Induced osmotic vorticity in the quantum hydrodynamical picture

TL;DR

This paper introduces a nonlinear wave equation with an imaginary quantum potential, revealing effects like non-unitary evolution and entropy production, and explores circulation effects in quantum hydrodynamics.

Contribution

It proposes a new nonlinear wave equation incorporating an imaginary quantum potential and analyzes its implications in quantum hydrodynamics.

Findings

Demonstrates non-unitary evolution and entropy production.

Establishes circulation effects in osmotic velocity.

Derives a time-invariant probability density equation.

Abstract

A nonlinear wave mechanical equation is proposed by inserting an imaginary quantum potential into the Schr\"{o}dinger 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.