Jim Lutsko

Jim Lutsko

he/him

My interests include Statistical Physics; Crystallization; Density Functional Theory, Simulation methods - particularly rare event techniques, Protein physics, Granular physics and Crystal Growth. I am based in the Physics of Complex Systems and Statistical Mechanics group at the Universite Libre de Bruxelles.

[089] Microscopic theory of anomalous diffusion based on particle interactions

We present a master equation formulation based on a Markovian random walk model that exhibits subdiffusion, classical diffusion, and superdiffusion as a function of a single parameter. The nonclassical diffusive behavior is generated by allowing for interactions between a population of walkers. At the macroscopic level, this gives rise to a nonlinear Fokker-Planck equation. The diffusive behavior is reflected not only in the mean squared displacement [〈r2(t)〉∼tγ with 0<γ≤1.5] but also in the existence of self-similar scaling solutions of the Fokker-Planck equation. We give a physical interpretation of sub- and superdiffusion in terms of the attractive and repulsive interactions between the diffusing particles and we discuss analytically the limiting values of the exponent γ. Simulations based on the master equation are shown to be in agreement with the analytical solutions of the nonlinear Fokker-Planck equation in all three diffusion regimes.

Recommended citation: James F. Lutsko and Jean Pierre Boon, "Microscopic theory of anomalous diffusion based on particle interactions", Phys. Rev. E, 88, 22108 (2013)
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