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

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Show simple item record Rodríguez-Fernández, Enrique Cuerno, Rodolfo 2022-01-26T09:46:24Z 2022-01-26T09:46:24Z 2020-05
dc.identifier.bibliographicCitation 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.
dc.identifier.issn 1539-3755
dc.description.abstract 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.
dc.description.sponsorship 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.
dc.format.extent 9
dc.language.iso eng
dc.publisher American Physical Society (APS)
dc.rights ©2020 American Physical Society.
dc.subject.other Growth processes
dc.subject.other Nonequilibrium statistical mechanics
dc.subject.other Fractals
dc.subject.other Interfaces
dc.subject.other Nonequilibrium systems
dc.subject.other Surface growth
dc.subject.other Critical phenomena
dc.subject.other Kardar-Parisi-Zhang equation
dc.subject.other Renormalization group
dc.subject.other Scaling methods
dc.subject.other Stochastic differential equations
dc.title Non-KPZ fluctuations in the derivative of the Kardar-Parisi-Zhang equation or noisy Burgers equation
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. FIS2015-66020-C2-1-P
dc.relation.projectID Gobierno de España. PGC2018-094763-B-I00
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 052126-1
dc.identifier.publicationissue 5
dc.identifier.publicationlastpage 052126-9
dc.identifier.publicationtitle Physical Review E
dc.identifier.publicationvolume 101
dc.identifier.uxxi AR/0000025983
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.contributor.funder Ministerio de Ciencia, Innovación y Universidades (España)
dc.affiliation.dpto UC3M. Departamento de Matemáticas
dc.affiliation.grupoinv UC3M. Grupo de Investigación: Interdisciplinar de Sistemas Complejos (GISC)
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