Unitary Quantum Lattice Algorithms for Turbulence
Abstract
A qubit unitary lattice algorithm is developed for the mean field evolution of the ground state of a Bose-Einstein condensate -- whether in a magnetic or optical trap. The algorithm consists of interleaved collide-stream operators which in diffusion ordering recovers the spinor Gross Pitaevskii equations and is ideally parallelized. The algorithm is benchmarked against exact one dimensional vector inelastic soliton collision solutions. Three dimensional quantum turbulence is examined for scalar Bose Einstein condensates and the compressible kinetic energy spectrum exhibits three different cascades -- indicative of three different length scales. We identified these as the classical regime (where the spectrum exhibited the Kolmogorov -5/3 spectrum of classical incompressible turbulence), a semiclassical regime and a quantum regime with a strong -3 spectral exponent). The incompressible kinetic energy exhibits basically only a -3 spectrum throughout the whole wave number range, indicative of the fact that the singular vortex core exhibit zero density at the core. Spinor BEC vortex-vortex collisions are then examined for spin-1 systems and it is shown that the spin-spin interaction term in the Hamiltonian is critical for reconnection: without the spin-spin interaction term the vortices are oblivious to each other. The evolution of nested skyrmions, with coreless vortices consisting of a vortex ring and a straight line vortex that closes on itself on a toridal manifold.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 23, 2016
- Accession Number
- AD1010305
Entities
People
- George Vahala
- Linda Vahala
Organizations
- College of William & Mary