Related papers: Exact Stochastic Mean-Field dynamics
This paper addresses congested transport, which can be described, at macroscopic scales, by a continuity equation with a pressure variable generated from the hard-congestion constraint (maximum value of the density). The main goal of the…
The dynamics of the expansion of a Lennard-Jones system, initially confined at high density and subsequently expanding freely in the vacuum, is confronted to an expanding statistical ensemble, derived in the diluted quasi-ideal Boltzmann…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which…
We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of…
We study some systems of interacting fields whose evolution is given by some singular stochastic partial differential equations of mean field type. We provide a robust setting for their study and prove a well-posedness result and a…
A stochastic system under the influence of a stochastic environment is correlated with both present and future states of the environment. Such a system can be seen as implicitly implementing a predictive model of future environmental…
An exact stochastic model for the thermalisation of quantum states is proposed. The model has various physically appealing properties. The dynamics are characterised by an underlying Schrodinger evolution, together with a nonlinear term…
We study statistical properties of a one dimensional infinite system of coalescing particles. Each particle moves with constant velocity $\pm v$ towards its closest neighbor and merges with it upon collision. We propose a mean-field theory…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
In the paper we consider the problem of the rigorous description of the kinetic evolution in the presence of initial correlations of quantum large particle systems. One of the developed approaches consists in the description of the…
Nonperturbative dynamics of quantum fields out of equilibrium is often described by the time evolution of a hierarchy of correlation functions, using approximation methods such as Hartree, large N, and nPI-effective action techniques. These…
We study the mean-field theory, and the properties of fluctuations, in an out of equilibrium Bose-Fermi system, across the transition to a quantum condensed phase. The system is driven out of equilibrium by coupling to multiple baths, which…
We review recent progress in the nonequilibrium dynamics of thermally isolated many-body quantum systems, evolving with an ensemble of Hamiltonians as opposed to deterministic evolution with a single time-dependent Hamiltonian. Such…
We propose a novel model for a glass-forming liquid which allows to switch in a continuous manner from a standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducing k additional particle-particle…
The exact equations of motion for microscopic density of classical particles number with account of inter-particle interactions and external field in closed form are derived. An integral equation for equilibrium distributions of the…
We study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove…
The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence. As a second main result, a…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…