Lighthill equation for quantum liquids

TL;DR

This paper derives a quantum analogue of the Lighthill equation from the Gross-Pitaevskii equation, providing insights into quantum fluid dynamics and foundational quantum principles.

Contribution

It introduces a novel quantum Lighthill equation for superfluid probability density, linking aeroacoustic methods with quantum fluid theory.

Findings

Provides a new equation involving second-order time derivatives

Discusses implications for quantum equilibrium and Born's rule

Suggests potential applications in quantum fluid analysis

Abstract

A quantum version of the Lighthill equation that originated in the field of theoretical aeroacoustics is derived for the probability density of a superfluid starting from the time-dependent Gross-Pitaevskii equation. It involves a second-order time derivative and should be supplemented by two-time boundary conditions. Its physical implications are discussed in relation to the quantum equilibrium hypothesis and the general applicability of Born's rule.