Related papers: Fast integral methods for the Neumann Green's func…
We introduce a Rigid-Body Fluctuating Immersed Boundary (RB-FIB) method to perform large-scale Brownian dynamics simulations of suspensions of rigid particles in fully confined domains, without any need to explicitly construct Green's…
We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher dimensions. Together with Cartan's estimates and discrepancy estimates, we establish explicit…
The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and…
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 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…
Using the Green function integral representation the Dyson-Schwinger equations are solved directly in Minkowski space. Essential ideas of the spectral techniques are discussed and applied on two renormalizable models: the Yukawa theory with…
Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic…
The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly-correlated systems. Although the development of quantum computers in the near future may enable us to compute energy…
A dynamic 3D Green's function for the homogeneous, isotropic and viscoelastic (of the Zener type) half-space is derived in a closed form. The results obtained here can be used as either stand-alone solutions for simple problems or in…
On the basis of spin and pairing fluctuation-exchange approximation, we study the superconductivity in quasi-two-dimensional Hubbard model. The integral equations for the Green's function are self-consistently solved by numerical…
Many-body Green's functions encode all the properties and excitations of interacting electrons. While these are challenging to be evaluated accurately on a classical computer, recent efforts have been directed towards finding quantum…
We introduce a general scheme to consistently truncate equations of motion for Green's functions. Our scheme is guaranteed to generate physical Green's functions with real excitation energies and positive spectral weights. There are free…
This article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated with the Poisson and Helmholtz equations in two dimensions. Following the…
Due to non-linear structure, iterative Green's function methods can result in multiple different solutions even for simple molecular systems. In contrast to the wave-function methods, a detailed and careful analysis of such molecular…
Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
We present and analyze fully discrete Nystr\"om methods for the solution of three classes of well conditioned boundary integral equations for the solution of two dimensional scattering problems by homogeneous dielectric scatterers.…
We present a numerically efficient technique to evaluate the Green's function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or `patches', are connected using self energy…
We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…
Elliptic problems along smooth surfaces embedded in three dimensions occur in thin-membrane mechanics, electromagnetics (harmonic vector fields), and computational geometry. In this work, we present a parametrix-based integral equation…