Is the quantum hydrodynamic analogy more general than the Schroedinger approach?

TL;DR

This paper explores the quantum hydrodynamic analogy (QHA), extending it to stochastic cases, and demonstrates that it can describe dissipative quantum dynamics beyond the standard Schrödinger framework, especially with local noise.

Contribution

The paper shows that QHA can model dissipative and stochastic quantum dynamics, surpassing the traditional Schrödinger approach in certain noisy and dissipative scenarios.

Findings

QHA reproduces standard quantum mechanics

QHA can describe dissipative Schrödinger equations

Breakdown of one-to-one correspondence with Schrödinger states in noisy cases

Abstract

The quantum hydrodynamic analogy (QHA), equivalent to the Schr\"odinger equation, is investigated and extended to the stochastic case. The investigation shows that in addition to reproducing the standard quantum mechanics the QHA model is able to generally describe the quantum stochastic dynamics leading to the dissipative Schr\"odinger equation given by Kostin [55] as a particular case. The inspection shows that the QHA is well suited for the treatment of problems where local noise (spatially distributed one) is introduced. In this case the analysis shows that the bi-univocal correspondence between the QHA and the Schr\"odinger approach breaks down and that the states described by the QHA do not have their corresponding ones into the Schr\"odinger description.