Two fluctuating interfaces with sticking interactions: Invariant measures and dynamics

TL;DR

This paper models two fluctuating interfaces with short-range attractive interactions, revealing complex dynamics and exact steady states related to DNA denaturation, including phase transitions and invariant measures.

Contribution

It introduces a non-equilibrium stochastic model of interacting interfaces and derives exact invariant measures, connecting to the Poland-Scheraga model of DNA denaturation.

Findings

Invariant measure has an inhomogeneous product form.

Exact steady state corresponds to the Poland-Scheraga model.

System exhibits diverse transient and steady-state behaviors.

Abstract

We introduce and study a non-equilibrium stochastic model of two fluctuating interfaces which interact through short-range attractive interactions at their points of contact. Beginning from an entangled state, the system exhibits diverse dynamics -- ranging from fast transients with small lifetimes to ultraslow evolution through quasi-stationary states -- and reaches stuck, entangled, or detached steady states. Near the stuck-detached transition, two distinct dynamical modes of evolution co-occur. When the two surfaces evolve through similar dynamics (both Edwards-Wilkinson or both Kardar-Parisi-Zhang), the invariant measure is determined and found to have an inhomogeneous product form. This exact steady state is shown to be the measure of the equilibrium Poland-Scheraga model of DNA denaturation.