Ideal-Gas Approach to Hydrodynamics

TL;DR

This paper uncovers a surprising mathematical link between ideal gases and hydrodynamics, showing that certain interacting hydrodynamic solutions can be exactly derived from noninteracting ideal gas dynamics, with implications for ultracold atomic gases.

Contribution

It introduces a novel method connecting ideal gas dynamics to complex hydrodynamic equations, providing exact solutions and explaining experimental observations.

Findings

Exact solutions for scale-invariant hydrodynamics derived from ideal gases

Explanation of density oscillations in ultracold gases

Recovery of dark soliton solutions in Bose condensates

Abstract

Transport is one of the most important physical processes in all energy and length scales. Ideal gases and hydrodynamics are, respectively, two opposite limits of transport. Here, we present an unexpected mathematical connection between these two limits; that is, there exist situations that the solution to a class of interacting hydrodynamic equations with certain initial conditions can be exactly constructed from the dynamics of noninteracting ideal gases. We analytically provide three such examples. The first two examples focus on scale-invariant systems, which generalize fermionization to the hydrodynamics of strongly interacting systems, and determine specific initial conditions for perfect density oscillations in a harmonic trap. The third example recovers the dark soliton solution in a one-dimensional Bose condensate. The results can explain a recent puzzling experimental observation in ultracold atomic gases by the Paris group and make further predictions for future experiments. We envision that extensive examples of such an ideal-gas approach to hydrodynamics can be found by systematical numerical search, which can find broad applications in different problems in various subfields of physics.