Avalanches of Bose-Einstein condensates in leaking optical lattices

We study the decay of an atomic Bose-Einstein condensate (BEC) population N(tau) from the leaking boundaries of an optical lattice (OL). For a rescaled interatomic interaction strength Lambda > Lambda(b), discrete breathers (DBs) are created that prevent the atoms from reaching the leaking boundaries. Collisions of other lattice excitations with the outermost DBs result in avalanches, i.e. steps in N(tau), which for a whole range of Lambda-values follow a scale-free distribution P(J = delta N) similar to 1/J(alpha). A theoretical analysis of the mixed phase space of the system indicates that 1 < alpha < 3, in agreement with our numerical findings.