Related papers: Longtime and chaotic dynamics in microscopic syste…
Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly…
The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when particles undergo instantaneous interactions such as collisions,…
We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…
We study the long time behavior of second order particle systems interacting through global Lipschitz kernels. Combining hypocoercivity method in [37] and relative entropy method in [25], we are able to overcome the degeneracy of diffusion…
We consider a long-range interacting system of $N$ particles moving on a spherical surface under an attractive Heisenberg-like interaction of infinite range, and evolving under deterministic Hamilton dynamics. The system may also be viewed…
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…
We study the Langevin dynamics of diffusive particles with regular pairwise interactions under mean-field scaling. By approximating empirical distributions with conditional distributions, we establish coercive and contractive properties for…
In a recent letter [Europhys. Lett. 95, 13001 (2011)] the question of whether the density of a time-dependent quantum system determines its external potential was reformulated as a fixed point problem. This idea was used to generalize the…
We study the stability in finite times of the trajectories of interacting particles. Our aim is to show that in average and uniformly in the number of particles, two trajectories whose initial positions in phase space are close, remain…
We study the behavior of systems in which the interaction contains a long-range component that does not dominate the critical behavior. Such a component is exemplified by the van der Waals force between molecules in a simple liquid-vapor…
We develop an instanton approach to the non-equilibrium dynamics in one-dimensional random environments. The long time behavior is controlled by rare fluctuations of the disorder potential and, accordingly, by the tail of the distribution…
We investigate the stationary and dynamic properties of the celebrated Nos\'e-Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
We consider a $N$-particle interacting particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation…
We study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behaviour of the Brownian particle…
We describe the macroscopic behaviour of a particle system with long-range interactions. We describe conditions on the interaction strength in dependency of the distance of the particles, such that the scaling limit of the particle system…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
We consider the asymptotic behaviour of the fluctuation process for large stochastic systems of interacting particles driven by both idiosyncratic and common noise with an interaction kernel \(k \in L^2(\R^d) \cap L^\infty(\R^d)\). Our…
Many systems exhibit a phase where the order parameter is spatially modulated. These patterns can be the result of a frustration caused by the competition between interaction forces with opposite effects. In all models with local…
We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases:…