Scaling and Localization in Multipole-Conserving Diffusion

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.Received 11 May 2023Revised 3 September 2023Accepted 30 January 2024DOI:https://doi.org/10.1103/PhysRevLett.132.137102© 2024 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAnomalous diffusionTransport phenomenaPhysical SystemsLattice models in statistical physicsTechniquesLangevin equationMonte Carlo methodsInterdisciplinary PhysicsStatistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics