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The probability density function tail of the Kardar–Parisi–Zhang equation in the strongly nonlinear regime

Johan Anderson (Institutionen för rymd- och geovetenskap, Plasmafysik och fusionsenergi) ; Jonas Johansson
Journal of Physics A: Mathematical and Theoretical (1751-8113). Vol. 49 (2016), 12, p. 505001.
[Artikel, refereegranskad vetenskaplig]

An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar–Parisi–Zhang equation is provided. The PDF tail exactly coincides with a Tracy–Widom distribution i.e. a PDF tail proportional to exp(-cw_2^(3/2)), where w_2 is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin–Siggia– Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no upper critical dimension.

Nyckelord: KPZ, MSR, Instantons, interface growth



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Denna post skapades 2016-11-23. Senast ändrad 2016-11-23.
CPL Pubid: 245574

 

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