Dynamical transition for a particle in a squared Gaussian potential

Details Dynamical transition for a particle in a squared Gaussian potential Dynamical transition for a particle in a squared Gaussian potential

2006-10-17

arxiv.org/abs/cond-mat/0610470v1

J. Phys. A: Math. Theor. 40, 919 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

18 pages, 4 figures .eps, JPA style

Scientific paper

10.1088/1751-8113/40/5/004

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by $\psi= \phi^2/2$ where $\phi$ is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.

Affiliated with

Also associated with

No associations

Rating

Dynamical transition for a particle in a squared Gaussian potential does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dynamical transition for a particle in a squared Gaussian potential, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamical transition for a particle in a squared Gaussian potential will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-390267