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KPZ equation with correlated noise: emergent symmetries and non-universal observables | | Steven Mathey
; Elisabeth Agoritsas
; Thomas Kloss
; Vivien Lecomte
; Léonie Canet
; | | Date: |
7 Nov 2016 | | Abstract: | We investigate the steady-state fluctuations of a growing one-dimensional
interface described by the KPZ dynamics with a noise featuring smooth spatial
correlations of characteristic range $xi$. We employ Non-perturbative
Functional Renormalization Group methods in order to resolve the properties of
the system at all scales. We show that the physics of the standard
(uncorrelated) KPZ equation emerges on large scales independently of $xi$.
Moreover, the Renormalization Group flow is followed from the initial condition
to the fixed point, that is from the microscopic dynamics to the large-distance
properties. This provides access the small-scale features (and their dependence
on the details of the noise correlations) as well as to the universal
large-scale physics. In particular, we compute the kinetic energy spectrum of
the steady state as well as its non-universal amplitude. The latter is
experimentally accessible by measurements at large scales and retains a
signature of the microscopic noise correlations. Our results are compared to
previous analytical and numerical results from independent approaches. They are
in agreement with direct numerical simulations for the kinetic energy spectrum
as well as with the prediction, obtained with the replica trick by Gaussian
variational method, of a crossover in $xi$ of the non-universal amplitude of
this spectrum. | | Source: | arXiv, 1611.2295 | | Services: | Forum | Review | PDF | Favorites | |
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