Related papers: Equation of Motion Method for Composite Field Oper…
Green's function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states. Here we investigate the cumulant form of the one-electron Green's function based on the…
In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of…
Nonperturbative dynamic theory has a particular advantage in studying the transport in a quantum impurity system in a steady state. Here, we develop a new approach for obtaining the retarded Green's function expressed in resolvent form. We…
We generalize the methods used in the theory of correlation dynamics and establish a set of equations of motion for many-body correlation green's functions in the non-relativistic case. These non-linear and coupled equations of motion…
We propose an integral formulation of macroscopic quantum electrodynamics in the Heisenberg picture for linear dispersive dielectric objects of finite size, utilizing the Hopfield-type approach. By expressing the electromagnetic field…
We develop a Green's function formalism for spin transport through heterostructures that contain metallic leads and insulating ferromagnets. While this formalism in principle allows for the inclusion of various magnonic interactions, we…
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…
Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for…
Based on the Green's function (GF) equation-of-motion formalism, we develop a method to expand the double time Green's function into Taylor series of the parameter $\lambda$ in the Hamiltonian $H=H_0 + \lambda H_1$. Here $H_0$ is the…
A Green's function method is developed for solving strongly-coupled gravity and matter in the semiclassical limit. In the strong-coupling limit, one assumes that Newton's constant approaches infinity. As a result, one may neglect second…
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…
We developed a gauge-covariant formulation of the non-equilibrium Green function method for the dynamical and/or non-uniform electromagnetic field by means of the deformational quantization method. Such a formulation is realized by…
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…
A review of electronic dynamics of single-impurity and many-impurity Anderson models is contained in this report. Those models are used widely for many of the applications in diverse fields of interest, such as surface physics, theory of…
Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain simple representations for the Green's function of the Dirac-Oscillator and Dirac-Coulomb problems. This is accomplished…
We study a new approach to determine the asymptotic behaviour of quantum many-particle systems near coalescence points of particles which interact via singular Coulomb potentials. This problem is of fundamental interest in electronic…
It has been shown that the Schwinger-Dyson equations for non-Hermitian theories implicitly include the Hilbert-space metric. Approximate Green functions for such theories may thus be obtained, without having to evaluate the metric…
The asymmetric Hubbard model is used in investigating the lattice gas of the moving particles of two types. The model is considered within the dynamical mean-field method. The effective single-site problem is formulated in terms of the…
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…
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…