Related papers: Half-plane Green`s function for anti-plane elastic…
The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…
Quasiparticle interference imaging (QPI) provides a route to characterize electronic structure from real space images acquired using scanning tunneling microscopy. It emerges due to scattering of electrons at defects in the material. The…
The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction is studied. Analytic expressions for the fermion Green's function,…
We write the Green function of the $d$-dimensional hypercubic lattice in a piecewise form covering the entire real frequency axis. Each piece is a single integral involving modified Bessel functions of the first and second kinds. The…
A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction…
We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on $\mathbb{Z}^d$ with certain slowly decaying long-range hopping and analytic cosine type potentials. As applications, we prove the…
A numerical explicit method to evaluates transient solutions of linear partial differential inhomogeneous equation with constant coefficients is proposed. A general form of the scheme for a specific linear inhomogeneous equation is shown.…
The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and…
We develop Green's function formalism to describe continuous multi-layered quasi-one-dimensional setups described by piece-wise constant single-particle Hamiltonians. The Hamiltonians of the individual layers are assumed to be quadratic…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
We present an efficient implementation of a surface Green's-function method for atomistic modeling of surfaces within the framework of density functional theory using a pseudopotential localized basis set approach. In this method, the…
We formulate a semiclassical theory for electron transport in open quantum systems with electron-phonon interactions adequate for situations when the system's phonon dynamics is comparable with the electron transport timescale. Starting…
Proceeding from the simplest field theoretical model of 2D metal, the normal phase Green functions of the weakly interacting fermions and the order parameter fluctuations (responsible for the attraction between fermions) are obtained. It is…
The problem of the strain of smectics subjected to a force distributed over a line in the basal plane has been solved.
Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of…
A relativistic Green function approach to the inclusive quasielastic (e,e') scattering is presented. The single particle Green function is expanded in terms of the eigenfunctions of the nonhermitian optical potential. This allows one to…
We derive an exact Green's function of the diffusion equation for a pair of spherical interacting particles in 2D subject to a back-reaction boundary condition.
The two-dimensional elastodynamic Green tensor is the primary building block of solutions of linear elasticity problems dealing with nonuniformly moving rectilinear line sources, such as dislocations. Elastodynamic solutions for these…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for the moment generating function of…