacobi Equation 360
A.4 Construction of Some Cutoff Functions 367
A.5 Propagation Estimates 368
A.6 Comparison of Two Dynamics 369
A.7 Schwartz s Global Inversion Theorem 372
B. Operators on Hilbert Spaces 373
B.I Self adjoint Operators 373
B.2 Convergence of Self adjoint Operators 376
B.3 Time Dependent Hamiltonians 379
B.4 Propagation Estimates 383
XII Contents
B.5 Limits of Unitary Operators 386
B.6 Schur s Lemma 386
B.7 Compact Operators in L2(HT) 387
C. Estimates on Functions of Operators 389
C.I Basic Estimates of Commutators 389
C.2 Almost Analytic Extensions 390
C.3 Commutator Expansions I 392
C.4 Commutator Expansions II 394
D. Pseudo differential and Fourier Integral Operators 397
D.O Introduction 397
D.I Symbols of Operators 399
D.2 Phase Space Correlation Functions 400
D.3 Symbols Associated with a Uniform Metric 401
D.4 Pseudo differential Operators Associated with a Uniform Metric 403
D.5 Symbols and Operators Depending on a Parameter 407
D.6 Weighted Spaces 410
D.7 Symbols Associated with Some Non uniform Metrics 410
D.8 Pseudo differential Operators Associated with the Metric g . . . 412
D.9 Essential Support of Pseudo differential Operators 414
D.10 Ellipticity 416
D.ll Functional Calculus for Pseudo differential Operators
Associated with the Metric g 418
D.12 Non stationary Phase Method 421
D.13 FIO s Associated with a Uniform Metric 422
D.14 FIO s Depending on a Parameter 425
D.15 FIO s Associated with the Metric gx 425
References 433
Subject Index 443
|
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| author | Dereziński, Jan 1957- Gérard, Christian |
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| dewey-full | 539.7/58/0151 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 539 - Modern physics |
| dewey-raw | 539.7/58/0151 |
| dewey-search | 539.7/58/0151 |
| dewey-sort | 3539.7 258 3151 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV011196133 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:05:37Z |
| institution | BVB |
| isbn | 3540620664 |
| language | English |
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| physical | XII, 444 S. graph. Darst. |
| publishDate | 1997 |
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| series2 | Texts and monographs in physics |
| spelling | Dereziński, Jan 1957- Verfasser (DE-588)11520816X aut Scattering theory of classical and quantum N-particle systems Jan Dereziński ; Christian Gérard Berlin [u.a.] Springer 1997 XII, 444 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts and monographs in physics Diffusion (Physique nucléaire) Diffusion (Physique) ram Dispersion (Mathématiques) Dispersion (Mathématiques) ram Physique mathématique - Théorie asymptotique Physique mathématique - Théorie asymptotique ram Théorie quantique Théorie quantique ram Mathematische Physik Quantentheorie Mathematical physics Asymptotic theory Quantum theory Scattering (Mathematics) Scattering (Physics) Vielteilchensystem (DE-588)4063491-7 gnd rswk-swf Streutheorie (DE-588)4183697-2 gnd rswk-swf Vielteilchensystem (DE-588)4063491-7 s Streutheorie (DE-588)4183697-2 s DE-604 Gérard, Christian Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007509846&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dereziński, Jan 1957- Gérard, Christian Scattering theory of classical and quantum N-particle systems Diffusion (Physique nucléaire) Diffusion (Physique) ram Dispersion (Mathématiques) Dispersion (Mathématiques) ram Physique mathématique - Théorie asymptotique Physique mathématique - Théorie asymptotique ram Théorie quantique Théorie quantique ram Mathematische Physik Quantentheorie Mathematical physics Asymptotic theory Quantum theory Scattering (Mathematics) Scattering (Physics) Vielteilchensystem (DE-588)4063491-7 gnd Streutheorie (DE-588)4183697-2 gnd |
| subject_GND | (DE-588)4063491-7 (DE-588)4183697-2 |
| title | Scattering theory of classical and quantum N-particle systems |
| title_auth | Scattering theory of classical and quantum N-particle systems |
| title_exact_search | Scattering theory of classical and quantum N-particle systems |
| title_full | Scattering theory of classical and quantum N-particle systems Jan Dereziński ; Christian Gérard |
| title_fullStr | Scattering theory of classical and quantum N-particle systems Jan Dereziński ; Christian Gérard |
| title_full_unstemmed | Scattering theory of classical and quantum N-particle systems Jan Dereziński ; Christian Gérard |
| title_short | Scattering theory of classical and quantum N-particle systems |
| title_sort | scattering theory of classical and quantum n particle systems |
| topic | Diffusion (Physique nucléaire) Diffusion (Physique) ram Dispersion (Mathématiques) Dispersion (Mathématiques) ram Physique mathématique - Théorie asymptotique Physique mathématique - Théorie asymptotique ram Théorie quantique Théorie quantique ram Mathematische Physik Quantentheorie Mathematical physics Asymptotic theory Quantum theory Scattering (Mathematics) Scattering (Physics) Vielteilchensystem (DE-588)4063491-7 gnd Streutheorie (DE-588)4183697-2 gnd |
| topic_facet | Diffusion (Physique nucléaire) Diffusion (Physique) Dispersion (Mathématiques) Physique mathématique - Théorie asymptotique Théorie quantique Mathematische Physik Quantentheorie Mathematical physics Asymptotic theory Quantum theory Scattering (Mathematics) Scattering (Physics) Vielteilchensystem Streutheorie |
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