Diffusion coefficient scaling of a free Brownian particle with velocity-dependent damping.

An analytical expression for the diffusion coefficient D of a free Brownian particle with velocity-dependent damping γ(v) is derived from the Green-Kubo formula. A special case of damping that decreases monotonically with velocity is considered. At high temperature T, the diffusion coefficient is found to exhibit two scaling types: (i) for a power-law decrease of damping with the particle's kinetic energy, γ(v)∝1/v^{2α}, it scales as D∝T^{α+1}; (ii) for a Gaussian function γ(v), it diverges at temperatures above a critical value T_{c} and behaves as D∝1/sqrt[T_{c}-T] at T slightly below T_{c}.

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 Lévy flights. At high temperatures T the diffusion coefficient scales as D∼T^{2+α}, where the parameter α determine the average damping force ∝1/(T^{α}P) on the particle at large momentum P and at high temperature.

Origin of dispersionless transport in spite of thermal noise.

The "dispersionless transport" of a weakly damped Brownian particle in a tilted periodic potential is defined by (i) a plateau of the particle's coordinate dispersion extending over a very broad time interval and (ii) by the impossibility to measure the diffusion coefficient within this plateau region. While the first part of this definition has been explained in the literature, the second part has been thought to follow from (i). Here, the impossibility to measure the diffusion coefficient is shown to be actually due to the wild fluctuations of the dispersion itself in the plateau region.