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PubMed2003

Hopping in a supercooled Lennard-Jones liquid: metabasins, waiting time distribution, and diffusion.

We investigate the jump motion among potential energy minima of a Lennard-Jones model glass former by extensive computer simulation. From the time series of minima energies, it becomes clear that the energy landscape is organized in superstructures called metabasins. We show that diffusion can be pictured as a random walk among metabasins, and that the whole temperature dependence resides in the distribution of waiting times. The waiting time distribution exhibits algebraic decays: tau(-1/2) for very short times and tau(-alpha) for longer times, where alpha approximately 2 near T(c). We demonstrate that solely the waiting times in the very stable basins account for the temperature dependence of the diffusion constant.

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PubMed2003

Long range hops and the pair annihilation reaction A+A-->0: renormalization group and simulation.

A simple example of a nonequilibrium system for which fluctuations are important is a system of particles which diffuse and may annihilate in pairs on contact. The renormalization group can be used to calculate the time dependence of the density of particles, and provides both an exact value for the exponent governing the decay of particles and an epsilon expansion for the amplitude of this power law. When the diffusion is anomalous, as when the particles perform Lévy flights, the critical dimension depends continuously on the control parameter for the Lévy distribution. The epsilon expansion can then become an expansion in a small parameter. We present the renormalization group calculation and compare these results with those of a simulation.

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PubMed2005

Hopping models of charge transfer in a complex environment: coupled memory continuous-time random walk approach.

Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard kinetic approach in description of the system is addressed either in the framework of continuous-time random walks (CTRWs) or fractional diffusion. In this paper the power of the CTRW approach is illustrated by use of the probabilistic formalism and limit theorems that allow one to rigorously predict the limiting distributions of the paths traversed by charges and to derive effective relaxation properties of the entire system of interest. In particular, the standard CTRW scenario is generalized to a new class of coupled memory CTRWs that effectively can lead to the well known Havriliak-Negami response. Application of the method is discussed for nonexponential electron-transfer processes controlled by dynamics of the surrounding medium.

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