Related papers: Variational discrete variable representation for e…
We consider propagating, spatially localised waves in a class of equations that contain variational and non-variational terms. The dynamics of the waves is analysed through a collective coordinate approach. Motivated by the variational…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
The main result is an explicit expression for the Pressure Metric on the Hitchin component of surface group representations into PSL(n,R) along the Fuchsian locus. The expression is in terms of a parametrization of the tangent space by…
We investigate bottomonia splittings by solving a Schrodinger-Pauli-type equation with parametrisations of QCD potentials around those that have been determined previously in lattice simulations. This is done both, in the continuum and on…
We study the asymptotic behaviour of the discrete elastic energies in presence of the prestrain metric $G$, assigned on the continuum reference configuration $\Omega$. When the mesh size of the discrete lattice in $\Omega$ goes to zero, we…
It is known that the variational methods are the most powerful tool for studying the Coulomb three-body bound state problem. However, they often suffer from loss of stability when the number of basis functions increases. This problem can be…
In this paper we propose a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The two lattices have slightly different lattice parameters and there is a small…
Variational quantum algorithms offer a promising framework for solving eigenvalue problems on near-term quantum hardware, yet their applicability beyond electronic structure calculations remains relatively unexplored. In this work, we…
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it…
We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The…
Excitons are electron-hole pairs appearing below the band gap in insulators and semiconductors. They are vital to photovoltaics, but are hard to obtain with time-dependent density-functional theory (TDDFT), since most standard…
We develop an analytical approach for studying lattice gauge theories within the plaquette representation where the plaquette matrices play the role of the fundamental degrees of freedom. We start from the original Batrouni formulation and…
We extend the epsilon-expansion of continuum chiral perturbation theory to nonzero lattice spacing in the framework of Wilson Chiral Perturbation Theory. We distinguish various regimes by defining the relative power counting of the quark…
Slater determinants have underpinned quantum chemistry for nearly a century, yet their full potential has remained challenging to exploit. In this work, we show that a variational wavefunction composed of a few hundred optimized…
We present the applications of wavelet analysis methods in constrained variational framework to calculation of dynamical aperture. We construct represention via exact nonlinear high-localized periodic eigenmodes expansions, which allows to…
A new approach to the theory of anisotropic exciton based on Fock transformation, i.e., on a stereographic projection of the momentum to the unit 4-dimensional (4D) sphere, is developed. Hyperspherical functions are used as a basis of the…
Teleportation of continuous variables can be described in two different ways, one in terms of Wigner functions, the other in terms of discrete basis states. The latter formulation provides the connection between the theory of teleportation…
A significant component of the cost of making predictions from lattice QCD stems from the computation of correlation functions on a given ensemble of gauge fields. This cost depends on the observable of interest and the details of its…
Perhaps the simplest first-principles approach to electronic structure is to fit the charge distribution of each orbital pair and use those fits wherever they appear in the entire electron-electron (EE) interaction energy. The charge…
We introduce physically relevant new models of two-dimensional (2D) fractional lattice media accounting for the interplay of fractional intersite coupling and onsite self-focusing. Our approach features novel discrete fractional operators…