Related papers: Dynamical clusters of infinite particle dynamics
We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense.…
The dynamics of open quantum systems (i.e., of quantum systems interacting with an uncontrolled environment) forms the basis of numerous active areas of research from quantum thermodynamics to quantum computing. One approach to modeling…
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…
We consider a two particle system on a star graph with $\delta$-function interaction. A class of eigensolutions is described which are constructed from appropriate one particle solutions, and hence are parametrised by two momenta. These…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force…
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
Let a finite set of interacting particles be given, together with a symmetry Lie group $G$. Here we describe all possible dynamics that are jointly equivariant with respect to the action of $G$. This is relevant e.g., when one aims to…
We investigate the dynamics of two interacting diffusing particles in an infinite effectively one dimensional system; the particles interact through a step-like potential of width b and height phi_0 and are allowed to pass one another. By…
We analyse the entanglement dynamics of the two particles interacting through gravity in the recently proposed experiments aiming at testing quantum signatures for gravity [Phy. Rev. Lett 119, 240401 & 240402 (2017)]. We consider the open…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
Continuous interpolates are described for classical dynamical systems defined by discrete time-steps. Functional conjugation methods play a central role in obtaining the interpolations. The interpolates correspond to particle motion in an…
Does the interaction graph of a finite dynamical system can force this system to have a "complex" dynamics ? In other words, given a finite interval of integers $A$, which are the signed digraphs $G$ such that every finite dynamical system…
An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…
Statistical mechanics explains the properties of macroscopic phenomena based on the movements of microscopic particles such as atoms and molecules. Movements of microscopic particles can be represented by large-scale interacting systems. In…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
A periodic temporal graph, in its simplest form, is a graph in which every edge appears exactly once in the first $\Delta$ time steps, and then it reappears recurrently every $\Delta$ time steps, where $\Delta$ is a given period length.…