Physics and mathematical tools: methods and examples
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| Main Authors: | , , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore ; Hackensack, NJ ; London
World Scientific
[2016]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seite 335-338, Index Seite 339-342 |
| Physical Description: | xiv, 342 Seiten Illustrationen, Diagramme |
| ISBN: | 9789814713238 9814713236 9789814713245 9814713244 |
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MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
R
Foreword v
Introduction xiii
1. Linear response and analyticity 1
1.1 General properties................................................. 2
1.1.1 Problem statement ...................................... . 2
1.1.2 Definition of the susceptibility........................... 6
1.1.3 Analyticity of the susceptibility ......................... 7
1.1.4 Parity properties and dissipation ......................... 9
1.1.5 Low and high frequency behaviours........................ 10
1.1.6 Kramers-Kronig relations.................................. 12
1.1.7 Sum rules ................................................ 16
1.1.8 Inhomogeneous perturbations .............................. 17
1.2 Applications and examples......................................... 18
1.2.1 Admittance of a RLC circuit............................... 18
1.2.2 Absorption and dispersion in a dielectric ................ 23
1.2.3 Oscillating flow in a capillary .......................... 27
1.2.4 Response of a plasma within Vlasov approximation .... 34
1.2.5 Conductivity and Kubo formula............................. 41
1.3 Exercises ........................................................ 47
2. Static Green’s functions 53
2.1 General properties................................................ 54
2.1.1 Definition and properties of Green’s function............. 54
2.1.2 Operatorial point of view................................. 58
2.1.3 Laplace operator.......................................... 61
2.1.4 Helmholtz operator........................................ 72
2.1.5 Laplace and Helmholtz operators in low dimensions .... 76
2.1.6 Inhomogeneous operators .................................. 85
2.2 Applications and examples....................................... . 90
vii
viii Physics and Mathematical Tools - Methods and Examples
2.2.1 Origin of the method of image charges....................... 90
2.2.2 Ball with uniform motion in a fluid......................... 93
2.2.3 Density of states of a quantum particle..................... 99
2.2.4 Scattering by a repulsive potential.........................103
2.2.5 Simple model for the wind blowing on a wall.................106
2.3 Exercises...........................................................Ill
3. Dynamical Green’s functions 125
3.1 General properties................................................ 126
3.1.1 Green’s functions and causality.............................126
3.1.2 Separable operators.........................................130
3.1.3 Diffusion equation..........................................136
3.1.4 Schrodinger equation........................................145
3.1.5 Bloch equation..............................................155
3.1.6 Wave equation...............................................158
3.2 Applications and examples...........................................174
3.2.1 Diffusion on a segment......................................174
3.2.2 Fraunhofer diffraction .....................................177
3.2.3 Emission of sound waves.....................................183
3.2.4 Wavefront in supersonic regime .............................188
3.2.5 On the instantaneity of heat propagation....................193
3.2.6 Polarisability of the hydrogen atom.........................199
3.3 Exercises...........................................................206
4. Saddle-point method 213
4.1 General properties..................................................214
4.1.1 Simple integral ............................................214
4.1.2 Integral on a path in the complex plane.....................221
4.1.3 Case of multiple integral ..................................228
4.2 Applications and examples...........................................233
4.2.1 Stirling’s formula and indistinguishability ................233
4.2.2 Equivalence of canonical and micro canonical ensembles . . 236
4.2.3 Harmonic crystal at low temperature.........................240
4.2.4 Ising model............................................... 244
4.2.5 Semi-classical approximation................................251
4.3 Exercises ..........................................................256
Appendix A Functions of a complex variable 263
Appendix B Laplace transform 267
Appendix C One-variable differential operators 271
ix
275
279
285
287
291
293
297
331
335
339
Contents
Hilbert spaces and Dirac notation
Gaussian integrals
Overview of coordinate transformations
Spherical harmonics
Functional derivative
Usual Green’s functions
Solutions of exercises
References
|
| any_adam_object | 1 |
| author | Alastuey, Angel Clusel, Maxime Magro, Marc 1970- Pujol, Pierre 1968- |
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| author_role | aut aut aut aut |
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| building | Verbundindex |
| bvnumber | BV043482159 |
| classification_rvk | SK 950 |
| classification_tum | PHY 011f |
| ctrlnum | (OCoLC)951677152 (DE-599)BVBBV043482159 |
| dewey-full | 530.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15 |
| dewey-search | 530.15 |
| dewey-sort | 3530.15 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV043482159 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:26:54Z |
| institution | BVB |
| isbn | 9789814713238 9814713236 9789814713245 9814713244 |
| language | English |
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| spelling | Alastuey, Angel Verfasser (DE-588)110196684X aut Physique et outils mathématiques (méthodes et exemples, 2009) Physics and mathematical tools methods and examples Angel Alastuey, CNRS, France & ENS de Lyon, France; Maxime Clusel; CNRS, France & Université de Montpellier, France; Marc Magro, ENS de Lyon, France; Pierre Pujol, Université Paul Sabatier, France Singapore ; Hackensack, NJ ; London World Scientific [2016] © 2016 xiv, 342 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis Seite 335-338, Index Seite 339-342 Mathematical physics Mathematical instruments Mathematical instruments fast Mathematical physics fast Mathematische Physik Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s DE-604 Clusel, Maxime Verfasser (DE-588)1101967196 aut Magro, Marc 1970- Verfasser (DE-588)1101967420 aut Pujol, Pierre 1968- Verfasser (DE-588)1101967706 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028898895&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alastuey, Angel Clusel, Maxime Magro, Marc 1970- Pujol, Pierre 1968- Physics and mathematical tools methods and examples Mathematical physics Mathematical instruments Mathematical instruments fast Mathematical physics fast Mathematische Physik Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4037952-8 |
| title | Physics and mathematical tools methods and examples |
| title_alt | Physique et outils mathématiques (méthodes et exemples, 2009) |
| title_auth | Physics and mathematical tools methods and examples |
| title_exact_search | Physics and mathematical tools methods and examples |
| title_full | Physics and mathematical tools methods and examples Angel Alastuey, CNRS, France & ENS de Lyon, France; Maxime Clusel; CNRS, France & Université de Montpellier, France; Marc Magro, ENS de Lyon, France; Pierre Pujol, Université Paul Sabatier, France |
| title_fullStr | Physics and mathematical tools methods and examples Angel Alastuey, CNRS, France & ENS de Lyon, France; Maxime Clusel; CNRS, France & Université de Montpellier, France; Marc Magro, ENS de Lyon, France; Pierre Pujol, Université Paul Sabatier, France |
| title_full_unstemmed | Physics and mathematical tools methods and examples Angel Alastuey, CNRS, France & ENS de Lyon, France; Maxime Clusel; CNRS, France & Université de Montpellier, France; Marc Magro, ENS de Lyon, France; Pierre Pujol, Université Paul Sabatier, France |
| title_short | Physics and mathematical tools |
| title_sort | physics and mathematical tools methods and examples |
| title_sub | methods and examples |
| topic | Mathematical physics Mathematical instruments Mathematical instruments fast Mathematical physics fast Mathematische Physik Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematical physics Mathematical instruments Mathematische Physik |
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