Collective classical and quantum fields in plasmas, superconductors, superfluid 3He, and liquid crystals:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
[2018]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xvii, 404 Seiten Diagramme |
| ISBN: | 9789813223936 9789813223943 |
Internformat
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| 245 | 1 | 0 | |a Collective classical and quantum fields in plasmas, superconductors, superfluid 3He, and liquid crystals |c Hagen Kleinert |
| 264 | 1 | |a New Jersey |b World Scientific |c [2018] | |
| 300 | |a xvii, 404 Seiten |b Diagramme | ||
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Datensatz im Suchindex
| _version_ | 1804177779060637696 |
|---|---|
| adam_text | Contents
Preface vii
1 Functional Integral Techniques 1
1.1 Nonrelativist ic Fields............................................ 2
1.1.1 Quantization of Free Fields................................ 2
1.1.2 Fluctuating Free Fields ................................... 4
1.1.3 Interactions............................................... 8
1.1.4 Normal Products........................................... 10
1.1.5 Functional Formulation.................................... 14
1.1.6 Equivalence of Functional and Operator Methods.............15
1.1.7 Grand-Canonical Ensembles at Zero Temperature..............16
1.2 Relativistic Fields................................................22
1.2.1 Lorentz and Poincare Invariance ...........................22
1.2.2 Relativistic Free Scalar Fields............................27
1.2.3 Electromagnetic Fields.....................................31
1.2.4 Relativistic Free Fermi Fields.............................34
1.2.5 Perturbation Theory of Relativistic Fields.................37
Notes and References.....................................................39
2 Plasma Oscillations 41
2.1 General Formalism..................................................41
2.2 Physical Consequences .............................................45
2.2.1 Zero Temperature...........................................46
2.2.2 Short-Range Potential......................................47
Appendix 2A Fluctuations around the Plasmon............................48
Notes and References.....................................................49
3 Superconductors 50
3.1 General Formulation................................................52
3.2 Local Interaction and Ginzburg-Landau Equations.............59
3.2.1 Inclusion of Electromagnetic Fields into the Pair Field Theory 69
3.3 Far below the Critical Temperature.................................72
3.3.1 The Gap ...................................................73
3.3.2 The Free Pair Field .......................................77
3.4 From BCS to Strong-Coupling Superconductivity......................91
3.5 Strong-Coupling Calculation of the Pair Field...............92
IX
X
3.6 Prom BCS Superconductivity near Te to the onset of pseudogap
behavior.....................................* * * ***
3.7 Phase Fluctuations in Two Dimensions and Kosterlitz-Tliouloss
Transition.......................................................
3.8 Phase Fluctuations in Three Dimensions .........................
3.9 Collective Classical Fields.....................................
3.9.1 Superconducting Electrons .................................
3.10 Strong-Coupling Limit of Pair Formation.........................
3.11 Composite Bosons................................................
3.12 Composite Fermions..............................................
3.13 Conclusion and Remarks..........................................
Appendix 3A Auxiliary Strong-Coupling Calculations....................
Appendix 3B Propagator of the Bilocal Pair Field........................133
Appendix 3C Fluctuations Around the Composite Field ....................133
Notes and References....................................................1 38
4 Superfluid 3He
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
Interatomic Potential...........
Phase Diagram...................
