Related papers: Convergence rate for numerical computation of the …
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…
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…
To analyze nonlinear dynamic systems, we developed a new technique based on the square matrix method. We propose this technique called the \convergence map" for generating particle stability diagrams similar to the frequency maps widely…
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…
We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh-refinement is driven by the local contributions of the weighted-residual error estimator. We prove that the adaptive…
An important problem in many-body physics is to reconstruct the spectral density from the imaginary-time domain Green's function. Typically, the imaginary-time Green's function is generated by Monte Carlo methods. As the one-point fermionic…
We study run and tumble particles on the one-dimensional lattice $\mathbb{Z}$. We explicitly compute the Fourier-Laplace transform of the position of the particle and as a consequence obtain explicit expressions for the diffusion constant…
Driven by the growing interest in numerical simulations of dislocation-interface interactions in general crystalline materials with elastic anisotropy, we develop algorithms for the integration of interface tractions needed to couple…
We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the…
We study estimates of the Green's function in $\mathbb{R}^d$ with $d \ge 2$, for the linear second order elliptic equation in divergence form with variable uniformly elliptic coefficients. In the case $d \ge 3$, we obtain estimates on the…
Since the breakthrough of twistronics a plethora of topological phenomena in two dimensions has appeared, specially relating topology and electronic correlations. These systems can be typically analyzed in terms of lattice models of…
A parallel algorithm for the implementation of the recursive Green's function technique, which is extensively applied in the coherent scattering formalism, is developed. The algorithm performs a domain decomposition of the scattering region…
We examine the formation of bound states on a generalized nonlinear impurity located at or near the beginning (surface) of a linear, tight-binding semi-infinite lattice. Using the formalism of lattice Green functions, we obtain in closed…
A method based on separated integration to estimate anharmonic corrections to energy and vibration of molecules in a second-order diagrammatic vibrational many-body Green's function formalism has already been presented. A severe bottleneck…
On the unit square, we introduce a method for accurately computing source-neutral Green's functions of the fractional Laplacian operator with either periodic or homogeneous Neumann boundary conditions. This method involves analytically…
We study the face-centered cubic lattice (fcc) in up to six dimensions. In particular, we are concerned with lattice Green's functions (LGF) and return probabilities. Computer algebra techniques, such as the method of creative telescoping,…
It is known that Green's functions can be expressed as continued fractions; the content at the $n$-th level of the fraction is encoded in a coefficient $b_n$, which can be recursively obtained using the Lanczos algorithm. We present a…
Anisotropic rotation averaging has recently been explored as a natural extension of respective isotropic methods. In the anisotropic formulation, uncertainties of the estimated relative rotations -- obtained via standard two-view…
An efficient implementation of the nonequilibrium Green function (NEGF) method combined with the density functional theory (DFT) using localized pseudo-atomic orbitals (PAOs) is presented for electronic transport calculations of a system…
A compact form for the static Green's function for symmetric loading of an elastic sphere is derived. The expression captures the singularity in closed form using standard functions and quickly convergent series. Applications to problems…