Classical Fluid Analogies for Schr\"odinger-Newton Systems

TL;DR

This paper explores how Schr"odinger-Newton systems, relevant in cosmology for ultra-light scalar particles, can be modeled using classical fluid dynamics concepts like viscosity, pressure, and Reynolds number, with certain limitations.

Contribution

It demonstrates that Schr"odinger-Newton systems can be described by classical fluid analogies, establishing a bridge between quantum gravitational models and classical fluid behavior.

Findings

Classical fluid concepts can approximate Schr"odinger-Newton systems.

A pseudo-Reynolds number can characterize these systems under certain conditions.

Restrictions are necessary for physical consistency in the fluid analogy.

Abstract

The Schr\"odinger-Poisson formalism has found a number of applications in cosmology, particularly in describing the growth by gravitational instability of large-scale structure in a universe dominated by ultra-light scalar particles. Here we investigate the extent to which the behaviour of this and the more general case of a Schr\"odinger-Newton system, can be described in terms of classical fluid concepts such as viscosity and pressure. We also explore whether such systems can be described by a pseudo-Reynolds number as for classical viscous fluids. The conclusion we reach is that this is indeed possible, but with important restrictions to ensure physical consistency.