Poincaré recurrence and spectral cascades in three-dimensional quantum turbulence.

The time evolution of the ground state wave function of a zero-temperature Bose-Einstein condensate (BEC) gas is well described by the Hamiltonian Gross-Pitaevskii (GP) equation. Using a set of appropriately interleaved unitary collision-stream operators, a qubit lattice gas algorithm is devised, which on taking moments, recovers the Gross-Pitaevskii (GP) equation under diffusion ordering (time scales as length(2)). Unexpectedly, there is a class of initial states whose Poincaré recurrence time is extremely short and which, as the grid resolution is increased, scales with diffusion ordering (and not as length(3)).