Exact height distribution in one-dimensional Edwards-Wilkinson interface with diffusing diffusivity
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| Format: | Preprint |
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2025
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| _version_ | 1866916793117835264 |
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| author | Dean, David S. Majumdar, Satya N. Sabhapandit, Sanjib |
| author_facet | Dean, David S. Majumdar, Satya N. Sabhapandit, Sanjib |
| contents | We study the height distribution of a one-dimensional Edwards-Wilkinson interface in the presence of a stochastic diffusivity $D(t)=B^2(t)$, where $B(t)$ represents a one-dimensional Brownian motion at time $t$. The height distribution at a fixed point is space is computed analytically. The typical height $h(x,t)$ at a given point in space is found to scale as $t^{3/4}$ and the distribution $G(H)$ of the scaled height $H=h/t^{3/4}$ is symmetric but with a nontrivial shape: while it approaches a nonzero constant quadratically as $H\to 0$, it has a non-Gaussian tail that decays exponentially for large $H$. We show that this exponential tail is rather robust and holds for a whole family of linear interface models parametrized by a dynamical exponent $z>1$, with $z=2$ corresponding to the Edwards-Wilkinson model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_01153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact height distribution in one-dimensional Edwards-Wilkinson interface with diffusing diffusivity Dean, David S. Majumdar, Satya N. Sabhapandit, Sanjib Statistical Mechanics We study the height distribution of a one-dimensional Edwards-Wilkinson interface in the presence of a stochastic diffusivity $D(t)=B^2(t)$, where $B(t)$ represents a one-dimensional Brownian motion at time $t$. The height distribution at a fixed point is space is computed analytically. The typical height $h(x,t)$ at a given point in space is found to scale as $t^{3/4}$ and the distribution $G(H)$ of the scaled height $H=h/t^{3/4}$ is symmetric but with a nontrivial shape: while it approaches a nonzero constant quadratically as $H\to 0$, it has a non-Gaussian tail that decays exponentially for large $H$. We show that this exponential tail is rather robust and holds for a whole family of linear interface models parametrized by a dynamical exponent $z>1$, with $z=2$ corresponding to the Edwards-Wilkinson model. |
| title | Exact height distribution in one-dimensional Edwards-Wilkinson interface with diffusing diffusivity |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2502.01153 |