Persistence exponent of the diffusion equation in epsilon dimensions

Details Persistence exponent of the diffusion equation in epsilon dimensions Persistence exponent of the diffusion equation in epsilon dimensions

1999-11-10

arxiv.org/abs/cond-mat/9911138v1

Physica A 277 (2000) 124

Physics

Condensed Matter

Statistical Mechanics

4 pages, latex, no figures

Scientific paper

10.1016/S0378-4371(99)00509-9

We consider the d-dimensional diffusion equation for a field phi(x,t) with
random initial condition, and observe that, when appropriately scaled, phi(0,t)
is Gaussian and Markovian in the limit d->0. This leads via the Majumdar-Sire
perturbation theory to a small-d expansion for the persistence exponent
theta(d). We find theta(d) = d/4 - 0.12065...d^{3/2} + ...

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