Non-KPZ fluctuations in the derivative of the Kardar-Parisi-Zhang equation or noisy Burgers equation Articles uri icon

publication date

  • May 2020

start page

  • 052126-1

end page

  • 052126-9


  • 5


  • 101

International Standard Serial Number (ISSN)

  • 1539-3755

Electronic International Standard Serial Number (EISSN)

  • 1550-2376


  • The Kardar-Parisi-Zhang (KPZ) equation is a paradigmatic model of nonequilibrium low-dimensional systems with spatiotemporal scale invariance, recently highlighting universal behavior in fluctuation statistics. Its space derivative, namely the noisy Burgers equation, has played a very important role in its study, predating the formulation of the KPZ equation proper, and being frequently held as an equivalent system. We show that, while differences in the scaling exponents for the two equations are indeed due to a mere space derivative, the field statistics behave in a remarkably different way: while the KPZ equation follows the Tracy-Widom distribution, its derivative displays Gaussian behavior, hence being in a different universality class. We reach this conclusion via direct numerical simulations of the equations, supported by a dynamic renormalization group study of field statistics.


  • Mathematics


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