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In open quantum systems hosting excitons, dissipation mechanisms critically shape the excitonic dynamics, band-structure and topological properties. A microscopic understanding of excitons in such non-Hermitian settings demands a…
We present a finite-element simulation tool for calculating light fields in 3D nano-optical devices. This allows to solve challenging problems on a standard personal computer. We present solutions to eigenvalue problems, like Bloch-type…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
The instantaneous Bethe-Salpeter equation, derived from the general Bethe-Salpeter formalism by assuming that the involved interaction kernel is instantaneous, represents the most promising framework for the description of hadrons as bound…
Classification is a machine learning method used in many practical applications: text mining, handwritten character recognition, face recognition, pattern classification, scene labeling, computer vision, natural langage processing. A…
Computational methods that automatically extract knowledge from data are critical for enabling data-driven materials science. A reliable identification of lattice symmetry is a crucial first step for materials characterization and…
By working out the Bethe sum rule, a boundary condition that takes the form of a linear equality is derived for the fine structure observed in ionization edges present in electron energy-loss spectra. This condition is subsequently used as…
Crystalline materials, with symmetrical and periodic structures, exhibit a wide spectrum of properties and have been widely used in numerous applications across electronics, energy, and beyond. For crystalline materials discovery,…
The Bethe ansatz in its several formulations is the common tool for the exact solution of one dimensional quantum Hamiltonians. This ansatz asserts that the several eigenfunctions of the Hamiltonians are given in terms of a sum of…
For solar conditions, we numerically integrate the density matrix equation for a thermal electron in the field of a Be-7 ion and other plasma ions and smeared-out electrons. Our results are in agreement with previous calculations that are…
Physicochemical characterization of materials is central to the field of science and engineering and is essential to design new/engineered materials with specific properties. Assays available for small-molecules, e.g., XRD, NMR, LC-MS,…
Accurately determining the crystallographic structure of a material, organic or inorganic, is a critical primary step in material development and analysis. The most common practices involve analysis of diffraction patterns produced in…
We demonstrate a method to systematically obtain eigenvalues and eigenstates of a many-body Hamiltonian describing collective neutrino oscillations. The method is derived from the Richardson-Gaudin framework, which involves casting the…
The capacitance of an arbitrarily shaped object is calculated with the same second-kind integral equation method used for computing static and dynamic polarizabilities. The capacitance is simply the dielectric permittivity multiplied by the…
Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph…
An iterative algorithm is adopted to construct approximate representations of matrices describing the scattering properties of arbitrary objects. The method is based on the implicit evaluation of scattering responses from iteratively…
The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue problems. Using examples, we show that discretization can:…
Three-dimensional phase contrast imaging of multiply-scattering samples in X-ray and electron microscopy is extremely challenging, due to small numerical apertures, the unavailability of wavefront shaping optics, and the highly nonlinear…
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…