Related papers: Exact Construction and Uniqueness of the Coupled-C…
At coupling strengths lambda = 1/2, 1, or 2, the Calogero-Sutherland model (CSM) is related to Brownian motion in a Wigner-Dyson random matrix ensemble with orthogonal, unitary, or symplectic symmetry. Using this relation in conjunction…
Let $g(z,x)$ denote the diagonal Green's matrix of a self-adjoint $m\times m$ matrix-valued Schr\"odinger operator $H= -\f{d^2}{dx^2}I_m +Q(x)$ in $L^2 (\bbR)^{m}$, $m\in\bbN$. One of the principal results proven in this paper states that…
A Wronskian determinant approach is suggested to study the energy and the wave function for one-dimensional Schrodinger equation. An integral equation and the corresponding Green's function are constructed. As an example, we employed this…
This paper elucidates the dual structure of the Schr\"{o}dinger dynamics in two correlated stages: (1) We first derive the real-valued Schr\"{o}dinger equation from scratch without referring to classical mechanics, wave mechanics, nor…
Free-particle Green's function plays a central role in the theoretical description of electron scattering and autoionization processes in quantum physics and chemistry. Recently, Gaussian basis set approaches have become increasingly…
We construct a Green function, which can identify the topological nature of interacting systems. It is equivalent to the single-particle Green function of effective non-interacting particles, the Bloch Hamiltonian of which is given by the…
Resonant solutions of the quantum Schr\"odinger equation occur at complex energies where the S-matrix becomes singular. Knowledge of such resonances is important in the study of the underlying physical system. Often the Schr\"odinger…
A simple model of noninteracting electrons with a separable one-body potential is used to discuss the possible pole structure of single particle Green's functions for fermions on unphysical sheets in the complex frequency plane as a…
We demonstrate that coupled-cluster singles-and-doubles Green's function (GFCCSD) method is a powerful and prominent tool drawing the electronic band structures and the total energies, which many theoretical techniques struggle to…
We present the multi-channel Dyson equation that combines two or more many-body Green's functions to describe the electronic structure of materials. In this work we use it to model photoemission spectra by coupling the one-body Green's…
Motivated by recent experimental refinements of stellar reaction rates, we establish a non-perturbative Green's function formalism based on the exact solution of the Dyson equation for sub-barrier proton-nucleus resonant scattering. By…
Consider a five-point discretization of a two-dimensional finite-gap for a fixed energy Schr\"{o}dinger operator. We construct the Green's function of the operator. In appears as the explicit formula in terms of the integral by the specific…
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…
Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead…
The exact reduced density-matrix functional is derived from the Luttinger-Ward functional of the single-particle Green's function. Thereby, a formal link is provided between diagrammatic many-body approaches using Green's functions on the…
We investigate the spin and pseudospin symmetry in the single-particle resonant states by solving the Dirac equation containing a Woods-Saxon potential with Green's function method. Taking double-magic nucleus $^{208}$Pb as an example,…
The Green function plays an essential role in the Kohn-Korringa-Rostocker (KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn-Sham equation and robust methods exist for…
We consider linear second order differential equation y''= f with zero Dirichlet boundary conditions. At the continuous level this problem is solvable using the Green function, and this technique has a counterpart on the discrete level. The…
We discuss the analytic and diagrammatic structure of ionization potential (IP) and electron affinity (EA) equation-of-motion coupled-cluster (EOM-CC) theory, in order to put it on equal footing with the prevalent $GW$ approximation. The…
Motivated by the desire to understand the causal structure of physical signals produced in curved spacetimes -- particularly around black holes -- we show how, for certain classes of geometries, one might obtain its retarded or advanced…