Two fluctuating interfaces with sticking interactions: Invariant measures and dynamics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908469282471936 |
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| author | Mahapatra, Samvit Bandyopadhyay, Malay Barma, Mustansir |
| author_facet | Mahapatra, Samvit Bandyopadhyay, Malay Barma, Mustansir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20350 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two fluctuating interfaces with sticking interactions: Invariant measures and dynamics Mahapatra, Samvit Bandyopadhyay, Malay Barma, Mustansir Statistical Mechanics Soft Condensed Matter Biological Physics 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. |
| title | Two fluctuating interfaces with sticking interactions: Invariant measures and dynamics |
| topic | Statistical Mechanics Soft Condensed Matter Biological Physics |
| url | https://arxiv.org/abs/2507.20350 |