Exact Short-Time Height Distribution in the One-Dimensional Kardar-Parisi-Zhang Equation and Edge Fermions at High Temperature
Résumé
We consider the early time regime of the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions in curved (or droplet) geometry. We show that for short time t, the probability distribution P(H, t) of the height H at a given point x takes the scaling form P(H, t) similar to exp[-Phi(drop)(H)/root t]where the rate function Phi(drop)(H) is computed exactly for all H. While it is Gaussian in the center, i.e., for small H, the probability distribution function has highly asymmetric non-Gaussian tails that we characterize in detail. This function Phi(drop)(H) is surprisingly reminiscent of the large deviation function describing the stationary fluctuations of finite-size models belonging to the KPZ universality class. Thanks to a recently discovered connection between the KPZ equation and free fermions, our results have interesting implications for the fluctuations of the rightmost fermion in a harmonic trap at high temperature and the full counting statistics at the edge.
Domaines
Physique [physics]Origine | Fichiers produits par l'(les) auteur(s) |
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