Abstract

A quantum lattice gas algorithm, based on interleaved unitary collide-stream operators, is used to study quantum turbulence of the ground state wave function of a Bose-Einstein condensate (BEC). The Gross-Pitaevskii equation is a Hamiltonian system for a compressible, inviscid quantum fluid. From simulations on a 5760<sup>3</sup> grid it was observed that a multi-cascade existed for the incompressible kinetic energy spectrum with universal features: the large spatial scales exhibit a classical Kolmogorov k <sup>-5/3</sup> spectrum while the very small scales exhibit a quantum Kelvin wave cascade k<sup>-3</sup> spectrum. Under certain conditions one can explicitly determine the Poincare recurrence of initial conditions as well as the intermittent destruction of the Kelvin wave cascade.

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