Year: 2020
Type: article
Abstract: We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance c(t) depending on time. We find that for c(t)∝t^{-α} there is a transition at α=1/2. When α>1/2, the solution saturates at large times towards a nonuniversal limiting distribution. When α<1/2 the fluctuation field is governed by scaling exponents depending on α and the limiting statistics are similar to the case when c(t) is constant. We investigate this problem using different methods: (1) Elementary changes of variables mapping the time-dependent case to variants of the KPZ equation with constant variance of the noise but in a deformed potential. (2) An exactly solvable discretization, the log-gamma polymer model. (3) Numerical simulations.
Source: Physical review. E
Institutions: Centre National de la Recherche Scientifique, Université Paris Cité, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Sorbonne Université, Laboratoire de Physique de l'Ecole Normale Supérieure, Université Paris-Sud, Université Paris-Saclay, Laboratoire de Physique Théorique et Modèles Statistiques
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W2975979453