Superfluid hydrodynamics in fractal dimension space

TL;DR

This paper develops a fractional Schrödinger equation-based two-fluid hydrodynamics model to describe superfluid helium in fractal geometries, predicting temperature-dependent coupling phenomena that can be experimentally tested.

Contribution

It introduces a novel fractional calculus approach to model superfluid helium in fractal spaces, extending traditional hydrodynamics to complex geometries.

Findings

Coupling of pressure and temperature oscillations predicted

Coupling diminishes at very low temperatures

Provides a testable experimental prediction

Abstract

The complex behavior of liquid ${}^4$He and liquid ${}^3$He in nanoporous media is determined by influence of randomly distributed geometrical confinement as well as by significant contribution from the atoms near walls. In the present paper fractional Schrodinger equation has been used for deriving two-fluid hydrodynamical equations for describing the motion of superfluid helium in the fractal dimension space. Nonlinear equations for oscillations of pressure and temperature are obtained and coupling of pressure and temperature oscillations is observed. Moreover coupling should disappear at very low temperatures which provide an experimental test for this theory.