Summary:
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.
Spanish layman's summary:
El modelo de KPZ sin viscosidad se ha propuesto como un modelo paradigmático de sistema cuántico altamente correlacionado. En este trabajo mostramos que sus propiedades estadísticas no se corresponden a ningún modelo reportado en la literatura.
English layman's summary:
The KPZ model without viscosity has been proposed as a paradigmatic model of a highly correlated quantum system. In this work we show that its statistical properties do not correspond to any model reported in the literature.
Keywords: physics, mathematical models, simulation.
JCR Impact Factor and WoS quartile: 2,400 - Q1 (2022); 2,200 - Q1 (2023)
DOI reference:
https://doi.org/10.1103/PhysRevE.106.024802
Published on paper: August 2022.
Published on-line: August 2022.
Citation:
E. Rodríguez-Fernández, S.N. Santalla, M. Castro, R. Cuerno, Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation. Physical Review E. Vol. 106, nº. 2, pp. 024802-1 - 024802-9, August 2022. [Online: August 2022]
