Breakdown of hydrodynamics below four dimensions in a fracton fluid

TL;DR

This paper reveals that hydrodynamic descriptions of certain chaotic many-body systems with multiple conserved quantities become unstable below four dimensions, leading to a new universality class of non-equilibrium dynamics.

Contribution

It introduces a fractonic generalization of hydrodynamics that captures the breakdown below four dimensions and provides numerical evidence for this transition in one-dimensional models.

Findings

Hydrodynamics becomes unstable below four dimensions for dipole-conserving fluids.

A new universality class of non-equilibrium dynamics emerges in one-dimensional models.

Numerical simulations support the breakdown of traditional hydrodynamics in these systems.

Abstract

We present the nonlinear fluctuating hydrodynamics which governs the late time dynamics of a chaotic many-body system with simultaneous charge/mass, dipole/center of mass, and momentum conservation. This hydrodynamic effective theory is unstable below four spatial dimensions: dipole-conserving fluids at rest become unstable to fluctuations, and are governed not by hydrodynamics, but by a fractonic generalization of the Kardar-Parisi-Zhang universality class. We numerically simulate many-body classical dynamics in one-dimensional models with dipole and momentum conservation, and find evidence for a breakdown of hydrodynamics, along with a new universality class of undriven yet non-equilbrium dynamics.