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

publication date

  • August 2022

start page

  • 024802-1

end page

  • 024802-9


  • 2


  • 106

International Standard Serial Number (ISSN)

  • 1539-3755

Electronic International Standard Serial Number (EISSN)

  • 1550-2376


  • 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.


  • Mathematics
  • Physics
  • Statistics


  • growth processes; nonequilibrium statistical mechanics; fractals; interfaces; nonequilibrium systems; surface growth; critical phenomena; kardar-parisi-zhang equation; scaling methods; stochastic differential equations