Related Experiment Video
Updated: Sep 22, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Hidden quasiconservation laws in fracton hydrodynamics
Oliver Hart1,2, Andrew Lucas1, Rahul Nandkishore1
1Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA.
Abstract:
We show that the simplest universality classes of fracton hydrodynamics in more than one spatial dimension, including isotropic theories of charge and dipole conservation, can exhibit hidden quasiconservation laws, in which certain higher multipole moments can only decay due to dangerously irrelevant corrections to hydrodynamics. We present two simple examples of this phenomenon. First, an isotropic dipole-conserving fluid in the infinite plane conserves an infinite number of harmonic multipole charges within linear response; we calculate the decay or growth of these charges due to dangerously irrelevant nonlinearities. Second, we consider a model with xy and x^{2}-y^{2} quadrupole conservation, in addition to dipole conservation, which is described by isotropic fourth-order subdiffusion, yet has dangerously irrelevant sixth-order corrections necessary to relax the harmonic multipole charges. We confirm our predictions for the anomalously slow decay of the harmonic conserved charges in each setting by using numerical simulations, both of the nonlinear hydrodynamic differential equations, and in quantum automaton circuits on a square lattice.
Related Concept Videos
Conservation of Energy
Conservation of Mass in Finite Cotrol Volume
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
Conservation of Mass in Fixed, Nondeforming Control Volume
In the case of a sewer pipe, which can be modeled...
Conservation of Mass in Moving, Nondeforming Control Volume
In the context of a detention basin, the conservation of mass states that the total mass of water entering the basin must equal the mass leaving the basin plus any accumulation of...
First Law: Particles in One-dimensional Equilibrium
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about...

