Die vorliegende Arbeit befasst sich mit der Anwendung des kürzlich entwickelten 'Functional Approach' zur Elektrodynamik in Medien auf das Modell des freien homogenen Elektronengases. Basierend auf einer ausschließlich mikroskopischen Feldtheorie wird gezeigt, dass mittels universell gültiger Relationen zwischen Antwortfunktionen sowohl alle relevanten optischen als auch magnetischen (linearen) Materialeigenschaften allein aus der Strom-Strom-Korrelation gewonnen werden können. Dabei ist es essentiell, alle Berechnungen auf dem vollen Stromdichteoperator aufzubauen, also auf der Summe aus diamagnetischem, orbitalem und spinoriellem Anteil. Weiterhin wird anhand der magnetischen Suszeptibilität demonstriert, dass im Allgemeinen die Unterscheidung zwischen eigenen und direkten Antwortfunktionen nicht zu vernachlässigen ist. Schließlich wird mit dem „Lindhard-Integral-Theorem“ bewiesen, dass nicht nur der longitudinale, sondern auch der transversale Anteil des vollen frequenz- und wellenvektorabhängigen fundamentalen Antworttensors des freien Elektronengases komplett durch das charakteristische Lindhard-Integral bestimmt ist.:Introduction
I Microscopic electrodynamics in media
1 Classical electrodynamics
1.1 Covariant formulation
1.2 Temporal gauge
1.3 Free Green function
1.4 Total functional derivatives
2 Electrodynamics in media
2.1 Field identifications
2.2 Fundamental response tensor
2.3 Universal response relations
2.4 Direct and proper response
2.5 Isotropic and combined limits
2.6 Full Green function
2.7 Wave equations in media and dispersion relations
II Application to the free electron gas
3 Fundamental response tensor
3.1 Electromagnetic current density
3.2 Kubo-Greenwood formulae
3.3 Diamagnetic, orbital and spinorial contribution
3.4 Spin susceptibility vs. spinorial current response
4 London model and diamagnetic response
4.1 Interpretation as response function
4.2 Application of universal response relations
4.3 Spin correction
5 Full current response
5.1 Dimensionless formulae
5.2 Lindhard integral theorem
5.3 Laurent expansions
5.4 Optical properties
5.5 Magnetic properties
Conclusion
Appendix A - Notation
Appendix B - Formulary
B.1 Basic analysis and vector calculus
B.2 Special relativity theory
B.3 Fourier transformation
B.4 Functional derivatives
B.5 Projectors and Helmholtz' theorem
B.6 Complex analysis
Appendix C - Yang-Mills gauge theory
C.1 Field strength tensor
C.2 Minimal coupling principle
C.3 Gauge invariant quantities and equations
Appendix D - Periodic solids
D.1 Partitioning of reciprocal space
D.2 Homogeneous limit
Appendix E - Electromagnetic spectrum
Bibliography
Acknowledgements
Errata / This thesis is concerned with the application of the recently developed 'Functional Approach' to electrodynamics of media to the model of the free homogeneous electron gas. Based on an exclusively microscopic field theory it is shown that with the help of universally valid relations between response functions, all relevant optical and magnetic (linear) materials properties can be extracted from the mere current-current response. For this purpose, it is essential to base all calculations on the full current density operator, i.e. the sum of diamagnetic, orbital and spinorial contributions. Furthermore, we use the example of the magnetic susceptibility to demonstrate that the distinction between proper and direct response functions is in general crucial. Lastly, with the “Lindhard integral theorem” we prove that not only the longitudinal but also the transverse part of the full frequency- and wavevector-dependent fundamental response tensor of the free electron gas is completely determined by the characteristic Lindhard integral.:Introduction
I Microscopic electrodynamics in media
1 Classical electrodynamics
1.1 Covariant formulation
1.2 Temporal gauge
1.3 Free Green function
1.4 Total functional derivatives
2 Electrodynamics in media
2.1 Field identifications
2.2 Fundamental response tensor
2.3 Universal response relations
2.4 Direct and proper response
2.5 Isotropic and combined limits
2.6 Full Green function
2.7 Wave equations in media and dispersion relations
II Application to the free electron gas
3 Fundamental response tensor
3.1 Electromagnetic current density
3.2 Kubo-Greenwood formulae
3.3 Diamagnetic, orbital and spinorial contribution
3.4 Spin susceptibility vs. spinorial current response
4 London model and diamagnetic response
4.1 Interpretation as response function
4.2 Application of universal response relations
4.3 Spin correction
5 Full current response
5.1 Dimensionless formulae
5.2 Lindhard integral theorem
5.3 Laurent expansions
5.4 Optical properties
5.5 Magnetic properties
Conclusion
Appendix A - Notation
Appendix B - Formulary
B.1 Basic analysis and vector calculus
B.2 Special relativity theory
B.3 Fourier transformation
B.4 Functional derivatives
B.5 Projectors and Helmholtz' theorem
B.6 Complex analysis
Appendix C - Yang-Mills gauge theory
C.1 Field strength tensor
C.2 Minimal coupling principle
C.3 Gauge invariant quantities and equations
Appendix D - Periodic solids
D.1 Partitioning of reciprocal space
D.2 Homogeneous limit
Appendix E - Electromagnetic spectrum
Bibliography
Acknowledgements
Errata
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:74721 |
| Date | 04 May 2021 |
| Creators | Wirnata, René |
| Contributors | Kortus, Jens, Cocchi, Caterina, TU Bergakademie Freiberg |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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