Spectral analysis for compressible quantum fluids

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 singular behavior near vortex cores thwarts the direct extension standard techniques. We develop a formal numerical for $\text{U}(1)$ symmetry-breaking suitable analyzing turbulent flows, with specific application to Gross--Pitaevskii fluid. Our builds naturally canonical approach velocity fields compressible establishes clear correspondence between densities, power autocorrelation functions, applicable residing velocity, pressure, interaction, potential formulation includes all also enables arbitrary resolution analysis, valuable feature analysis. A central trapped planar Bose--Einstein condensate provides an analytically tractable example features interest both infrared ultraviolet regimes. Sampled distributions modeling dipole gas, plasma, clustered regimes exhibit correlation increasing energy, consistent known qualitative across clustering transition. The presented here offers rigorous tool superfluid atomic or polariton condensates.