Exact expression for the diffusion propagator in a family of time-dependent anharmonic potentials

Details Exact expression for the diffusion propagator in a family of time-dependent anharmonic potentials Exact expression for the diffusion propagator in a family of time-dependent anharmonic potentials

1999-10-08

arxiv.org/abs/cond-mat/9910140v1

Physics

Condensed Matter

Statistical Mechanics

RevTex, 19 pgs. Accepted in Physical Review E

Scientific paper

10.1103/PhysRevE.60.2540

We have obtained the exact expression of the diffusion propagator in the time-dependent anharmonic potential $V(x,t)={1/2}a(t)x^2+b\ln x$. The underlying Euclidean metric of the problem allows us to obtain analytical solutions for a whole family of the elastic parameter a(t), exploiting the relation between the path integral representation of the short time propagator and the modified Bessel functions. We have also analyzed the conditions for the appearance of a non-zero flow of particles through the infinite barrier located at the origin (b<0).

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