Power spectrum of mass and activity fluctuations in a sandpile

Details Power spectrum of mass and activity fluctuations in a sandpile Power spectrum of mass and activity fluctuations in a sandpile

2012-03-27

arxiv.org/abs/1203.5912v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 10 figures

Scientific paper

We consider a directed abelian sandpile on a strip of size $2\times n$, driven by adding a grain randomly at the left boundary after every $T$ time-steps. We establish the exact equivalence of the problem of mass fluctuations in the steady state and the number of zeroes in the ternary-base representation of the position of a random walker on a ring of size $3^n$. We find that while the fluctuations of mass have a power spectrum that varies as $1/f$ for frequencies in the range $ 3^{-2n} \ll f \ll 1/T$, the activity fluctuations in the same frequency range have a power spectrum that is linear in $f$.

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