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.

arXiv commentv3: The exposition has been improved in the letter. Letter: 7 pages. Supplementary material: 33 pages

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Cited by in corpus (4)

• Universality classes of spin transport in one-dimensional isotropic magnets: the onset of logarithmic anomalies
• Hydrodynamics in lattice models with continuous non-Abelian symmetries
• Fluctuations of the log-gamma polymer free energy with general parameters and slopes
• A stationary model of non-intersecting directed polymers