Phase space fractons

TL;DR

This paper classifies classical fracton models with phase-space multipole conservation laws, introducing a self-dual model that exhibits quasi-periodic dynamics and non-ergodic behavior.

Contribution

It generalizes fracton models to include phase-space moments and introduces a novel self-dual model with unique dynamical properties.

Findings

Classified all classical fracton models with phase-space multipole conservation.

Introduced a self-dual model conserving dipole and quadrupole moments in position and momentum.

Found quasi-periodic orbits that avoid ergodic exploration in phase space.

Abstract

Perhaps the simplest approach to constructing models with sub-dimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and classify all possible classical fracton models with phase-space multipole conservation laws. We focus on a new self-dual model that conserves both dipole and quadrupole moments in position and momentum; we analyze its dynamics and find quasi-periodic orbits in phase space that evade ergodic exploration of the full phase space.