Blast in a One-Dimensional Cold Gas: From Newtonian Dynamics to Hydrodynamics

Abstract

It is known that a gas composed of a large number of atoms following Newtonian dynamics can be described by the continuum laws of hydrodynamics. Proving this rigorously is one of the outstanding open problems in physics and mathematics. Surprisingly, precise numerical demonstrations of the equivalence of the hydrodynamic and microscopic descriptions are rare. We test this equivalence in the context of the classic problem of the evolution of a blast-wave, a problem that is expected to be at the limits where hydrodynamics would work. We study a one-dimensional gas for which the hydrodynamic Euler equations for the conserved fields of density, momentum and energy are known to have self-similar scaling solutions. Our microscopic model consists of hard point particles with alternate masses, which is a non-integrable system with strong mixing dynamics. Our extensive microscopic simulations find a remarkable agreement with hydrodynamics, with deviations in a small core region that are understood as arising due to heat conduction.