Related papers: Optimal lattice configurations for interacting spa…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic,convex-repulsive…
We consider a lattice gas interacting by the exclusion rule in the presence of a random field given by i.i.d. bounded random variables in a bounded domain in contact with particles reservoir at different densities. We show, in dimensions $d…
We show that the timed Dicke states of a collection of three-level atoms can form a tight-binding lattice in momentum space. This lattice, coined the superradiance lattice (SL), can be constructed based on electromagnetically induced…
The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positions and featuring the interplay of two-body atomic…
A theoretical approach was developed for an exact numerical description of a pair of ultracold atoms interacting via a central potential that are trapped in a three-dimensional optical lattice. The coupling of center-of-mass and…
Contact interactions can be used to describe a system of particles at unitarity, contribute to the leading part of nuclear interactions and are numerically non-trivial because they require a proper regularization and renormalization scheme.…
We study the statistics of the force felt by a particle in the class of spatially correlated distribution of identical point-like particles, interacting via a $1/r^2$ pair force (i.e. gravitational or Coulomb), and obtained by randomly…
We study ballistic aggregation on a two dimensional square lattice, where particles move ballistically in between momentum and mass conserving coalescing collisions. Three models are studied based on the shapes of the aggregates: in the…
We study the impact of classical short-range nonlinear interactions on transport in lattices with no dispersion. The single particle band structure of these lattices contains flat bands only, and cages non-interacting particles into compact…
Correlation of interacting particles is studied in their dynamics and localization in ideal and disordered lattice systems with the help of numerical tools. Both 1D and 2D systems are considered. In 1D lattices with long-range hopping,…
We study a system of dipolar molecules confined in a two-dimensional trap and subject to an optical square lattice. The repulsive long-range dipolar interaction $D/r^3$ favors an equilateral triangular arrangement of the molecules, which…
By adjusting the tunnelling couplings over longer than nearest neighbor distances it is possible in discrete lattice models to reproduce the properties of the lowest energy band of a real, continuous periodic potential. We propose to…
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…
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…
We present the results of numerical calculations of the groundstates of weakly-interacting Bose-Einstein condensates containing large numbers of vortices. Our calculations show that these groundstates appear to be close to uniform…
We investigate the macroscopic dynamics of sets of an arbitrary finite number of weakly amplitude-modulated pulses in a multidimensional lattice of particles. The latter are assumed to exhibit scalar displacement under pairwise,…
The lattice dynamics of coesite has been studied by a combination of diffuse x-ray scattering, inelastic x-ray scattering and an ab initio lattice dynamics calculation. The combined technique gives access to the full lattice dynamics in…
We investigate the ground state of a one-dimensional lattice system that hosts two different kinds of excitations (species) which interact with a power-law potential. Interactions are only present between excitations of the same kind and…
Particles interacting through long-range attraction and short-range repulsion given by power-laws have been widely used to model physical and biological systems, and to predict or explain many of the patterns they display. Apart from rare…