Related papers: Linear Algebraic Calculation of Green's function f…
In this paper, the Green's function and decomposition technique is proposed for solving the coupled Lane-Emden equations. This approach depends on constructing Green's function before establishing the recursive scheme for the series…
Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on…
We describe how to apply the recursive Green's function method to the computation of electronic transport properties of graphene sheets and nanoribbons in the linear response regime. This method allows for an amenable inclusion of several…
We present the Composite Operator Method (COM) as a modern approach to the study of strongly correlated electronic systems, based on the equation of motion and Green's function method. COM uses propagators of composite operators as building…
We present and review an efficient method to calculate the retarded Green's function in multi-terminal nanostructures; which is needed in order to calculate the conductance through the system and the local particle densities within it. 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…
We have developed a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods permit efficient calculations on ill-conditioned systems with long…
A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…
A local-orbital based ab initio approach to obtain the Green function for large heterogeneous systems is developed. First a Green function formalism is introduced based on exact diagonalization. Then the self energy is constructed from an…
In a recent series of scanning probe experiments, it became possible to visualize local electron flow in a two-dimensional electron gas. In this paper, a Green's function technique is presented that enables efficient calculation of the…
A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the…
The local and overall responses of nonlinear composites are classically investigated by the Finite Element Method. We propose an alternate method based on Fourier series which avoids meshing and which makes direct use of microstructure…
We present a new method for the computation of self-energy corrections in large supercells. It eliminates the explicit summation over unoccupied states, and uses an iterative scheme based on an expansion of the Green's function around a set…
Accurate modeling of the electronic structure of warm dense matter is a challenging problem whose solution would allow a better understanding of material properties like equation of state, opacity, and conductivity, with resulting…
The Green's function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of Green's function impedes the research of…
In this paper, we build on the work of [T. Hughes, G. Sangalli, VARIATIONAL MULTISCALE ANALYSIS: THE FINE-SCALE GREENS' FUNCTION, PROJECTION, OPTIMIZATION, LOCALIZATION, AND STABILIZED METHODS, SIAM Journal of Numerical Analysis, 45(2),…
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…
Given input-output pairs of an elliptic partial differential equation (PDE) in three dimensions, we derive the first theoretically-rigorous scheme for learning the associated Green's function $G$. By exploiting the hierarchical low-rank…
The Hubbard model, a cornerstone in the field of condensed matter physics, serves as a fundamental framework for investigating the behavior of strongly correlated electron systems. This paper presents a novel perspective on the model,…
We discuss an integral equation approach that enables fast computation of the response of nonlinear multi-degree-of-freedom mechanical systems under periodic and quasi-periodic external excitation. The kernel of this integral equation is a…