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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 ...
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.
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 ...
is the derivative of the Green's function along the inward-pointing unit normal vector ^. The integration is performed on the boundary, with measure d s {\displaystyle ds} . The function ν ( s ) {\displaystyle \nu (s)} is given by the unique solution to the Fredholm integral equation of the second kind,
This method is a specific application of Green's functions. [citation needed] The method of images works well when the boundary is a flat surface and the distribution has a geometric center. This allows for simple mirror-like reflection of the distribution to satisfy a variety of boundary conditions.
Diffusion Monte Carlo (DMC) or diffusion quantum Monte Carlo [1] is a quantum Monte Carlo method that uses a Green's function to calculate low-lying energies of a quantum many-body Hamiltonian. Introduction and motivation of the algorithm