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Quantum Statistical Field TheoryAn Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity$
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Norman J. Morgenstern Horing

Print publication date: 2017

Print ISBN-13: 9780198791942

Published to Oxford Scholarship Online: January 2018

DOI: 10.1093/oso/9780198791942.001.0001

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Random Phase Approximation Plasma Phenomenology, Semiclassical and Hydrodynamic Models; Electrodynamics

Random Phase Approximation Plasma Phenomenology, Semiclassical and Hydrodynamic Models; Electrodynamics

(p.238) 10 Random Phase Approximation Plasma Phenomenology, Semiclassical and Hydrodynamic Models; Electrodynamics
Quantum Statistical Field Theory

Norman J. Morgenstern Horing

Oxford University Press

Chapter 10 reviews both homogeneous and inhomogeneous quantum plasma dielectric response phenomenology starting with the RPA polarizability ring diagram in terms of thermal Green’s functions, also energy eigenfunctions. The homogeneous dynamic, non-local inverse dielectric screening functions (K) are exhibited for 3D, 2D, and 1D, encompassing the non-local plasmon spectra and static shielding (e.g. Friedel oscillations and Debye-Thomas-Fermi shielding). The role of a quantizing magnetic field in K is reviewed. Analytically simpler models are described: the semiclassical and classical limits and the hydrodynamic model, including surface plasmons. Exchange and correlation energies are discussed. The van der Waals interaction of two neutral polarizable systems (e.g. physisorption) is described by their individual two-particle Green’s functions: It devolves upon the role of the dynamic, non-local plasma image potential due to screening. The inverse dielectric screening function K also plays a central role in energy loss spectroscopy. Chapter 10 introduces electromagnetic dyadic Green’s functions and the inverse dielectric tensor; also the RPA dynamic, non-local conductivity tensor with application to a planar quantum well. Kramers–Krönig relations are discussed. Determination of electromagnetic response of a compound nanostructure system having several nanostructured parts is discussed, with applications to a quantum well in bulk plasma and also to a superlattice, resulting in coupled plasmon spectra and polaritons.

Keywords:   random phase approximation/RPA, thermodynamic/thermal Green’s functions, Debye–Thomas–Fermi shielding, Friedel oscillations, RPA ring diagram, surface plasmons, quantum plasma dielectric response, dielectric screening, quantizing magnetic field, hydrodynamic model, exchange and correlation energies, van der Waals interaction, electromagnetic dyadic Green’s functions, inverse dielectric and conductivity tensors, non-local, quantum well, Kramers–Krönig relations, nanostructure, superlattice, polaritons

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