Related papers: Thomson problem in the disk
Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…
Correspondences between the Thomson Problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change configurations of $N\le 100$ electrons into…
The partition function and free energy of a quantum many-body system determine its physical properties in thermal equilibrium. Here we study the computational complexity of approximating these quantities for $n$-qubit local Hamiltonians.…
We present a method for treatment of three charged particles. The proposed method has universal character and is applicable both for bound and continuum states. A finite rank approximation is used for Coulomb potential in three-body system…
Two of the most iconic systems of quantum physics are the particle in a box and the Coulomb potential (the third is, of course, the harmonic oscillator). In this expository paper, we consider the quantum solution to the problem of an…
We study the minimum energy configuration of a uniform distribution of negative charge subject to Coulomb repulsive self-interaction and attractive interaction with a fixed positively charged domain. After having established existence and…
This paper presents a method for achieving equilibrium in the ISING Hamiltonian when confronted with unevenly distributed charges on an irregular grid. Employing (Multi-Edge) QC-LDPC codes and the Boltzmann machine, our approach involves…
Non-empty space reading of Maxwell equations as local energy identities explains why a Coulomb field is carried rigidly by electrons in experiments. The analytical solution of the Poisson equation defines the sharp radial shape of charged…
Motivated by the long-debated question about the internal stability of the electron, the force densities acting on the charge density of the 1s electron in the H atom are investigated. The problem is mapped onto the canonical formalism for…
We develop a quantum algorithm for estimating the free energy as well as the total Gibbs state of interacting quantum Coulomb gases and molecular systems in dimensions $d \in \{2,3\}$ at finite temperature. These systems lie beyond the…
This paper is dedicated to studying various aspects of topological defects, appearing in mean-field theory treatments of physical systems such as ultracold atomic gases and gauge field theories. We start by investigating topological charge…
We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large…
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…
We consider Hamiltonian with $N$ point interactions in $\R^d, d=2,3,$ all with the same coupling constant, placed at vertices of an equilateral polygon $\PP_N$. It is shown that the ground state energy is locally maximized by a regular…
We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics by introducing the concept of high-order topological charges, with novel phenomena being predicted. Through a dimension reduction…
We study a one dimensional Coulomb system, where two charged colloids are neutralized by a collection of point counterions, with global neutrality. Temperature being given, two situations are addressed: the colloids are either kept at fixed…
Fault-tolerant quantum computation requires minimizing non-Clifford gates, whose implementation via magic state distillation dominates the resource costs. While $T$-count minimization is well-studied, dedicated $CCZ$ factories shift the…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
We discuss the classical and quantum chaos of closed strings on a recently constructed charged confining holographic background. The confining background corresponds to the charged soliton, which is a solution of minimal $d=5$ gauged…
We calculate electrostatic potential landscapes for an external probe charge in the presence of a set of metallic islands. Our numerical calculation in three dimensions (3D)uses an efficient grid relaxation technique. The well-known…