Scaling and localization in multipole-conserving diffusion

Jung Hoon Han; Ethan Lake; Sunghan Ro

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arXiv · 2304.03276

Scaling and localization in multipole-conserving diffusion

Jung Hoon Han·Ethan Lake·Sunghan Ro

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Abstract

We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are exponentially localized near system boundaries. It also yields an unusual approach to equilibrium, which in $d$ dimensions exhibits scaling with dynamical exponent $z = 4+d$. Similar phenomena occur for dynamics that conserves higher moments of the density, which we systematically classify using a family of nonlinear diffusion equations. In the quantum setting, analogous fermionic systems are shown to form real-space Fermi surfaces, while bosonic versions display a real-space analog of Bose-Einstein condensation.

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Jung Hoon Han, Ethan Lake, Sunghan Ro. 2023-04-06. Scaling and localization in multipole-conserving diffusion. https://arxiv.org/abs/2304.03276

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