Poincare Recurrence and Spectral Cascades in Three-Dimensional Quantum Turbulence

Authors

George Vahala
Jeffrey Yepez
Linda L. Vahala, Old Dominion UniversityFollow
Min Soe
Bo Zhang
Sean Ziegeler

Document Type

Article

Publication Date

2011

DOI

10.1103/PhysRevE.84.046713

Publication Title

Physical Review E

Volume

84

Issue

046713

Pages

1-17

Abstract

The time evolution of the ground state wave function of a zero-temperature Bose-Einstein condensate (BEC) gas is well described by the Hamiltonian Gross-Pitaevskii (GP) equation. Using a set of appropriately interleaved unitary collision-stream operators, a qubit lattice gas algorithm is devised, which on taking moments, recovers the Gross-Pitaevskii (GP) equation under diffusion ordering (time scales as length²). Unexpectedly, there is a class of initial states whose Poincaré recurrence time is extremely short and which, as the grid resolution is increased, scales with diffusion ordering (and not as length³). The spectral results of J. Yepez et al. [Phys. Rev. Lett. 103, 084501 (2009).] for quantum turbulence are revised and it is found that it is the compressible kinetic energy spectrum that exhibits three distinct spectral regions: a small-k classical-like Kolmogorov k^−5/3, a steep semiclassical cascade region, and a large-k quantum vortex spectrum k⁻³. For most evolution times the incompressible kinetic energy spectrum exhibits a somewhat robust quantum vortex spectrum of k⁻³ for an extended range in k with a k^−3.4 spectrum for intermediate k. For linear vortices of winding number 1 there is an intermittent loss of the quantum vortex cascade with its signature seen in the time evolution of the kinetic energy E_kin(t ), the loss of the quantum vortex k⁻³ spectrum in the incompressible kinetic energy spectrum as well as the minimalization of the vortex core isosurfaces that would totally inhibit any Kelvin wave vortex cascade. In the time intervals around these intermittencies the incompressible kinetic energy also exhibits a multicascade spectrum.

Original Publication Citation

Vahala, G., Yepez, J., Vahala, L., Soe, M., Zhang, B., & Ziegeler, S. (2011). Poincaré recurrence and spectral cascades in three-dimensional quantum turbulence. Physical Review E, 84(046713), 1-17. doi: 10.1103/PhysRevE.84.046713

Repository Citation

Vahala, George; Yepez, Jeffrey; Vahala, Linda L.; Soe, Min; Zhang, Bo; and Ziegeler, Sean, "Poincare Recurrence and Spectral Cascades in Three-Dimensional Quantum Turbulence" (2011). Electrical & Computer Engineering Faculty Publications. 59.
https://digitalcommons.odu.edu/ece_fac_pubs/59