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Published on: September 19, 2017
Stochastic growth in time-dependent environments
Guillaume Barraquand1, Pierre Le Doussal1, Alberto Rosso2
1Laboratoire de Physique de l'École Normale Supérieure, ENS, CNRS, Université PSL, Sorbonne Université, Université de Paris, 24 rue Lhomond, 75231 Paris, France.
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.
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