Non-KPZ fluctuations in the derivative of the Kardar-Parisi-Zhang equation or noisy Burgers equation
Editorial:
American Physical Society (APS)
Fecha de edición:
2020-05
Cita:
Rodríguez-Fernández, E. & Cuerno, R. (2020). Non-KPZ fluctuations in the derivative of the Kardar-Parisi-Zhang equation or noisy Burgers equation. Physical Review E, 101(5), 052126.
ISSN:
1539-3755
Patrocinador:
Ministerio de Economía y Competitividad (España)
Ministerio de Ciencia, Innovación y Universidades (España)
Agradecimientos:
We acknowledge valuable comments by B. G. Barreales, M. Castro, J. Krug, P. Rodríguez-López, and J. J. Ruiz-Lorenzo. This work has been supported by Ministerio de Economía y Competitividad, Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación, and Fondo Europeo de Desarrollo Regional (Spain and European Union) through Grants No. FIS2015-66020-C2-1-P and No. PGC2018-094763-B-I00. E.R.-F. also acknowledges financial support from Ministerio de Educación, Cultura y Deporte (Spain) through Formación del Profesorado Universitario sco-larship No. FPU16/06304.
Proyecto:
Gobierno de España. FIS2015-66020-C2-1-P
Gobierno de España. PGC2018-094763-B-I00
Palabras clave:
Growth processes
,
Nonequilibrium statistical mechanics
,
Fractals
,
Interfaces
,
Nonequilibrium systems
,
Surface growth
,
Critical phenomena
,
Kardar-Parisi-Zhang equation
,
Renormalization group
,
Scaling methods
,
Stochastic differential equations
Derechos:
©2020 American Physical Society.
Resumen:
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 eq
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.
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