Related papers: Proof that the maximally localized Wannier functio…
We have adapted the maximally-localized Wannier function approach of [I. Souza, N. Marzari and D. Vanderbilt, Phys. Rev. B 65, 035109 (2002)] to the density functional theory based Siesta method [J. M. Soler et al., J. Phys.: Cond. Mat. 14,…
Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more…
We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize…
Exponentially-localized Wannier functions are a basis of the Fermi projection of a Hamiltonian consisting of functions which decay exponentially fast in space. In two and three spatial dimensions, it is well understood for periodic…
The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the…
We prove a Wegner estimate for alloy type models merely assuming that the single site potential is lower bounded by a characteristic function of a thick set, that is a particular set of positive measure. The proof is based on two…
With its monoelemental composition, various crystalline forms and an inherently strong spin-orbit coupling, bismuth has been regarded as an ideal prototype material to expand our understanding of topological electronic structures. In…
With the aim of understanding the localization topology correspondence for non periodic gapped quantum systems, we investigate the relation between the existence of an algebraically well-localized generalized Wannier basis and the…
The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…
We develop a wavelet like representation of functions in $L^p(\mathbb{R})$ based on their Fourier--Hermite coefficients; i.e., we describe an expansion of such functions where the local behavior of the terms characterize completely the…
We develop the theory of minimal realizations and factorizations of rational functions where the coefficient space is a ring of the type introduced in our previous work, the scaled quaternions, which includes as special cases the…
We use supersymmetric localization to study probes of four dimensional Lagrangian N=2 superconformal field theories. We first derive a unique equation for the eigenvalue density of these theories. We observe that these theories have a…
A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the…
The Hartree-Fock equations are modified to directly yield Wannier functions following a proposal of Shukla et al. [Chem. Phys. Lett. 262, 213-218 (1996)]. This approach circumvents the a posteriori application of the Wannier transformation…
We show that a considerable part of the theory of (ultra)distributions and hyperfunctions can be extended to more singular generalized functions, starting from an angular localizability notion introduced previously. Such an extension is…
We derive an {\em ab initio} $\pi$-band tight-binding model for $AB$ stacked bilayer graphene based on maximally localized Wannier wave functions (MLWFs) centered on the carbon sites, finding that both intralayer and interlayer hopping is…
We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized…
We investigate the full pair-distribution function of a homogeneous suspension of spherical active Brownian particles interacting by a Weeks-Chandler-Andersen potential in two spatial dimensions. The full pair-distribution function depends…
The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed in the probabilistic literature, in comparison with the quarter plane analogue model. In this context, our main result is to prove that the…
Standard regularized training procedures correspond to maximizing a posterior distribution over parameters, known as maximum a posteriori (MAP) estimation. However, model parameters are of interest only insomuch as they combine with the…