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Article overview
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Local average height distribution of fluctuating interfaces | Naftali R. Smith
; Baruch Meerson
; Pavel V. Sasorov
; | Date: |
1 Sep 2016 | Abstract: | Height fluctuations of growing surfaces can be characterized by the
probability distribution of height in a spatial point at a finite time.
Recently, there has been spectacular progress in the studies of this quantity
for the Kardar-Parisi-Zhang equation in $1+1$ dimensions. Is the finite-time
one-point height distribution well defined in higher dimensions or for other
surface growth models? Here we show that, at or above a critical dimension, the
answer to this question is negative for a whole class of simple stochastic
surface growth models. As a remedy, we introduce a emph{local average height},
whose probability density is well defined in any dimension and for all models
of this class. The weak-noise theory (WNT) for these models yields the "optimal
path" of the interface conditioned on a non-equilibrium fluctuation of the
local average height. As an illustration, we consider the conserved
Edwards-Wilkinson (EW) equation, where the finite-time one-point height
distribution is ill-defined in all physical dimensions. We also determine the
optimal path of the interface in a closely related problem of the finite-time
emph{height-difference} distribution for the non-conserved EW equation in
$1+1$ dimension. | Source: | arXiv, 1609.0264 | Services: | Forum | Review | PDF | Favorites |
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