Related papers: Recursive Green's function method for multi-termin…
A double-tip scanning tunneling microscope with nanometer scale tip separation has the ability to access the single electron Green's function in real and momentum space based on second order tunneling processes. Experimental realization of…
Non-equilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method…
We propose a new procedure by using the recursive Green's functions which remove all the repetition terms from the time-independent perturbation series for finite-level quantum systems. These Green's functions are introduced as a…
The simulation of quantum transport in nanodevices requires the solution of the Dyson and Keldysh equations, a task dominated by the inversion of massive, block-tridiagonal matrices. While the Recursive Green's Function (RGF) method has…
We consider the application of the recursion method to the calculation of one-particle Green's functions for strongly correlated systems and propose a new way how to extract the information about the infinite system from the exact…
During the past three decades, the advantageous concept of the Green's function has been extended from linear systems to nonlinear ones. At that, there exist a rigorous and an approximate extensions. The rigorous extension introduces the…
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…
High-order derivatives of Green's functions are a key ingredient in Taylor-based fast multipole methods, Barnes-Hut $n$-body algorithms, and quadrature by expansion (QBX). In these settings, derivatives underpin either the formation,…
We present here generalization of the recursion method of Haydock et al [1] for the calculation of Green matrices (in angular momentum space). Earlier approaches concentrated on the diagonal elements, since the focus was on spectral…
We introduce a performance-optimized method to simulate localization problems on bipartite tight-binding lattices. It combines an exact renormalization group step to reduce the sparseness of the original problem with the recursive Green's…
This work presents a Green's function approach, originally implemented in graphene with well-defined edges, to the surface of a strong 3D Topological Insulator (TI) with a sequence of proximitized superconducting (S) and ferromagnetic (F)…
We derive expressions for the electromagnetic Green's function for a layered system using a transfer matrix technique. The expressions we arrive at makes it possible to study symmetry properties of the Green's function, such as reciprocity…
We present a high order numerical method for the solution of the Neumann Green's function in two dimensions. For a general closed planar curve, our computational method resolves both the interior and exterior Green's functions with the…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
We present a method which uses density functional theory (DFT) to treat transport through a single molecule connected to two conducting leads for the weak and intermediate coupling. This case is not accessible to standard non-equilibrium…
In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by extension, Schr\"odinger's equation. The…
It is shown that the conventional many-body techniques to calculate the Green's functions can be applied to the wide, compressible edge of a quantum Hall bar. The only ansatz we need is the existence of stable density modes that yields a…
We present an ongoing development of an existing code for calculating ground-state, steady-state, and transient properties of many-particle systems. The development involves the addition of the full four-index two electron integrals, which…
To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved…
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…