Weak scaling of the contact distance between two fluctuating interfaces with system size

Autor(en)

Clemens Moritz, Marcello Sega, Max Innerbichler, Phillip L. Geissler, Christoph Dellago

Abstrakt

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance l. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance and determine how its most likely value l* depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that l* scales weakly with system size, i.e., the dependence of l* on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim(L ->infinity) (l*/L) = 0. In particular, for (2+1)-dimensional interfaces l* is an algebraic function of log L, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. This weak scaling implies that such domains remain topologically intact until l becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.

Organisation(en)

Computergestützte Physik und Physik der Weichen Materie

Externe Organisation(en)

Forschungszentrum Jülich, University of California, Berkeley, Erwin Schrödinger Institut

Journal

Physical Review E

Band

102

Anzahl der Seiten

21

ISSN

2470-0045

DOI

https://doi.org/10.1103/PhysRevE.102.062801

Publikationsdatum

12-2020

Peer-reviewed

Ja

ÖFOS 2012

103015 Kondensierte Materie, 103029 Statistische Physik

ASJC Scopus Sachgebiete

Condensed Matter Physics, Statistical and Nonlinear Physics, Statistics and Probability

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/cfd0a3a2-2e6c-4b8f-bd48-d7658b405a2c