Ideal-Gas Approach to Hydrodynamics

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.

10 pages, 4 figures

References in corpus (4)

• Theory of ultracold Fermi gases
• Dynamical symmetry and breathers in a two-dimensional Bose gas
• SU(1,1) echoes for breathers in quantum gases
• Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves

Cited by in corpus (5)

• Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases
• Theory of radial oscillations in metal nanoparticles driven by optically induced electron density gradients
• Dynamical nonlinear excitations induced by interaction quench in a two-dimensional box-trapped Bose-Einstein condensate
• Scale and conformal invariance in rotating interacting few-fermion systems
• The origin of the period-$2T/7$ quasi-breathing in disk-shaped Gross-Pitaevskii breathers