Observing symmetrybroken optimal paths of stationary KardarParisiZhang interface via a largedeviation sampling of directed polymers in random media
Abstract
Consider the shorttime probability distribution $\mathcal{P}(H,t)$ of the onepoint interface height difference $h(x=0,\tau=t)h(x=0,\tau=0)=H$ of the stationary interface $h(x,\tau)$ described by the KardarParisiZhang equation. It was previously shown that the optimal path  the most probable history of the interface $h(x,\tau)$ which dominates the higher tail of $\mathcal{P}(H,t)$  is described by any of \emph{two} ramplike structures of $h(x,\tau)$ traveling either to the left, or to the right. These two solutions emerge, at a critical value of $H$, via a spontaneous breaking of the mirror symmetry $x\leftrightarrowx$ of the optimal path, and this symmetry breaking is responsible for a secondorder dynamical phase transition in the system. Here we employ a largedeviation Monte Carlo sampling algorithm in conjunction with the mapping between the KPZ interface and the directed polymer in a random potential at high temperature. This allows us to observe the optimal paths, which determine each of the two tails of $\mathcal{P}(H,t)$, down to probability densities as small as $10^{500}$. The observed mirrorsymmetrybroken traveling optimal paths for the higher tail, and mirrorsymmetric paths for the lower tail, are in good quantitative agreement with analytical predictions.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.08705
 Bibcode:
 2021arXiv210608705H
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 8 pages, 6 figures