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The goal of this thesis is to obtain new exact results for models of active particles in one dimension, focusing on two different aspects: their behavior in the presence of long-range interactions and their first-passage properties. In the…
Numerical models indicate that collective animal behaviour may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely…
We consider a system of particles lined up on a finite interval with Coulomb 3-dimensional interactions between close neighbours, i.e. only a few other neighbours apart. This model was introduced by Malyshev (2015) to study the flow of…
The corrections for two pion correlations due to electromagnetic final state interactions at high secondary multiplicities are investigated. It is shown that these result in a noticeable deviation from the standard Gamov factor. This…
We augment the time-linear formulation of the Kadanoff-Baym equations for systems of interacting electrons and quantized phonons or photons with the $G\widetilde{W}$ approximation, the Coulomb interaction $\widetilde{W}$ being dynamically…
We study the difference between on site Hubbard and long range Coulomb repulsions for two interacting particles in a disordered chain. While Hubbard repulsion can only yield weak critical chaos with intermediate spectral statistics, Coulomb…
A model of the mean-field interacting boson gas trapped by a weak harmonic potential is considered by the \textit{boson random point fields} methods. We prove that in the Weak Harmonic Trap (WHT) limit there are two phases distinguished by…
The spatial structure of transmitters in wireless networks plays a key role in evaluating the mutual interference and hence the performance. Although the Poisson point process (PPP) has been widely used to model the spatial configuration of…
In this paper we continue the investigation of the lattice gas model. The main improvement is that we use two strengths for bonds: one between like particles and another between unlike particle to implement the isospin-dependence of nuclear…
We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects…
We derive and evaluate expressions for the frictional Coulomb drag between disordered two-dimensional electron gas layers. Our derivation is based on the memory-function formalism and the expression for the drag reduces to previously known…
We study the phase behavior and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive model (YRPM) of oppositely charged hard spheres with diameter s using Monte Carlo simulations. We determine the gas-liquid and…
We present a detailed Monte Carlo study of correlations in an interacting two-dimensional Bose gas. The data for one-particle density matrix in coordinate representation are compared to the results for the local many-particle density…
The dynamics of a globally neutral system of diffusing Coulomb charges in two dimensions, driven by an applied electric field, is studied in a wide temperature range around the Berezinskii-Kosterlitz-Thouless transition. I argue that the…
We consider a classical system of n charged particles in an external confining potential, in any dimension d larger than 2. The particles interact via pairwise repulsive Coulomb forces and the coupling parameter scales like the inverse of n…
We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the…
We provide a Poisson approximation result for dependent thinnings of Gibbs point processes as well as qualitative and quantitative central limit theorems for geometric functionals of Gibbs point processes in increasing observation windows.…
The edge density and temperature of tokamak plasmas are strongly correlated with energy and particle confinement and their quantification is fundamental to understanding edge dynamics. These quantities exhibit behaviours ranging from sharp…
Molecular dynamics simulations of two-dimensional soft Yukawa fluids are performed to analyze the effect that the range of interaction has on coexisting densities and line tension. The attractive one-component fluid and equimolar mixtures…
For the two-dimensional one-component Coulomb plasma, we derive an asymptotic expansion of the free energy up to order $N$, the number of particles of the gas, with an effective error bound $N^{1-\kappa}$ for some constant $\kappa > 0$.…