Power spectrum of mass and activity fluctuations in a sandpile
Abstract
We consider a directed abelian sandpile on a strip of size
2×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
≪f≪1/T
, the activity fluctuations in the same frequency range have a power spectrum that is linear in
f
.