Related papers: Optimized norm-conserving Vanderbilt pseudopotenti…
Convex optimization recently emerges as a compelling framework for performing super resolution, garnering significant attention from multiple communities spanning signal processing, applied mathematics, and optimization. This article offers…
We consider the coupled propagation of an optical field and its second harmonic in a quadratic nonlinear medium governed by a coupled system of Schrodinger equations. We prove the existence of ring-profiled optical vortex solitons appearing…
We present a zero-range pseudopotential applicable for all partial wave interactions between neutral atoms. For p- and d-waves we derive effective pseudopotentials, which are useful for problems involving anisotropic external potentials.…
Nonrelativistic two-body scattering by a short-ranged potential is studied using the renormalisation group. Two fixed points are identified: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of the…
We prove that the Newton product of efficient polynomial projectors is still efficient. Various polynomial approximation theorems are established involving Newton product projectors on spaces of holomorphic functions on a neighborhood of a…
We develop an automated procedure to select the local potential of a separable pseudopotential that minimizes transferability errors for the isolated atom, and we show that this optimization leads to significant improvements in the accuracy…
Dual quaternions have gained significant attention due to their wide applications in areas such as multi-agent formation control, 3D motion modeling, and robotics. A fundamental aspect in dual quaternion research involves the projection…
This article is a continuation of arXiv:2401.14977. We study the concentration properties of spectral projectors on manifolds, in connection with the uncertainty principle. In arXiv:2401.14977, the second author proved an optimal…
The plasmon resonance has found important application in various systems, e.g., nanoantennas, solar panels, refractive index sensors. Unfortunately, a few analytical solutions for such systems are known. The work aims to find a solution for…
The purpose of this note is to investigate the concentration properties of spectral projectors on manifolds. This question has been intensively studied (by Logvinenko--Sereda, Nazarov, Jerison--Lebeau, Kovrizhkin,…
We propose a systematic method of analyzing pseudopotential transferability based on linear-response properties of the free atom, including self-consistent chemical hardness and polarizability. Our calculation of hardness extends the…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
We have implemented recently developed multiple-projector pseudopotentials into the planewave based auxiliary-field quantum Monte Carlo (pw-AFQMC) method. Multiple-projector pseudopotentials can yield smaller planewave cut-offs while…
We present an alternative organizational scheme for developing effective theories of 2- and 3-body systems that is systematic, accurate, and efficient with controlled errors. To illustrate our approach we consider the bound state and…
We formulate a new quasi-Hermitian delta-shell pseudopotential for higher partial wave scattering, and show that any such potential must have an energy-dependent regularization. The quasi-Hermiticity of the Hamiltonian leads to a complete…
Given a compact Riemannian surface $M$, with Laplace-Beltrami operator $\Delta$, for $\lambda > 0$, let $P_{\lambda,\lambda^{-\frac{1}{3}}}$ be the spectral projector on the bandwidth $[\lambda-\lambda^{-\frac{1}{3}}, \lambda +…
First-principles calculations in crystalline structures are often performed with a planewave basis set. To make the number of basis functions tractable two approximations are usually introduced: core electrons are frozen and the diverging…
Based on the needs of convergence proofs of preconditioned proximal point methods, we introduce notions of partial strong submonotonicity and partial (metric) subregularity of set-valued maps. We study relationships between these two…
In this paper we address the global stability problem for double-bubbles in the plane. This is accomplished by combining the "improved convergence theorem" for planar clusters developed in arXiv:1409.6652 with an ad hoc analysis of the…
The projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and…