Related papers: Localization in the Incommensurate Systems: A Plan…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
The scale invariant properties of wave functions in finite samples of one dimensional random systems with correlated disorder are analyzed. The random dimer model and its generalizations are considered and the wave functions are compared.…
We investigate spectral and dynamical localization of a quantum system of $ n $ particles on $ \mathbb{R}^d $ which are subject to a random potential and interact through a pair potential which may have infinite range. We establish two…
We report an approach to obtain effective pair potentials which describe the structure of two-dimensional systems of active Brownian particles. The pair potential is found by an inverse method, which matches the radial distribution function…
We develop a semi-discrete optimal transport scheme for the compressible semi-geostrophic equations, a system that plays an important role in modelling large-scale atmospheric dynamics and frontogenesis. Unlike the incompressible case, the…
Key challenges in developing underwater acoustic localization methods are related to the combined effects of high reverberation in intricate environments. To address such challenges, recent studies have shown that with a properly designed…
In this paper we study in detail the localized wave functions defined in Phys. Rev. Lett. {\bf 76}, 1613 (1994), in connection with the scarring effect of unstable periodic orbits in highly chaotic Hamiltonian system. These functions appear…
Over the past few years it has been pointed out that direct inversion of accurate but approximate ground state densities leads to Kohn-Sham exchange-correlation (xc) potentials that can differ significantly from the exact xc potential of a…
Localization properties of quasi-one dimensional quantum wire nanostructures are investigated using the transfer matrix-Lyapunov exponent technique. We calculate the localization length as a function of the effective mean-field mobility…
We generalize effective energy variational techniques to study appropriately quantized solitonic field configurations. Our approach rests on collective quantization ideas and is specifically designed for the numerical evaluation of soliton…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
Eigenspectra that fill regions in the complex plane have been intriguing to many, inspiring research from random matrix theory to esoteric semi-infinite bounded non-Hermitian lattices. In this work, we propose a simple and robust ansatz for…
Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…
Power-law noises abound in nature and have been observed extensively in both time series and spatially varying environmental parameters. Although, recent years have seen the extension of traditional stochastic partial differential equations…
There are many classical random walk in random environment results that apply to ergodic random planar environments. We extend some of these results to random environments in which the length scale varies from place to place, so that the…
Programmable, intelligent surfaces can manipulate electromagnetic waves impinging upon them, producing arbitrarily shaped reflection, refraction and diffraction, to the benefit of wireless users. Moreover, in their recent form of…
Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's…
Wavelength determines the length scale of the cross section when electromagnetic waves are scattered by an electrically small object. The cross section diverges for resonant scattering, and diminishes for non-resonant scattering, when…
We study the sampling of spatial fields using sensors that are location-unaware but deployed according to a known statistical distribution. It has been shown that uniformly distributed location-unaware sensors cannot infer bandlimited…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…