Scaling and universality in Brownian motion on a stochastic harmonic oscillator chain

Diffusion of a Brownian particle along a stochastic harmonic oscillator chain is investigated. In contrast to the usually discussed Brownian motion driven by Gaussian white noise, the particle at high temperatures performs long L??vy flights. At high temperatures T the diffusion coefficient scales as D ??? T 2+??, where the parameter ?? determine the average damping force oc 1/(T ??P) on the particle at large momentum P and at high temperature. The exponent ?? depends on the particle-chain interaction and chain properties. It is shown that the mean time t??f necessary to perform a flight of l lattice constant scales with l as t??f oc l2/3 at high temperatures and flight lengths. Last, the flight length probability distribution is found to decay as 1/l?? with the exponent ?? = 4/3 being universal, i.e., independent of the model parameters.

Automated summary

Diffusion of Brownian particle in a stochastic harmonic oscillator chain is studied. The particle exhibits long Lévy flights at high temperatures, in contrast to the usual Brownian motion driven by Gaussian white noise. The diffusion coefficient and the average damping force depend on the temperature, and the average flight time and flight length have a certain proportionality at high temperatures. The probability distribution of flight lengths decays with a universal exponent.