Abstract
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.
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