Related papers: Statistical density of particles in one dimensiona…
We investigate a one-dimensional system of $N$ particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the $N$ particles do…
We study a one-dimensional gas of $N$ Brownian particles that diffuse independently, but are {\it simultaneously} reset to the origin at a constant rate $r$. The system approaches a non-equilibrium stationary state (NESS) with long-range…
We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…
We investigate systems of self-propelled particles with alignment interaction. Compared to previous work, the force acting on the particles is not normalized and this modification gives rise to phase transitions from disordered states at…
Particles have been used for more than a decade to visualize and study the dynamics of quantum vortices in superfluid helium. In this work we study how the dynamics of a collection of particles set inside a vortex reflects the motion of the…
In this paper, we study the probability distribution of the observable $s = (1/N)\sum_{i=N-N'+1}^N x_i$, with $1 \leq N' \leq N$ and $x_1<x_2<\cdots< x_N$ representing the ordered positions of $N$ particles in a $1d$ one-component plasma,…
We consider $N$ classical particles interacting via the Coulomb potential in spatial dimension $d$ and in the presence of an external trap, at equilibrium at inverse temperature $\beta$. In the large $N$ limit, the particles are confined…
We consider the statistical properties of the gravitational field F in an infinite one-dimensional homogeneous Poisson distribution of particles, using an exponential cut-off of the pair interaction to control and study the divergences…
We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability…
We investigate the work fluctuations in an overdamped non-equilibrium process that is stopped at a stochastic time. The latter is characterized by a first passage event that marks the completion of the non-equilibrium process. In…
We study equilibrium states of an infinite system of interacting particles in a Euclidean space. The particles bear `unbounded' spins with a given symmetric a priori distribution. The interaction between the particles is pairwise and splits…
We present a complete theory for the full particle statistics of the positions of bulk and extremal particles in a one-dimensional Coulomb Gas (CG) with an arbitrary potential, in the typical and large deviations regimes. Typical…
The analytical probability distribution of finite systems obeying Bose-Einstein statistics in one, two, and three dimensions are investigated by using a canonical ensemble approach. Starting from the canonical partition function of the…
Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space…
The dynamics of a tagged particle immersed in a fluid of particles of the same size but different mass is studied when the system is confined between two hard parallel plates separated a distance smaller than twice the diameter of the…
We perform numerical simulations of a simple model of one-patch colloidal particles to investigate: (i) the behavior of the gas-liquid phase diagram on moving from a spherical attractive potential to a Janus potential and (ii) the…
We consider a finite or countable collection of one-dimensional Brownian particles whose dynamics at any point in time is determined by their rank in the entire particle system. Using Transportation Cost Inequalities for stochastic…
We consider a lattice model in which a tracer particle moves in the presence of randomly distributed immobile obstacles. The crowding effect due to the obstacles interplays with the quasi-confinement imposed by wrapping the lattice onto a…