Dynamics of the Desai-Zwanzig model in multi-well and random energy landscapes

Abstract

We analyze a variant of the Desai-Zwanzig model [J. Stat. Phys. {\bf 19}1-24 (1978)]. In particular, we study stationary states of the mean field limit for a system of weakly interacting diffusions moving in a multi-well potential energy landscape, coupled via a Curie-Weiss type (quadratic) interaction potential. The location and depth of the local minima of the potential are either deterministic or random. We characterize the structure and nature of bifurcations and phase transitions for this system, by means of extensive numerical simulations and of analytical calculations for an explicitly solvable model. Our numerical experiments are based on Monte Carlo simulations, the numerical solution of the time-dependent nonlinear Fokker-Planck (McKean-Vlasov equation), the minimization of the free energy functional and a continuation algorithm for the stationary solutions.

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Cited by in corpus (5)

• Classical dynamical density functional theory: from fundamentals to applications
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• Dimension reduction of noisy interacting systems
• Response Theory Identifies Reaction Coordinates and Explains Critical Phenomena in Noisy Interacting Systems
• Mean-field limits for interacting diffusions with colored noise: phase transitions and spectral numerical methods