Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascades

TL;DR

This study uses a novel quantum lattice gas algorithm to simulate quantum turbulence in a BEC, revealing distinct power law spectra for Kelvin wave and Kolmogorov cascades across different scales.

Contribution

Introduces an accurate determination of the quantum Kelvin wave cascade spectrum and demonstrates the coexistence of classical and quantum turbulence spectra in BEC simulations.

Findings

Quantum Kelvin wave cascade spectrum k^{-3} accurately determined

Classical Kolmogorov spectrum k^{-5/3} observed at large scales

Kelvin wave spectrum remains robust across grid sizes

Abstract

A novel unitary quantum lattice gas algorithm is used to simulate quantum turbulence of a BEC described by the Gross-Pitaevskii equation on grids up to 5760^3. For the first time, an accurate power law scaling for the quantum Kelvin wave cascade is determined: k^{-3}. The incompressible kinetic energy spectrum exhibits very distinct power law spectra in 3 ranges of k-space: a classical Kolmogorov k^{-5/3} spectrum at scales much greater than the individual quantum vortex cores, and a quantum Kelvin wave cascade spectrum k^{-3} on scales of order the vortex cores. In the semiclassical regime between these two spectra there is a pronounced steeper spectral decay, with non-universal exponent. The Kelvin k^{-3} spectrum is very robust, even on small grids, while the Kolmogorov k^{-5/3} spectrum becomes more and more apparent as the grids increase from 2048^3 grids to 5760^3.