Induced osmotic vorticity in the quantum hydrodynamical picture

• URL: http://arxiv.org/abs/2106.13225v3
• Date: Wed, 10 Nov 2021 10:50:55 GMT
• Title: Induced osmotic vorticity in the quantum hydrodynamical picture
• Authors: C Dedes
• Abstract summary: Solution entails attenuation related effects as non-unitary evolution, non-exponential quantum decay and entropy production. Time-invariant equation for the probability density is derived, analogous to the tensor Lighthill equation in aeroacoustics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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