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We formulate the dynamical mean field theory directly in the continuum. For a given definition of the local Green's function, we show the existence of a unique functional, whose stationary point gives the physical local Green's function of…
We explore the electrodynamic coupling between a plane wave and an infinite two-dimensional periodic lattice of magneto-electric point scatterers, deriving a semi-analytical theory with consistent treatment of radiation damping,…
We approximate a Euclidean version of a D+1 dimensional manifold with a bifurcate Killing horizon by a product of a two-dimensional Rindler space and a D-1 dimensional manifold M. We obtain approximate formulas for the Green functions. We…
Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's…
In a recent series of scanning probe experiments, it became possible to visualize local electron flow in a two-dimensional electron gas. In this paper, a Green's function technique is presented that enables efficient calculation of the…
We present theory of the carrier-optical interaction in 1D systems based on the non-equilibrium Greens function formalism in the 4x4 k.p model. As a representative parameters we chose the GaAs. Although theory is presented in 4x4 k.p many…
We derive an exact closed-form representation for the Euclidean thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space. This can be interpreted as the real part of a complex analytic function of a…
Radiative corrections to an atom are calculated near a half-space that has arbitrarily-shaped small depositions upon its surface. The method is based on calculation of the classical Green's function of the macroscopic Maxwell equations near…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
A modified Green operator is proposed as an improvement of Fourier-based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary…
We develop a microscopic large-$N$ theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory, which reduces to the well-known random…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
In this work, we present a new result which concerns the derivation of the Green function relative to the time-independent Schrodinger equation in two dimensional space. The system considered in this work is a quantum particle that have an…
The standard solution to time-harmonic electromagnetic scattering problems in homogeneous layered media relies on the use of the electric field dyadic Green's function. However, for small values of the governing angular frequency $\omega$,…
A method is given to obtain the Green's function for the Poisson equation in any arbitrary integer dimension under periodic boundary conditions. We obtain recursion relations which relate the solution in d-dimensional space to that in…
1D lattice summations of the 3D Green's function are needed in many applications such as photonic crystals, antenna arrays, and so on. Such summations are usually divided into two cases, depending on the location of the observer: Out of the…
A periodizing scheme and the method of fundamental solutions are used to solve acoustic wave scattering from doubly-periodic three-dimensional multilayered media. A scattered wave in a unit cell is represented by the sum of the near and…
In this work we introduce the Dual Boson Diagrammatic Monte Carlo technique for strongly interacting electronic systems. This method combines the strength of dynamical mean-filed theory for non-perturbative description of local correlations…
We present a numerically efficient technique to evaluate the Green's function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or `patches', are connected using self energy…
We establish a variational formula for the exponential decay rate of the Green function of Brownian motion evolving in a random stationary and ergodic nonnegative potential. Such a variational formula is established by Schroeder in 'Green's…