Exact Short-Time Height Distribution in the One-Dimensional Kardar-Parisi-Zhang Equation and Edge Fermions at High Temperature - Laboratoire de Physique Théorique de l'Ecole Normale Supérieure Accéder directement au contenu
Article Dans Une Revue Physical Review Letters Année : 2016

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.
Fichier principal
Vignette du fichier
PhysRevLett.117.070403-accepted.pdf (549.7 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01379490 , version 1 (16-12-2023)

Identifiants

Citer

Pierre Le Doussal, Satya N. Majumdar, Alberto Rosso, Grégory Schehr. Exact Short-Time Height Distribution in the One-Dimensional Kardar-Parisi-Zhang Equation and Edge Fermions at High Temperature. Physical Review Letters, 2016, 117 (7), pp.070403. ⟨10.1103/PhysRevLett.117.070403⟩. ⟨hal-01379490⟩
36 Consultations
3 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More