Preparation of Functional Integral
145
I
17
19
19
19
10
4.3.1 Action of the System.....................................1
4.3.2 Dipole Interaction.......................................I
4.3.3 Euclidean Action.........................................I
4.3.4 From Particles to Quasiparticles ........................1
4.3.5 Approximate Quasiparticle Action.........................I
4.3.6 Effective Interaction....................................1
4.3.7 Pairing Interaction.......................................158
Transformation from Fundamental to Collective Fields.............159
General Properties of a Collective Action........................164
Comparison with 0(3)-Symmetric Linear a-Model....................169
Hydrodynamic Properties Close to T,..............................170
Bending the Superfluid 3He-A .....................................178
4.8.1 Monopoles ...............................................j 79
4.8.2 Line Singularities........................................182
4.8.3 Soli tons................................................
4.8.4 Localized Lumps...........................................1^7
4.8.5 Use of Topology in the A-Phase...........................| ^8
4.8.6 Topology in the B-Phase..................................1 )0
Hydrodynamic Properties at All Temperatures T Tf...............193
4.9.1 Derivation of Gap Equation...............................10 1
4.9.2 Ground State Properties.................................. 100
4.9.3 Bending Energies......................................... 208
4.9.4 Fermi-Liquid Corrections................................. 218
Large Currents and Magnetic Fields in the Ginzburg-Landau Regime 227
XI
4.10.1 B-Phase...................................................228
4.10.2 A-Phase...................................................239
4.10.3 Critical Current in Other Phases for T ~ Tc........240
4.11 Is 3He-A a Superfluid?............................................248
4.11.1 Magnetic Field and Transition between A- and B-Phases . . 272
4.12 Large Currents at Any Temperature T TC...........................274
4.12.1 Energy at Nonzero Velocities..............................274
4.12.2 Gap Equations.............................................275
4.12.3 Superfluid Densities and Currents.........................283
4.12.4 Critical Currents.........................................285
4.12.5 Ground State Energy at Large Velocities...................289
4.12.6 Fermi Liquid Corrections .................................289
4.13 Collective Modes in the Presence of Current at all Temperatures
T Tc............................................................292
4.13.1 Quadratic Fluctuations ...................................292
4.13.2 Time-Dependent Fluctuations at Infinite Wavelength .... 295
4.13.3 Normal Modes..............................................298
4.13.4 Simple Limiting Results at Zero Gap Deformation ..........301
4.13.5 Static Stability..........................................303
4.14 Fluctuation Coefficients..........................................304
4.15 Stability of Superflow in the B-Phase under Small Fluctuations for
T ~TC.............................................................307
Appendix 4A Hydrodynamic Coefficients for T ^ Tc......................312
Appendix 4B Hydrodynamic Coefficients for All T Tc .........315
Appendix 4C Generalized Ginzburg-Landau Energy........................319
Notes and References....................................................319
5 Liquid Crystals 323
5.1 Maier-Saupe Model and Generalizations.............................324
5.1.1 General Properties........................................324
5.1.2 Landau Expansion..........................................326
5.1.3 Tensor Form of Landau-de Gennes Expansion.................327
5.2 Landau-de Gennes Description of Nematic Phase.....................328
5.3 Bending Energy....................................................336
5.4 Light Scattering..................................................338
5.5 Interfacia] Tension between Nematic and Isotropic Phases..........347
5.6 Cholesteric Liquid Crystals.......................................351
5.6.1 Small Fluctuations above T ...............................354
5.6.2 Some Experimental Facts...................................355
5.6.3 Mean-Field Description of Cholesteric Phase...............357
5.7 Other Phases......................................................362
Appendix 5A Biaxial Maier-Saupe Model...................................365
Notes and References....................................................368
Xll
6 Exactly Solvable Field-Theoretic Models 371
6.1 Pet Model in Zero Plus One Time Dimensions....................371
6.1.1 The Generalized BCS Model in a Degenerate Shell.......379
6.1.2 The Hilbert Space of the Generalized BOS Model........390
6.2 Thirring Model in 1+1 Dimensions...............................393
6.3 Supersymmetry in Nuclear Physics...............................397
Notes and References................................................397
Index 399
Collective Classical and Quantum Fields
in Plasmas, Superconductors, Superfluid 3He, and Liquid Crystals
This is an introductory book dealing with collective phenomena in many-body systems. A gas
of bosons or fermions can show oscillations of various types of density. These are described by
different combinations of field variables. Especially delicate is the competition of these variables.
In superfluid He, for example, the atoms can be attracted to each other by molecular forces,
whereas they are repelled from each other at short distance due to a hardcore repulsion. The
attraction gives rise to Cooper pairs, and the repulsion is overcome by paramagnon oscillations.
The combination is what finally led to the discovery of superfluidity in He. In general, the
competition between various channels can most efficiently be studied by means of a classical
version of the Hubbard-Stratonovich transformation.
A gas of electrons is controlled by the interplay of plasma oscillations and pair formation.
In a system of rod- or disc-like molecules, liquid crystals are observed with directional
orientations that behave with unusual five-fold or seven-fold symmetry patterns. The existence
of such a symmetry was postulated in 1975 by the author and K. Maki. An aluminium material
of this type was later manufactured by Dan Shechtman which won him the 2014 Nobel prize.
The last chapter presents some solvable models, of which one of them was the first to illustrate
the existence of broken supersymmetry in nuclei.
|
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| id | DE-604.BV044457781 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:53:30Z |
| institution | BVB |
| isbn | 9789813223936 9789813223943 |
| language | English |
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| physical | xvii, 404 Seiten Diagramme |
| publishDate | 2018 |
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| publisher | World Scientific |
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| spelling | Kleinert, Hagen 1941- Verfasser (DE-588)113534426 aut Collective classical and quantum fields in plasmas, superconductors, superfluid 3He, and liquid crystals Hagen Kleinert New Jersey World Scientific [2018] xvii, 404 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Feldtheorie (DE-588)4016698-3 gnd rswk-swf Kollektive Anregung (DE-588)4263280-8 gnd rswk-swf Funktionalintegral (DE-588)4155673-2 gnd rswk-swf Kollektive Anregung (DE-588)4263280-8 s Feldtheorie (DE-588)4016698-3 s Funktionalintegral (DE-588)4155673-2 s DE-604 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=029858548&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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=029858548&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kleinert, Hagen 1941- Collective classical and quantum fields in plasmas, superconductors, superfluid 3He, and liquid crystals Feldtheorie (DE-588)4016698-3 gnd Kollektive Anregung (DE-588)4263280-8 gnd Funktionalintegral (DE-588)4155673-2 gnd |
| subject_GND | (DE-588)4016698-3 (DE-588)4263280-8 (DE-588)4155673-2 |
| title | Collective classical and quantum fields in plasmas, superconductors, superfluid 3He, and liquid crystals |
| title_auth | Collective classical and quantum fields in plasmas, superconductors, superfluid 3He, and liquid crystals |
| title_exact_search | Collective classical and quantum fields in plasmas, superconductors, superfluid 3He, and liquid crystals |
| title_full | Collective classical and quantum fields in plasmas, superconductors, superfluid 3He, and liquid crystals Hagen Kleinert |
| title_fullStr | Collective classical and quantum fields in plasmas, superconductors, superfluid 3He, and liquid crystals Hagen Kleinert |
| title_full_unstemmed | Collective classical and quantum fields in plasmas, superconductors, superfluid 3He, and liquid crystals Hagen Kleinert |
| title_short | Collective classical and quantum fields in plasmas, superconductors, superfluid 3He, and liquid crystals |
| title_sort | collective classical and quantum fields in plasmas superconductors superfluid 3he and liquid crystals |
| topic | Feldtheorie (DE-588)4016698-3 gnd Kollektive Anregung (DE-588)4263280-8 gnd Funktionalintegral (DE-588)4155673-2 gnd |
| topic_facet | Feldtheorie Kollektive Anregung Funktionalintegral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029858548&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029858548&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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