Two fluctuating interfaces with sticking interactions: Invariant measures and dynamics

Samvit Mahapatra; Malay Bandyopadhyay; Mustansir Barma

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arXiv · 2507.20350

Two fluctuating interfaces with sticking interactions: Invariant measures and dynamics

Samvit Mahapatra·Malay Bandyopadhyay·Mustansir Barma

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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.

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Samvit Mahapatra, Malay Bandyopadhyay, Mustansir Barma. 2025-07-27. Two fluctuating interfaces with sticking interactions: Invariant measures and dynamics. https://arxiv.org/abs/2507.20350

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