Related papers: Algorithms for estimating spectral density functio…

A systematic and easy-to-use method is developed to calculate directly the doubly heavy hadron spectral density in the coordinate space. The correlation function is expressed in terms of hypergeometric functions, and the spectral density is…

Given $n$ i.i.d. observations, we study the problem of estimating the spectrum of weighted Laplace operators of the form $\Delta_f=\Delta + \alpha \nabla \log f\cdot \nabla$, where $f$ is a positive probability density on a known compact…

We study the potential utility of classical techniques of spectral sparsification of graphs as a preprocessing step for digital quantum algorithms, in particular, for Hamiltonian simulation. Our results indicate that spectral sparsification…

In this article, we consider the extended Kohn-Sham model for atoms subjected to cylindrically-symmetric external potentials. The variational approximation of the model and the construction of appropriate discretization spaces are detailed…

In this paper density functionals for Coulomb systems subjected to electric and magnetic fields are developed. The density functionals depend on the particle density, $\rho$, and paramagnetic current density, $j^p$. This approach is…

We study Hill's differential equation with potential expressed by elliptic functions which arises in some problems of physics and mathematics. Analytical method can be applied to study the local properties of the potential in asymptotic…

We give the details of the calculation of the spectral functions of the 1D Hubbard model using the spin-charge factorized wave-function for several versions of the U -> +\infty limit. The spectral functions are expressed as a convolution of…

We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral…

We develop a sparse spectral method for a class of fractional differential equations, posed on $\mathbb{R}$, in one dimension. These equations can include sqrt-Laplacian, Hilbert, derivative and identity terms. The numerical method utilizes…

Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes…

We shall give a priori conditions on the illuminations $\phi_i$ such that the solutions to the Helmholtz equation $-div(a \nabla u^i)-k q u^i=0$ in \Omega, $u^i=\phi_i$ on $\partial\Omega$, and their gradients satisfy certain non-zero and…

Kohn-Sham density functional theory (DFT) is the standard method for first-principles calculations in computational chemistry and materials science. More accurate theories such as the random-phase approximation (RPA) are limited in…

In this paper, we apply rough paths techniques to provide an approximation of the solution of stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter $H>1/2$. Here, the involved stochastic…

We describe a new, short proof of some facts relating the gap lengths of the spectrum of a potential of Hill's equation to its regularity. For example, a real potential is in a weighted Gevrey-Sobolev space if and only if its gap lengths…

We consider Schr\"odinger operators on the line with potentials that are periodic with respect to the coordinate variable and real analytic with respect to the energy variable. We prove that if the imaginary part of the potential is bounded…

Within the finite-field Kohn-Sham framework, static electric response properties of diatomic molecules are presented. The electronic energy, dipole moment ({\boldmath$\mu$}), static dipole polarizability ({\boldmath$\alpha$}) and…

We summarize our recent determination [1] of the spectral density of the Wilson operator in the p-regime of Wilson chiral perturbation theory. We discuss the range of validity of our formula and a possible extension to our computation in…

This paper concerns the analysis of random second order linear differential equations. Usually, solving these equations consists of computing the first statistics of the response process, and that task has been an essential goal in the…

Quantum fidelity between two density matrices, $F(\rho_1,\rho_2)$ is usually defined as the trace of the operator ${\cal F}=\sqrt{\sqrt{\rho_1} \rho_2 \sqrt{\rho_1}}$. We study the logarithmic spectrum of this operator, which we denote by…

We introduce here a natural functional associated to any $b \in QH_* (M, \omega)$: \emph{spectral length functional}, on the space of "generalized paths" in $ \text {Ham}(M, \omega)$, closely related to both the Hofer length functional and…