Related papers: Chebyshev-BdG: an efficient numerical approach to …
We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then the classical Remez algorithm provides a fast and precise…
We present an alternative representation for the anisotropic Eliashberg equations of superconductivity, whose numerical solution yields an efficiency gain of several orders of magnitude with respect to the conventional representation in…
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
We analyze Su-Schrieffer-Heeger (SSH) models using the doubling method for orthogonal polynomial sequences. This approach yields the analytical spectrum and exact eigenstates of the models. We demonstrate that the standard SSH model is…
We propose the reduced-shifted Conjugate-Gradient (RSCG) method, which is numerically efficient to calculate a matrix element of a Green's function defined as a resolvent of a Hamiltonian operator, by solving linear equations with a desired…
We propose an algorithm for determining the zeros of the electric conductivity in large molecular nanonstructures such as graphene sheets. To this end, we employ the inverse graph method, whereby non-zeros of the Green's functions are…
We propose an efficient procedure to obtain Green's functions by combining the shifted conjugate orthogonal conjugate gradient (shifted COCG) method with the nonequilibrium Green's function (NEGF) method based on a real-space…
Semantic segmentation and hyperspectral unmixing are two central problems in spectral image analysis. The former assigns each pixel a discrete label corresponding to its material class, whereas the latter estimates pure material spectra,…
The Non-Equilibrium Green's Function (NEGF) method combined with ab initio calculations has been widely used to study charge transport in molecular junctions. However, the significant computational demands of high-resolution calculations…
Quantum many-body methods provide a systematic route to computing electronic properties of molecules and materials, but high computational costs restrict their use in large-scale applications. Due to the complexity in many-electron…
A mixed basis approach based on density functional theory is extended to one-dimensional(1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the…
We present an efficient method for the computation of homogenized coefficients of divergence-form operators with random coefficients. The approach is based on a multiscale representation of the homogenized coefficients. We then implement…
A surface integral equation solver is proposed for fast and accurate simulation of interconnects embedded in stratified media. A novel technique for efficient computation of the multilayer Green's function is proposed. Using the Taylor…
In this paper we analyze the quantum homological invariants (the Poincar\'e polynomials of the $\mathfrak{sl}_N$ link homology). In the case when the dimensions of homologies of appropriate topological spaces are precisely known, the…
Computing topological invariants in two-dimensional quasicrystals and super-moire matter is a remarkable open challenge, due to the absence of translational symmetry and the colossal number of sites inherent to these systems. Here, we…
A self-consistent method for calculating electron transport through a molecular device is proposed. It is based on density functional theory electronic structure calculations under periodic boundary conditions and implemented in the…
We propose an implementation of the Smooth Selection Embedding Method (SSEM) in the setting of Chebyshev polynomials. The SSEM is a hybrid fictitious domain / collocation method which solves boundary value problems in complex domains by…
Homogenization is a technique commonly used in multiscale computational science and engineering for predicting collective response of heterogeneous materials and extracting effective mechanical properties. In this paper, a three-dimensional…
We discuss the general transport properties of superconducting quantum point contacts. We show how these properties can be obtained from a microscopic model using nonequilibrium Green function techniques. For the case of a one-channel…
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…