Related papers: Spectral functions and localization landscape theo…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in presence an arbitrary number…
We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…
A spectral approach to building the exterior calculus in manifold learning problems is developed. The spectral approach is shown to converge to the true exterior calculus in the limit of large data. Simultaneously, the spectral approach…
We develop a general method for calculating statistical properties of the speckle pattern of coherent waves propagating in disordered media. In some aspects this method is similar to the Boltzmann-Langevin approach for the calculation of…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed…
Based on the concept of a nonequilibrium steady state, we present a novel method to experimentally determine energy landscapes acting on colloidal systems. By measuring the stationary probability distribution and the current in the system,…
Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions,…
We consider single particle Schrodinger operators with a gap in the en ergy spectrum. We construct a complete, orthonormal basis function set for the inv ariant space corresponding to the spectrum below the spectral gap, which are…
We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet…
Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily…
Bound states of the generalized spiked harmonic oscillator potential are calculated accurately by using the generalized pseudospectral method. Energy eigenvalues, various expectation values, radial densities are obtained through a…
The Wigner function formalism has been applied to the analysis of elastic scattering processes. The new element of known formalism is the choice of the phase space on which the Wigner function is defined. This phase space is 4-dimensional…
The technique of Weinberg's spectral-function sum rule is a powerful tool for a study of models in which global symmetry is dynamically broken. It enables us to convert information on the short-distance behavior of a theory to relations…
We compute non-perturbative spectral functions in a scalar $\phi^4$-theory in three spacetime dimensions via the spectral functional renormalisation group. This approach allows for the direct, manifestly Lorentz covariant computation of…
We develop a procedure to modify the correlations of a speckle potential. This procedure, that is suitable for spatial light modulator devices, allows one to increase the localization efficiency of the speckle in a narrow energy region…
An Ewald decomposition of the two-dimensional Yukawa potential and its derivative is presented for both the periodic and the free-space case. These modified Bessel functions of the second kind of zeroth and first degrees are used e.g. when…
Novel results for the self-consistent single-particle spectral function and self-energy are presented for non-degenerate one-component Coulomb systems at various densities and temperatures. The GW^0-method for the dynamical self-energy is…