Quantum hydrodynamic theory of quantum fluctuations in dipolar Bose–Einstein condensate

Traditional quantum hydrodynamics of Bose–Einstein condensates (BECs) is restricted by the continuity and Euler equations. The Bohm potential (the part momentum flux) has a nontrivial that can evolve under fluctuations. fluctuations are effect appearance particles in excited states during evolution BEC mainly consisting state with lowest energy. To cover this phenomenon terms hydrodynamic methods, we need to derive equations for flux current flux. equation contains interaction leading In dipolar BECs, deal long-range interaction. Its contribution proportional average macroscopic dipole–dipole (DDI) appearing mean-field regime. third derivative potential. It responsible Higher derivatives correspond small scale contributions DDI. lead existence second wave solution. introduce instability BECs. If attractive, but being smaller than repulsive short-range presented first constant, there long-wavelength instability. There more complex picture area transits into stability interval where two waves exist.