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Green's functions and retarded potentials

Mauro Fabrizio and Morro Angelo

in Electromagnetism of Continuous Media: Mathematical Modelling and Applications

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198527008
eISBN:
9780191713316
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527008.003.0002
Subject:
Mathematics, Applied Mathematics

This chapter gives a concise and self-contained presentation of the use of Green’s functions to solve linear problems with a given point source. Specific functions are determined for the harmonic ... More


Scattering by a Buried Object

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0012
Subject:
Mathematics, Numerical Analysis

This chapter presents a model problem for scattering by a buried object. The ground is modeled by a two-layered medium (the air and the earth) with a planar interface. For the two-layered medium, it ... More


DYNAMICS OF IMPERFECT LATTICES

A.M. Stoneham

in Theory of Defects in Solids: Electronic Structure of Defects in Insulators and Semiconductors

Published in print:
2001
Published Online:
September 2007
ISBN:
9780198507802
eISBN:
9780191709920
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507802.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

Defects and impurities affect the vibrations of a solid, and hence properties such as infra-red spectra and thermal conductivity. There can be new, high-frequency, local modes; there can be new, ... More


Green’s functions and the dynamical action principle

JAGDISH MEHRA and KIMBALL A. MILTON

in Climbing the Mountain: The Scientific Biography of Julian Schwinger

Published in print:
2003
Published Online:
February 2010
ISBN:
9780198527459
eISBN:
9780191709593
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527459.003.0009
Subject:
Physics, History of Physics

In a remarkable lecture Julian Schwinger delivered at the University of Nottingham on July 14, 1993, on the occasion of his receiving an honorary degree, entitled ‘The Greening of quantum field ... More


Causality and Green’s functions

Sandip Tiwari

in Semiconductor Physics: Principles, Theory and Nanoscale

Published in print:
2020
Published Online:
November 2020
ISBN:
9780198759867
eISBN:
9780191820830
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198759867.003.0013
Subject:
Physics, Condensed Matter Physics / Materials

The chapter elucidates causality to prevent its erroneous use. It then develops Green’s functions to analyze and predict systems under stimulation in the presence of cause and chance. Causality is ... More


The Green’s function in linear elasticity

Adrian P. Sutton

in Physics of Elasticity and Crystal Defects

Published in print:
2020
Published Online:
August 2020
ISBN:
9780198860785
eISBN:
9780191893001
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198860785.003.0004
Subject:
Physics, Condensed Matter Physics / Materials, Crystallography: Physics

The elastostatic Green’s tensor function is the solution of a differential equation for the displacement field created by a unit point force in an infinite continuum. Its symmetry is derived using ... More


Retarded Green’s Functions

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 5 introduces single-particle retarded Green’s functions, which provide the probability amplitude that a particle created at (x, t) is later annihilated at (x′,t′). Partial Green’s functions, ... More


Tunneling Matrix Elements

C. Julian Chen

in Introduction to Scanning Tunneling Microscopy: Second Edition

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199211500
eISBN:
9780191705991
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199211500.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents systematic methods to evaluate the tunneling matrix elements in the Bardeen tunneling theory. A key problem in applying the Bardeen tunneling theory to STM is the evaluation of ... More


Electric Fields and Currents in Biological Tissue

Paul L. Nunez and Ramesh Srinivasan

in Electric Fields of the Brain: The neurophysics of EEG

Published in print:
2006
Published Online:
May 2009
ISBN:
9780195050387
eISBN:
9780199865673
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195050387.003.0004
Subject:
Neuroscience, Neuroendocrine and Autonomic, Techniques

This chapter continues the physical principles of Chapter 3 in the context of biological tissue. Electrophysiology spans about five orders of magnitude of spatial scale, ranging from the ... More


Interacting Electron–Hole–Phonon System

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 11 employs variational differential techniques and the Schwinger Action Principle to derive coupled-field Green’s function equations for a multi-component system, modeled as an interacting ... More


Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator ... More


TDDFT and many-body theory

Carsten A. Ullrich

in Time-Dependent Density-Functional Theory: Concepts and Applications

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199563029
eISBN:
9780191775130
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199563029.003.0013
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents various techniques from many-body theory to construct time-dependent exchange-correlation (xc) functionals. The first section introduces a perturbation theory along the ... More


Thermodynamic Green’s Functions and Spectral Structure

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the ... More


Electrostatics of semiconductor nanostructures

Thomas Ihn

in Semiconductor Nanostructures: Quantum states and electronic transport

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199534425
eISBN:
9780191715297
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534425.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

Semiconductor nanostructures consist of materials with dielectric properties. Doping introduces charge distributions, and metallic surface gates establish boundary conditions for electrostatic ... More


Approximate and Numerical Approaches

M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko

in Advances in the Casimir Effect

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199238743
eISBN:
9780191716461
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199238743.003.0006
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter considers several approximate methods developed to calculate the Casimir energy and force for nontrivial geometries, where the separation of variables is not possible. One of these ... More


Propagators and Green’s functions

Tom Lancaster and Stephen J. Blundell

in Quantum Field Theory for the Gifted Amateur

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199699322
eISBN:
9780191779435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199699322.003.0017
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces Green’s functions and shows how they are related to a propagator, the amplitude that a particle in some spacetime position will be later found at another spacetime position.


Poisson Kernels and Green’s Representation Formula

Ali Taheri

in Function Spaces and Partial Differential Equations: Volume 1 - Classical Analysis

Published in print:
2015
Published Online:
September 2015
ISBN:
9780198733133
eISBN:
9780191797712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198733133.003.0002
Subject:
Mathematics, Analysis

This chapter establishes Green’s representation formula and using it to arrive at Greens functions and Poisson kernels. Presenting explicit examples of Greens functions and Poisson kernels in ... More


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

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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 ... More


MICROSCOPIC DERIVATION OF THE TDGL EQUATION

Anatoly Larkin and Andrei Varlamov

in Theory of Fluctuations in Superconductors

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528159
eISBN:
9780191713521
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528159.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents the basic aspects of the microscopic description of fluctuation phenomena in superconductors. The notion of fluctuation propagator as the vertex part of the electron: electron ... More


MATERIAL DEFORMATION

Nasr M. Ghoniem and Daniel D. Walgraef

in Instabilities and Self-Organization in Materials: Volume I: Fundamentals of Nanoscience, Volume II: Applications in Materials Design and Nanotechnology

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199298686
eISBN:
9780191720222
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199298686.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the main elements of continuum theory, which will be utilized further in later sections dealing with a variety of applications. First, a basic review of vector and tensor ... More


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