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arXiv · 1310.8013

Universal aspects of curved, flat & stationary-state Kardar-Parisi-Zhang statistics

Timothy Halpin-Healy·Yuexia Lin
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Abstract

Motivated by the recent exact solution of the {\it stationary-state} Kardar-Parisi-Zhang (KPZ) statistics by Imamura & Sasamoto (Phys. Rev. Lett. {\bf 108}, 190603 (2012)), as well as a precursor experimental signature unearthed by Takeuchi (Phys. Rev. Lett. {\bf 110}, 210604 (2013)), we establish here the universality of these phenomena, examining scaling behaviors of directed polymers in a random medium, the stochastic heat equation with multiplicative noise, and kinetically roughened KPZ growth models. We emphasize the value of cross KPZ-Class universalities, revealing crossover effects of experimental relevance. Finally, we illustrate the great utility of KPZ scaling theory by an optimized numerical analysis of the Ulam problem of random permutations.

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Timothy Halpin-Healy, Yuexia Lin. 2013-10-30. Universal aspects of curved, flat & stationary-state Kardar-Parisi-Zhang statistics. https://doi.org/10.1103/physreve.89.010103

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