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Stochastic growth in time-dependent environments

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 $c(t)\propto t^{-\alpha}$ there is a transition at $\alpha=1/2$. When $\alpha>1/2$, the solution saturates at large times towards a non-universal limiting distribution. When $\alpha<1/2$ the fluctuation field is governed by scaling exponents depending on $\alpha$ 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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https://hal.archives-ouvertes.fr/hal-02565202
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Submitted on : Wednesday, May 6, 2020 - 11:44:13 AM
Last modification on : Friday, October 15, 2021 - 1:41:41 PM

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Guillaume Barraquand, Pierre Le Doussal, Alberto Rosso. Stochastic growth in time-dependent environments. Physical Review E , American Physical Society (APS), 2020, 101 (4), ⟨10.1103/PhysRevE.101.040101⟩. ⟨hal-02565202⟩

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