Related papers: Mean-field limits of Riesz-type singular flows
We consider Mckean-Vlasov type stochastic differential equations with multiplicative noise arising from the random vortex method. Such an equation can be viewed as the mean-field limit of interacting particle systems with singular…
Mean field theory for the time evolution of quantum meson fields is studied in terms of the functional Schroedinger picture with a time-dependent Gaussian variational wave functional. We first show that the equations of motion for the…
We investigate dynamics of deformable self-propelled particles with a repulsive interaction whose magnitude depends on the relative direction of elongation of a pair of particles. A collective motion of the particles appears in two…
There is a wide-spread belief in the literature on Bose-Einstein condensation of interacting atoms that all variants of mean-field theory incorrectly describe the condensation phase transition, exhibiting, instead of the necessary…
We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high…
We consider a system consisting of $n$ particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle ``jumps forward'' at some time points, with the instantaneous rate…
We investigate the dynamics of overdamped $D$-dimensional systems of particles repulsively interacting through short-ranged power-law potentials, $V(r)\sim r^{-\lambda}\;(\lambda/D>1)$. We show that such systems obey a non-linear diffusion…
We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein distance. The two equations are coupled through a…
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated to the probability density of oscillators with a given…
We obtain new asymptotic results about systems of $ N $ particles governed by Riesz interactions involving $ k $-nearest neighbors of each particle as $N\to\infty$. These results include a generalization to weighted Riesz potentials with…
We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a…
We study the large field limit in Schr\"odinger equations with magnetic vector potentials describing translationally invariant $B$-fields with respect to the $z$-axis. In a first step, using regular perturbation theory, we derive an…
We introduce a system of self-propelled agents (active Brownian particles) with velocity alignment in two spatial dimensions and derive a mean-field theory from the microscopic dynamics via a nonlinear Fokker-Planck equation and a moment…
Understanding strongly correlated systems driven out of equilibrium is a challenging task necessitating the simultaneous treatment of quantum mechanics,dynamical constraints and strong interactions. A Mott insulator subjected to a uniform…
In this paper we consider the multispecies stirring process on the discrete torus. We prove a large deviation principle for the trajectory of the vector of densities of the different species. The technique of proof consists in extending the…
We consider the dynamical evolution of two planets orbiting in the vicinity of a first order mean motion reso- nance while simultaneously undergoing eccentricity damping and convergent migration. Following Goldreich & Schlichting (2014), we…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
Consider a finite system of diffusing particles coupled through a reactive boundary. Each particle is reflected, but may react with the boundary according to a killing mechanism which depends on the current reactivity of the boundary and…
We present exact solutions for the non-equilibrium steady states of a class of dissipative spinless fermionic systems with arbitrary Hamiltonian pairing terms, global charging energy interactions, and uniform single particle loss on every…
Dissipation and fluctuations of one-body observables in heavy-ion reactions around the Coulomb barrier are investigated with a microscopic stochastic mean-field approach. By projecting the stochastic mean-field dynamics on a suitable…