Related papers: Evolution of states of an infinite particle system…
The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An…
An infinite system of point particles placed in $\mathds{R}^d$ is studied. Its constituents perform random jumps with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states…
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…
The study of quantum systems evolving from initial states to distinguishable, orthogonal final states is important for information processing applications such as quantum computing and quantum metrology. However, for most unitary evolutions…
We consider finite-volume approximations of Fokker-Planck equations on bounded convex domains in $\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker-Planck…
The moving puncture method is analyzed for a single, non-spinning black hole. It is shown that the puncture region is not resolved by current numerical codes. As a result, the geometry near the puncture appears to evolve to an infinitely…
The Marcus-Lushnikov process is a finite stochastic particle system in which each particle is entirely characterized by its mass. Each pair of particles with masses $x$ and $y$ merges into a single particle at a given rate $K(x,y)$. We…
In this work, we study a class of nonlocal-in-time kinetic models of incompressible dilute polymeric fluids. The system couples a macroscopic balance of linear momentum equation with a mezoscopic subdiffusive Fokker-Planck equation…
We generalize the spherical collapse model for the formation of bound objects to apply in a Universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact…
We study open quantum systems whose evolution is governed by a master equation of Kossakowski-Gorini-Sudarshan-Lindblad type and give a characterization of the convex set of steady states of such systems based on the generalized Bloch…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the…
The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a…
We derive a stochastic wave equation for an inflaton in an environment of an infinite number of fields. We study solutions of the linearized stochastic evolution equation in an expanding universe. The Fokker-Planck equation for the inflaton…
We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of robots, feeling each other in terms of their distance,…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
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…
The work continues the author's many-year research in theory of maximal branching processes, which are obtained from classical branching processes by replacing the summation of descendant numbers with taking the maximum. One can say that in…
General birth-and-death as well as hopping stochastic dynamics of infinite multicomponent particle systems in the continuum are considered. We derive the corresponding evolution equations for quasi-observables and correlation functions. We…
We consider a branching particle model in which particles move inside a Euclidean domain according to the following rules. The particles move as independent Brownian motions until one of them hits the boundary. This particle is killed but…