Related papers: Efficient basis expansion for describing linear an…
We take a critical view at the basic definition of extended single particle states in a non-translationally invariant system. For this, we present the case of a hierarchical lattice and incorporate long range interactions that are also…
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…
We derive an automatic procedure for generating a set of highly localized, non-orthogonal orbitals for linear scaling quantum Monte Carlo calculations. We demonstrate the advantage of these orbitals in calculations of the total energy of…
Multipolar expansions are a foundational tool for describing basis functions in quantum mechanics, many-body polarization, and other distributions on the unit sphere. Progress on these topics is often held back by complicated and competing…
We introduce a systematic framework to derive the effective Hamiltonian governing the coherent dynamics of non-Markovian open quantum systems. By applying the minimal dissipation principle, we uniquely isolate the coherent contribution to…
In mixed quantum-classical simulations of molecule-metal surface interactions, the discretization of the metallic electronic continuum typically results in a closed-system representation that fails to capture the open-system nature of the…
Quantitatively accurate electronic structure calculations rely on the proper description of electron correlation. A judicious choice of the approximate quantum chemistry method depends upon the importance of dynamic and nondynamic…
We suggest an alternative mathematical model for the electron in which the dynamical variables are a coframe (field of orthonormal bases) and a density. The electron mass and external electromagnetic field are incorporated into our model by…
We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…
This paper presents a coordinate free pre-metric formulation of charge free Maxwell-Minkowski electrodynamics, and of the developed by the authors non-linear Extended Electrodynamics. First we introduce some formal relations from…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
We devise fast and provably accurate algorithms to transform between an $N\times N \times N$ Cartesian voxel representation of a three-dimensional function and its expansion into the {ball harmonics}, that is, the eigenbasis of the…
A basis set expansion is performed to find the eigenvalues and wave functions for an electron on a toroidal surface $T^2$ subject to a constant magnetic field in an arbitrary direction. The evolution of several low-lying states as a…
The work presents a simple formalism which proposes an estimate of the ground state energy from a single reference function. It is based on a perturbative expansion but leads to non linear coupled equations. It can be viewed as well as a…
We present a method for total energy minimizations and molecular dynamics simulations based either on tight-binding or on Kohn-Sham hamiltonians. The method leads to an algorithm whose computational cost scales linearly with the system…
We review our recently developed electronic structure calculation methods used for the dynamics of large-scale solids or liquids with an efficient algorithm for large scale simultaneous linear equations. The electronic structure calculation…
We introduce a generic method for computing groundstates that is applicable to a wide range of spatially anisotropic 2D many-body quantum systems. By representing the 2D system using a low-energy 1D basis set, we obtain an effective 1D…
Extensive variational computations are reported for the ground state energy of the non-relativistic two-electron atom. Several different sets of basis functions were systematically explored, starting with the original scheme of Hylleraas.…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
We present a computationally efficient approach to perform systematically convergent real-space all-electron Kohn-Sham DFT calculations for solids using an enriched finite element (FE) basis. The enriched FE basis is constructed by…