2000 character limit reached
Scaling and localization in multipole-conserving diffusion
Published 6 Apr 2023 in cond-mat.stat-mech, cond-mat.quant-gas, and quant-ph | (2304.03276v3)
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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- The nonlinearity measured by m𝑚mitalic_m discussed here refers to the largest power of the density appearing on the RHS of the master equation. When the hopping process is such that at most one particle hops from any given site, all terms on the RHS will be of the same order. In other cases (such as the 3-site dipole hopping process discussed in App. II) smaller powers may additionally appear. In this appendix we are interested in determining the minimal value that the largest power on the RHS can be.
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