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The evolution of the ground state wave function of a zero-temperatureBose-Einstein condensate (BEC) is well described by the HamiltonianGross-Pitaevskii (GP) equation. Using a set of appropriately interleavedunitary collision-streaming operators, a quantum lattice gas algorithm isdevised which on taking moments recovers the Gross-Pitaevskii (GP) equation indiffusion ordering (time scales as square of length). Unexpectedly, there is aclass of initial conditions in which their Poincare recurrence is extremelyshort. Further it is shown that the Poincare recurrence time scales withdiffusion ordering as the the grid is increased. The spectral results of Yepezet.al. [1] for quantum turbulence are corrected and it is found that it is thecompressible kinetic energy spectrum that exhibits the 3 cascade regions: asmall k classical Kolmogorov k^(-5/3) spectrum, a steep semi-classical cascaderegion, and a large k quantum Kelvin wave cascade k^(-3) spectrum. Theincompressible kinetic energy spectrum exhibits basically a single cascadepower law of k^(-3). For winding number 1 linear vortices it is also shown thatthere is an intermittent loss of Kelvin wave cascade with its signature seen inthe time evolution of the kinetic energy, the loss of the k^(-3) spectrum inthe incompressible kinetic energy spectrum as well as the minimization of thevortex core isosurfaces that inhibits the Kelvin wave cascade.

Poincare recurrence and intermittent loss of quantum Kelvin wave cascades in quantum turbulence