Continuum Theory with Memory for Avalanches in Self-Organized Criticality

Details Continuum Theory with Memory for Avalanches in Self-Organized Criticality Continuum Theory with Memory for Avalanches in Self-Organized Criticality

1996-03-12

arxiv.org/abs/cond-mat/9603085v1

Physics

Condensed Matter

12 pages, Revtex, uuencoded, (2 ps-figures included)

Scientific paper

The propagator for the activity in a broad class of self-organized critical models obeys an imaginary-time Schr\"odinger equation with a nonlocal, history-dependent potential representing memory. Consequently, the probability for an avalanche to spread beyond a distance $r$ in time $t$ has an anomalous tail $\exp{[-C\,x^{1/(D-1)}]}$ for $x=r^D/t \gg 1$ and $D>2$, indicative of glassy dynamics. The theory is verified for an exactly solvable model, where $D=4$ and $C=3/4$, and for the Bak-Sneppen model where it is tested numerically.

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