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We present a new approach to the analysis of entanglement in smooth bipartite continuous-variable states. One or both parties perform projective filterings via preliminary measurements to determine whether the system is located in some…
We survey recent results on first-passage processes in unbounded cones and their applications to ordering of particles undergoing Brownian motion in one dimension. We first discuss the survival probability S(t) that a diffusing particle, in…
We study the following microscopic model of infection or epidemic reaction: red and blue particles perform independent nearest-neighbor continuous-time symmetric random walks on the integer lattice $\mathbb{Z}$ with jump rates $D_R$ for red…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…
Let $X,Y$ be finite sets, $r,s,h, \lambda \in \mathbb{N}$ with $s\geq r, X\subsetneq Y$. By $\lambda \binom{X}{h}$ we mean the collection of all $h$-subsets of $X$ where each subset occurs $\lambda$ times. A coloring of…
We consider a simple one dimensional quantum system consisting of a heavy and a light particle interacting via a point interaction. The initial state is chosen to be a product state, with the heavy particle described by a coherent…
We study the early time and coarsening dynamics in the Light-Heavy model, a system consisting of two species of particles ($light$ and $heavy$) coupled to a fluctuating surface (described by tilt fields). The dynamics of particles and tilts…
Possible phase transition of strongly interacting matter from hadron to a quark-gluon plasma state have in the past received considerable interest. The clustering of color sources provides a framework of the the partonic interactions in the…
In computational models of particle packings with periodic boundary conditions, it is assumed that the packing is attached to exact copies of itself in all possible directions. The periodicity of the boundary then requires that all of the…
We consider a system of charged particles moving on the real line driven by electrostatic interactions. Since we consider charges of both signs, collisions might occur in finite time. Upon collision, some of the colliding particles are…
We review two general criteria for deciding whether a pure bipartite quantum state describing a system of two identical particles is entangled or not. The first one considers the possibility of attributing a complete set of objective…
Motivated by a variety of online matching platforms, we consider demand and supply units which are located i.i.d. in [0,1]^d, and each demand unit needs to be matched with a supply unit. The goal is to minimize the expected average distance…
We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node…
We simulated random walk of rectangular particles on a square lattice with periodic boundary conditions. Two kind of particles were investigated, viz., so-called `blind' and `myopic' particles. We found that steady state patterns occurred…
We study flocking in one dimension, introducing a lattice model in which particles can move either left or right. We find that the model exhibits a continuous nonequilibrium phase transition from a condensed phase, in which a single `flock'…
The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our…
In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains. For this goal, we consider a system of either two…
We present a new numerical model to simulate settling trajectories of discretized individual or a mixture of particles of different geometrical shapes in a quiescent fluid and their flow trajectories in a flowing fluid. Simulations unveiled…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
We describe a new mechanism of dark matter production in the early Universe, based on the dynamics of a first order phase transition. We assume that dark matter particles acquire mass during the phase transition, making it energetically…