Related papers: Combinatorial universality in three-speed ballisti…
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 consider the system of particles on a finite interval with pair-wise nearest neighbours interaction and external force. This model was introduced by Malyshev to study the flow of charged particles on a rigorous mathematical level. It is…
We discuss a particle system of 5 neighbors with two independent conserved densities. The mean momentum uniquely depends on a pair of the densities and a three-dimensional fundamental diagram is obtained. It shows the phase transition of…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…
We study the late-time dynamics of two particles confined in one spatial dimension and subject to two-body losses. The dynamics is exactly described by a non-Hermitian Hamiltonian that can be analytically studied both in the continuum and…
Introducing a general class of one-dimensional single-file systems (meaning that particle crossings are prohibited) of interacting hardcore particles with internal degrees of freedom (called charge), we exhibit a novel type of dynamical…
We study a far-from-equilibrium system of interacting particles, hopping between sites of a 1d lattice with a rate which increases with the number of particles at interacting sites. We find that clusters of particles, which initially…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
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…
Hyperuniform states are an efficient way to fill up space for disordered systems. In these states the particle distribution is disordered at the short scale but becomes increasingly uniform when looked at large scales. Hyperuniformity…
We investigate the static and the dynamic properties of an binary, equimolar, size-symmetric mixture of ultrasoft particles in the vicinity of the critical point of the system. Based on the generalized exponential potential (GEM) of order…
Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas is studied in the framework of an exact analytic approach. For an initial symmetric three-velocity distribution, the problem can be solved exactly and it is…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
Place an $A$-particle at each site of a graph independently with probability $p$ and otherwise place a $B$-particle. $A$- and $B$-particles perform independent continuous time random walks at rates $\lambda_A$ and $\lambda_B$, respectively,…
We consider an inhomogeneous symmetric simple exclusion process on a one-dimensional lattice with open boundary conditions. The time scale is continuous. Particles of different types arrive to the utmost left and the utmost right site. If a…
We study the Fleming-Viot particle process formed by N interacting continuous-time asymmetric random walks on the cycle graph, with uniform killing. We show that this model has a remarkable exact solvability, despite the fact that it is…
A collisionless continuous medium in Euclidean space is discussed, i.e. a continuum of free particles moving inertially, without interacting with each other. It is shown that the distribution density of such medium is weakly converging to…
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…
We study in further detail particle models displaying a boundary-induced absorbing state phase transition [Phys. Rev. E. {\bf 65}, 046104 (2002) and Phys. Rev. Lett. {\bf 100}, 165701 (2008)] . These are one-dimensional systems consisting…