The uphill turtle race: on short time nucleation probabilities

Details The uphill turtle race: on short time nucleation probabilities The uphill turtle race: on short time nucleation probabilities

2002-05-16

arxiv.org/abs/cond-mat/0205357v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, submitted to J. Stat. Phys

Scientific paper

The short time behavior of nucleation probabilities is studied by representing nucleation as diffusion in a potential well with escape over a barrier. If initially all growing nuclei start at the bottom of the well, the first nucleation time on average is larger than the inverse nucleation frequency. Explicit expressions are obtained for the short time probability of first nucleation. For very short times these become independent of the shape of the potential well. They agree well with numerical results from an exact enumeration scheme. For a large number N of growing nuclei the average first nucleation time scales as 1/\log N in contrast to the long-time nucleation frequency, which scales as 1/N. For linear potential wells closed form expressions are obtained for all times.

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