Turbulent fluid dynamics typically involves excitations on many different
    length scales. Classical incompressible fluids can be cleanly represented in
    Fourier space enabling spectral analysis of energy cascades and other
    turbulence phenomena. In quantum fluids, additional phase information and
    singular behaviour near vortex cores thwarts the direct extension of standard
    spectral techniques. We develop a formal and numerical spectral analysis for
    $U(1)$ symmetry-breaking quantum fluids suitable for analyzing turbulent flows,
    with specific application to the Gross-Pitaevskii fluid. Our analysis builds
    naturally on the canonical approach to spectral analysis of velocity fields in
    compressible quantum fluids, and establishes a clear correspondence between
    energy spectral densities, power spectral densities, and autocorrelation
    functions, applicable to energy residing in velocity, quantum pressure,
    interaction, and potential energy of the fluid. Our formulation includes all
    quantum phase information and also enables arbitrary resolution spectral
    analysis, a valuable feature for numerical analysis. A central vortex in a
    trapped planar Bose-Einstein condensate provides an analytically tractable
    example with spectral features of interest in both the infrared and ultraviolet
    regimes. Sampled distributions modelling the dipole gas, plasma, and clustered
    regimes exhibit velocity correlation length increasing with vortex energy,
    consistent with known qualitative behaviour across the vortex clustering
    transition. The spectral analysis of compressible quantum fluids presented here
    offers a rigorous tool for analysing quantum features of superfluid turbulence
    in atomic or polariton condensates.

    Source link


    Leave A Reply