Related papers: On particles in equilibrium on the real line
Coulomb law is one of the fundamental laws in Physics. It describes the magnitude of the electrostatic force between two electric charges. Counterintuitively the repulsion force between two equal electric charges in a vacuum, stated by the…
Controllable nonlinear quantum interactions are a much sought after target for modern quantum technologies. They are typically difficult and costly to engineer for bespoke purposes. However controllable nonlinearities may have always been…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…
We study a physical system of $N$ interacting particles in $\mathbb{R}^d$, $d\geq1$, subject to pair repulsion and confined by an external field. We establish a large deviations principle for their empirical distribution as $N$ tends to…
We discuss the basic principles of a self-organization of a finite number of charged particles interacting via the 1/r Coulomb potential in a disk geometry. Our approach is based on the cyclic symmetry and periodicity of the Coulomb…
We introduce a simple dynamical rule in which each particle locates a particle that is farthest from it and moves towards it. Repeated application of this algorithm results in the formation of unusual dynamical patterns: during the process…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…
Quasi one-dimensional systems are systems of particles in domains which are of infinite extent in one direction and of uniformly bounded size in all other directions, e.g. on a cylinder of infinite length. The main result proven here is…
Within the framework of the hypothesis offered by authors about a complex-valued nature of physical quantities the stability of basic equations of the classical physics concerning complex-valued perturbations of parameters and boundary…
The $n$-body problem with a purely repulsive Coulomb interaction is considered. It is shown that for large times $t$ the distance between any two particles grows linearly in $t$. The trajectory of each particle is asymptotically a straight…
Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some…
The possibility that like-charges can attract each other under the mediation of mobile counterions is by now well documented experimentally, numerically, and analytically. Yet, obtaining exact results is in general impossible, or restricted…
We discuss the stability of three- and four-particle system interacting by pure Coulomb interactions, as a function of the masses and charges of the particles. We present a certain number of general properties which allow to answer a…
It is shown that an ensemble of particles with tripolar (colour) charges will necessarily cohere in a hierarchy of structures, from simple clusters and strings to complex aggregates and cyclic molecule-like structures. The basic…
At time zero, there are $N$ identical point particles in the line (1D) which are characterized by their positions and velocities. Both values are given randomly and independently from each other, with arbitrary probability densities. Each…
A system of identical particles interacting through an isotropic potential that allows for two preferred interparticle distances is numerically studied. When the parameters of the interaction potential are adequately chosen, the system…
The nonequilibrium phase transition in a system of diffusing, coagulating particles in the presence of a steady input and evaporation of particles is studied. The system undergoes a transition from a phase in which the average number of…
We present a novel form of relativistic quantum mechanics and demonstrate how to solve it using a recently derived unitary perturbation theory, within partial wave analysis. The theory is tested on a relativistic problem, with two spinless,…
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…