  The evolution of the ground state wave function of a zero-temperature
Bose-Einstein condensate (BEC) is well described by the Hamiltonian
Gross-Pitaevskii (GP) equation. Using a set of appropriately interleaved
unitary collision-streaming operators, a quantum lattice gas algorithm is
devised which on taking moments recovers the Gross-Pitaevskii (GP) equation in
diffusion ordering (time scales as square of length). Unexpectedly, there is a
class of initial conditions in which their Poincare recurrence is extremely
short. Further it is shown that the Poincare recurrence time scales with
diffusion ordering as the the grid is increased. The spectral results of Yepez
et.al. [1] for quantum turbulence are corrected and it is found that it is the
compressible kinetic energy spectrum that exhibits the 3 cascade regions: a
small k classical Kolmogorov k^(-5/3) spectrum, a steep semi-classical cascade
region, and a large k quantum Kelvin wave cascade k^(-3) spectrum. The
incompressible kinetic energy spectrum exhibits basically a single cascade
power law of k^(-3). For winding number 1 linear vortices it is also shown that
there is an intermittent loss of Kelvin wave cascade with its signature seen in
the time evolution of the kinetic energy, the loss of the k^(-3) spectrum in
the incompressible kinetic energy spectrum as well as the minimization of the
vortex core isosurfaces that inhibits the Kelvin wave cascade.
