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Information compression plays a central role in diverse fields of modern science and technology, from communication theory to machine learning. In condensed-matter physics, the intermediate representation (IR) basis has recently been…
Transport in molecular electronic devices is different from that in semiconductor mesoscopic devices in two important aspects: (1) the effect of the electronic structure and (2) the effect of the interface to the external contact. A…
We consider the expansion of wave packets governed by the free Schr\"odinger equation. This seemingly simple task plays an important role in simulations of various quantum experiments and in particular in the field of matter-wave…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
In this work we present a numerical method to solve the set of Dyson-like equations arising the context of non-equilibrium Green's functions. The technique is based on the self-consistent solution of the Dyson equations for the interacting…
We derive formulas for the matrix elements of the lattice Green function for the discrete Poisson equation on an infinite square lattice. The partial difference equation for the matrix elements is solved by reducing it to a series of first…
The electromagnetic Green's function is expressed from the inverse Helmholtz operator, where a second frequency has been introduced as a new degree of freedom. The first frequency results from the frequency decomposition of the…
The in-in formalism and its influence functional generalization are widely used to describe the out-of-equilibrium dynamics of unitary and open quantum systems, respectively. In this paper, we build on these techniques to develop an…
Green's function theory has emerged as a powerful many-body approach not only in condensed matter physics but also in quantum chemistry in recent years. We have developed a new all-electron implementation of the BSE@GW formalism using…
We develop a theoretical framework to determine distribution functions in nonequilibrium systems coupled to equilibrium reservoirs, by using the nonequilibrium Green's function technique. As a paradigmatic example, we consider the…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
The self-energy method for quantum impurity models expresses the correlation part of the self-energy in terms of the ratio of two Green's functions and allows for a more accurate calculation of equilibrium spectral functions than is…
A general formula for the orbital magnetic moment of interacting electrons in solids is derived using the many-electron Green function method. The formula factorizes into two parts, a part that contains the information about the…
Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and…
Time-dependent nonequilibrium Green's functions (TDNEGF) are shown to provide a flexible, effective tool for the description of quantum mechanical single particle scattering on a spatially localized, time-dependent potential. Focusing on…
The essential quantum many-body physics of an ultracold quantum gas relies on the single-particle Green's functions.\ We demonstrate that it can be extracted by the spectrum of electromagnetically induced transparency (EIT).\ The…
Green's functions are highly useful in analyzing the dynamical behavior of polynomials in their escaping set. The aim of this paper is to construct an analogue of Green's functions for planar quasiregular mappings of degree two and constant…
We explore the computation of high-harmonic generation spectra by means of Gaussian basis sets in approaches propagating the time-dependent Schr{\"o}dinger equation. We investigate the efficiency of Gaussian functions specifically designed…
Using a path integral approach and bosonization, we calculate the low energy asymptotics of the one particle Green's function for a ``magnetically incoherent'' one dimensional strongly interacting electron gas at temperatures much greater…
An accurate expression of the kinetic energy density of an electronic distribution in terms of the single particle reduced density matrix for atomic and molecular systems is a long-standing problem in electron structure theory. Existing…