English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the relaxation of an initial non-equilibrium state in aone-dimensional fluid of hard rods. Since it is an interacting integrablesystem, we expect it to reach the Generalized Gibbs Ensemble (GGE) at longtimes for generic initial conditions. Here we show that there exist initialconditions for which the system does not reach GGE even at very long times andin the thermodynamic limit. In particular, we consider an initial condition ofuniformly distributed hard-rods in a box with the left half having particleswith a singular velocity distribution (all moving with unit velocity) and theright half particles in thermal equilibrium. We find that the density profilefor the singular component does not spread to the full extent of the box andkeeps moving with a fixed effective speed at long times. We show that suchdensity profiles can be well described by the solution of the Euler equationsalmost everywhere except at the location of the shocks, where we observe slightdiscrepancies due to dissipation arising from the initial fluctuations of thethermal background. To demonstrate this effect of dissipation analytically, weconsider a second initial condition with a single particle at the origin withunit velocity in a thermal background. We find that the probabilitydistribution of the position of the unit velocity quasi-particle has diffusivespreading which can be understood from the solution of the Navier-Stokesequation of the hard rods. Finally, we consider an initial condition with aspread in velocity distribution for which we show convergence to GGE. Ourconclusions are based on molecular dynamics simulations supported by analyticalarguments.

Thermalization and hydrodynamics in an interacting integrable system: the case of hard rods