Description of KPZ interface growth by stochastic Loewner evolution

Yusuke Kosaka Shibasaki

paper

Description of KPZ interface growth by stochastic Loewner evolution

arXiv:2604.03711

Abstract

In this study, we investigate the relationship between the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) equation and the stochastic Loewner equation (SLE), which is a one parameter family of the conformal mappings involving stochasticity. The author shows the correspondence between 1D KPZ equation with height function $h (x, t) = (3 t^{2} x + x^{3}) /6 t$ and Loewner equation driven by a nonlinear stochastic process, wherein the 1D dynamics of interface growth is characterized by Loewner entropy $S_{L oe w} ≃ - ln t / I^º$ . These results were numerically verified with discussions in relation to the universality in non-equilibrium statistical physics.

14 pages, 2 figures