Dynamic entropic repulsion for interacting interfaces

TL;DR

This paper investigates the asymptotic behavior of two interacting interfaces constrained by exclusion rules, revealing that their heights grow proportionally to the square root or logarithm of time depending on the dimension, and identifies the leading coefficients.

Contribution

It extends the study of entropic repulsion to systems with two interacting interfaces, providing precise asymptotics and coefficients for their height growth over time.

Findings

Height asymptotics are proportional to √log t in dimensions ≥ 3.

Height asymptotics are proportional to log t in two dimensions.

Leading coefficients of height growth are explicitly identified.

Abstract

The dynamic entropic repulsion for the Ginzburg-Landau $\nabla\phi$ interface model was discussed in [Deuschel-N. 2007] and the asymptotics of the height of the interface was identified. This paper studies a similar problem for two interfaces on the wall which are interacting with one another by the exclusion rule. Each leading order of the asymptotics of height is $\sqrt{\log t}$ as $t\to\infty$ for the system on $\integer^d,\,d\ge3$, $\log t$ for the system on $\integer^2$. The coefficient of the leading term for each interface is also identified.