Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation

TL;DR

This paper uncovers a new universality class for the zero surface tension KPZ equation, revealing anomalous kinetic roughening and distinct scaling exponents through numerical simulations, with implications for quantum and classical systems.

Contribution

It identifies and characterizes a novel universality class for the tensionless KPZ equation, previously not understood analytically, using numerical methods and connecting to related models.

Findings

Discovered a distinct universality class for zero tension KPZ.

Revealed anomalous kinetic roughening in this class.

Connected the results to quantum spin chain experiments and related models.

Abstract

The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is becoming an overarching paradigm for the scaling of nonequilibrium, spatially extended, classical and quantum systems with strong correlations. Recent analytical solutions have uncovered a rich structure regarding its scaling exponents and fluctuation statistics. However, the zero surface tension or zero viscosity case eludes such analytical solutions and has remained ill-understood. Using numerical simulations, we elucidate a well-defined universality class for this case that differs from that of the viscous case, featuring intrinsically anomalous kinetic roughening, despite previous expectations for systems with local interactions and time-dependent noise and ballistic dynamics. The latter may be relevant to recent quantum spin chain experiments which measure KPZ and ballistic relaxation under different conditions. We identify the ensuing set of scaling exponents in previous discrete interface growth models related with isotropic percolation, and show it to describe the fluctuations of additional continuum systems related with the noisy Korteweg-de Vries equation. Along this process, we additionally elucidate the universality class of the related inviscid stochastic Burgers equation.