A unitary quantum lattice gas algorithm for two dimensional quantum turbulence

TL;DR

This paper introduces a quantum lattice gas algorithm to simulate two-dimensional quantum turbulence in Bose-Einstein condensates, revealing the effects of nonlinear interactions on recurrence times and energy cascades.

Contribution

It presents a novel unitary quantum lattice gas algorithm for simulating 2D quantum turbulence and analyzes the impact of nonlinear interactions on Poincaré recurrence and energy cascades.

Findings

Short Poincaré recurrence times are observed in certain regimes.

Strengthening nonlinear interactions destroys recurrence times.

No inverse energy cascades are detected in the studied parameter regime.

Abstract

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.