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The general study of Green's function written in the above form, and its relationship to the function spaces formed by the eigenvectors, is known as Fredholm theory. There are several other methods for finding Green's functions, including the method of images, separation of variables, and Laplace transforms. [1]
In many-body theory, the term Green's function (or Green function) is sometimes used interchangeably with correlation function, but refers specifically to correlators of field operators or creation and annihilation operators. The name comes from the Green's functions used to solve inhomogeneous differential equations, to which they are loosely ...
Green's functions can be expanded in terms of the basis elements (harmonic functions) which are determined using the separable coordinate systems for the linear partial differential equation. There are many expansions in terms of special functions for the Green's function. In the case of a boundary put at infinity with the boundary condition ...
As a result, it is used in calculation of Green's functions for method of moments for such geometries. [5] Other uses include the descriptions of dipolar emissions near surfaces in nanophotonics, [6] [7] [8] holographic inverse scattering problems, [9] Green's functions in quantum electrodynamics [10] and acoustic or seismic waves. [11]
The GW approximation (GWA) is an approximation made in order to calculate the self-energy of a many-body system of electrons. [1] [2] [3] The approximation is that the expansion of the self-energy Σ in terms of the single particle Green's function G and the screened Coulomb interaction W (in units of =)
The new method, called CGFMD (Causal Green's Function Molecular Dynamics) is the temporal equivalent of the MSGF and is based upon the use of causal or retarded Green's functions. It has been applied [ 25 ] to simulate the propagation of ripples in graphene, [ 9 ] where it has been shown that the CGFMD can model time scales over 6 to 9 orders ...
The coherent potential approximation (CPA) is a method, in theoretical physics, of finding the averaged Green's function of an inhomogeneous (or disordered) system. The Green's function obtained via the CPA then describes an effective medium whose scattering properties represent the averaged scattering properties of the disordered system being approximated.
In many-body physics, the problem of analytic continuation is that of numerically extracting the spectral density of a Green function given its values on the imaginary axis. It is a necessary post-processing step for calculating dynamical properties of physical systems from Quantum Monte Carlo simulations, which often compute Green function ...