Simulations of dense vortex lattices and Quantum Turbulence using the Gross-Pitaevskii equation

Michikazu Kobayashi, Ionut Danaila, Corentin Lothodé +3 more

Francky Luddens, Ionut Danaila, Marc Brächet +4 more

George Vahala, Jeffrey Yepez, Linda L. Vahala

The ground state wave function for a Bose Einstein condensate is well described by the Gross-Pitaevskii equation. A Type-II quantum algorithm is devised that is ideally parallelized even on a classical computer. Only 2 qubits are required per spatial node. With unitary local collisions, streaming of entangled states and a spatially inhomogeneous unitary gauge rotation one recovers the Gross-Pitaevskii equation. Quantum vortex reconnection is simulated - even without any viscosity or resistivity (which are needed in classical vortex reconnection).

Chiun‐Chang Lee, Tai‐Chia Lin

The relaxation of turbulence is crucial for the formation of vortex lattices and vortex sheets separated by an interface in rapidly rotating two-component Bose–Einstein condensates (BECs) depicted by two-component systems of Gross–Pitaevskii equations (GPEs). To see the relaxation, we study the incompressible limit of two-component systems of GPEs with initial data having a large number of vortices and an interface. The incompressible limit may provide the relaxation of turbulence such that the turbulent flow can be self-organized into vortex crystals. Recently, a rich variety of dynamical phenomena ranging from shock-wave formation to anisotropic sound propagation has been observed in rotating BECs. To see the dynamical phenomena of rotating two-component BECs, we study the compressible limit of two-component systems of GPEs. The compressible limit may describe geostrophic flow and provide rich dynamical phenomena in rotating two-component BECs.

Tsuyoshi Kadokura, Hiroki Saito

Numerical simulations of the Gross-Pitaevskii equation reveal that parent and child vortices tend to be orthogonal to each other in quantum turbulence. This is a manifestation of the energy cascades and may be responsible for Kolmogorov's law in superfluids.

Ionut Danaila