Induced osmotic vorticity in the quantum hydrodynamical picture
arXiv:2106.13225
Abstract
A nonlinear wave mechanical equation is proposed by inserting an imaginary quantum potential into the Schrödinger equation. An explicit expression for its solution is given under certain assumptions and it is shown that it entails attenuation related effects as non-unitary evolution, non-exponential quantum decay and entropy production. In the quantum hydrodynamical formulation the existence of circulation effects for the osmotic velocity field is established. Finally, a time-invariant equation for the probability density is derived, analogous to the tensor Lighthill equation in aeroacoustics, which admits both retarded and advanced solutions.
appendix on two-particle case