A unitary quantum lattice gas algorithm for two dimensional quantum turbulence

Quantum vortex structures and energy cascades are examined for two dimensional quantum turbulence (2D QT) at zero temperature. A special unitary evolution algorithm, the quantum lattice gas (QLG) algorithm, is employed to simulate the Bose-Einstein condensate (BEC) governed by the Gross-Pitaevskii (GP) equation. A parameter regime is uncovered in which, as in 3D QT, there is a short Poincar\'e recurrence time. It is demonstrated that such short recurrence times are destroyed as the nonlinear interaction is strengthened. The similar loss of Poincar\'e recurrence is also reported in 3D QT [1] Energy cascades for 2D QT are considered to examine whether 2D QT exhibits inverse cascades as in 2D classical turbulence. In the parameter regime considered, the spectra analysis reveals no such dual cascades-dual cascades being a hallmark of 2D classical turbulence.