相关论文: Crystallization to the square lattice for a two-bo…
We devise a new technique to prove two-dimensional crystallization results in the square lattice for finite particle systems. We apply this strategy to energy minimizers of configurational energies featuring two-body short-ranged particle…
We investigate two-dimensional crystallization phenomena, i.e. minimality of a lattice's patch for interaction energies, with pair potentials of type $(x,y)\mapsto V(\|x-y\|)$ where $\|\cdot\|$ is an arbitrary norm on $\mathbb{R}^2$ and…
We present two-dimensional crystallization results in the square lattice for finite particle systems consisting of two different atomic types. We identify energy minimizers of configurational energies featuring two-body short-ranged…
We consider finite discrete systems consisting of two different atomic types and investigate ground-state configurations for configurational energies featuring two-body short-ranged particle interactions. The atomic potentials favor some…
We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or equivalently on the set of atomic measures. It consists of…
We address finite crystallization in two dimensions in the presence of a flat crystalline substrate. Particles interact through short-range two- and three-body potentials favoring local square-lattice arrangements. An additional interaction…
We address the question of whether three-dimensional crystals are minimizers of classical many-body energies. This problem is of conceptual relevance as it presents a significant milestone towards understanding, on the atomistic level,…
It is shown that at least one particle is bound in the $N$-particle semi-relativistic Pauli-Fierz model with negative potential $V(\bx)$. It is assumed that the particles have no spin and obey the Bose or Boltzmann statistics, and the one…
An approximate quantum-mechanical two-body equation for spinless particles incorporating relativistic kinematics is derived. The derivation is based on the relativistic energy-momentum relation $mc^{2}+\epsilon =…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
We study a system of particles in two dimensions interacting via a dipolar long-range potential $D/r^3$ and subject to a square-lattice substrate potential $V({\bf r})$ with amplitude $V$ and lattice constant $b$. The isotropic interaction…
We consider a 3--body system in $\mathbb{R}^3$ with non--positive potentials and non--negative essential spectrum. Under certain requirements on the fall off of pair potentials it is proved that if at least one pair of particles has a zero…
Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between…
We report on a study of a finite system of classical confined particles in two-dimensions in the presence of a uniform magnetic field and interacting via a two-body repulsive potential. We develop a simple analytical method of analysis to…
Pairing of valence electrons can lead to energy minimization of a crystal. It can be proved by use of representation of the valence electrons as plane waves in periodic potential of the crystal.
We present a general method for deriving the energy shift of an interacting system of $N$ spinless particles in a finite volume. To this end, we use the nonrelativistic effective field theory (NREFT), and match the pertinent low-energy…
We study the ground state of a system of spinless electrons interacting through a screened Coulomb potential in a lattice ring. By using analytical arguments, we show that, when the effective interaction compares with the kinetic energy,…
The ground-state of two-dimensional (2D) systems of classical particles interacting pairwisely by the generalized Lennard-Jones potential is studied. Taking the surface area per particle $A$ as a free parameter and restricting oneself to…
We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying…
The ground state energy per particle of a dilute, homogeneous, two-dimensional Bose gas, in the thermodynamic limit is shown rigorously to be $E_0/N = (2\pi \hbar^2\rho /m){|\ln (\rho a^2)|^{-1}}$, to leading order, with a relative error at…