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Journal of Chemical Biological and Physical Sciences

A Theoretical study of hydrodynamic Instability and Quantum turbulence in atomic Bose Einstein Condensate BECs) and evaluation of incompressible and compressible kinetic energy in 2D non-uniform BECs and spin dependent interaction energy for spinor BECs

Published Oct 30, 2018• 0 citations
Publisher
DOI
10.24214/jcbps.c.8.4.41432

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We summarize the recent theoretical and numerical works on spin turbulence (ST) in spin-1 spinor Bose-Einstein condensates. When the system is excited from the ground state, it goes through hydrodynamic instability to ST in which the spin density vector has various disordered direction. The properties of ST depend on whether the spin-dependent interaction is ferromagnetic or antiferromagnetic. ST has some characteristics different from other kinds of turbulence in quantum fluids. Firstly, the spectrum of the spin-dependent interaction energy exhibits the characteristic power law different from the usual Kolmogorov -5/3 law. Secondly, ST can show the spin-glass-like behavior; the spin density vectors are spatially random but temporally frozen.
Spin-superflow turbulence (SST) in spin-1 ferromagnetic spinor Bose-Einstein condensates is theoretically and numerically studied by using the spin-1 spinor Gross-Pitaevskii (GP) equations. SST is turbulence in which the disturbed spin and superfluid velocity fields are coupled. Applying the Kolmogorov-type dimensional scaling analysis to the hydrodynamic equations of spin and velocity fields, we theoretically find that the $\ensuremath{-}5/3$ and $\ensuremath{-}7/3$ power laws can appear in spectra of the superflow kinetic and the spin-dependent interaction energies, respectively. Our numerical calculation of the GP equations with a phenomenological small-scale energy dissipation confirms SST with the coexistence of disturbed spin and superfluid velocity field with two power laws.
We study numerically the spin turbulence (ST) in spin-1 ferromagnetic spinor Bose-Einstein condensates (BECs). ST is characterized by a $\ensuremath{-}7/3$ power law in the spectrum of the spin-dependent interaction energy. The direction of the spin density vector is spatially disordered but temporally frozen in ST, showing an analogy with the spin-glass state. Thus, we introduce the order parameter of spin glass into ST in spinor BECs. When ST develops through some instability, the order parameter grows with a $\ensuremath{-}7/3$ power law, thus succeeding in describing ST well.