## 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*

- 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*

- 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