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

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.

9 pages, 8 figures, Physical Review E (in press, 2022)

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Cited by in corpus (12)

• Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
• The unpredicted scaling of the one-dimensional Kardar-Parisi-Zhang equation
• Phase diagram of one-dimensional driven-dissipative exciton-polariton condensates
• The inviscid fixed point of the multi-dimensional Burgers-KPZ equation
• Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation
• Influence of coupling symmetries and noise on the critical dynamics of synchronizing oscillator lattices
• Numerical Integration of the KPZ and Related Equations on Networks: The Case of the Cayley Tree
• The stochastic porous medium equation in one dimension
• The non-perturbative sides of the Kardar-Parisi-Zhang equation
• Nonconserved critical dynamics of the two-dimensional Ising model as a surface kinetic roughening process
• Universal interface fluctuations in the contact process
• Unveiling the different scaling regimes of the one-dimensional Kardar-Parisi-Zhang--Burgers equation using the functional renormalisation group