# Turbulence scaling laws across the superfluid to supersolid transition

## TL;DR

This paper explores quantum turbulence in a two-dimensional supersolid, revealing unique scaling laws in wave and vortex turbulence due to the supersolid's broken translation symmetry, confirmed by numerical simulations.

## Contribution

It predicts new turbulence scaling laws in supersolids and confirms them through numerical simulations, advancing understanding of quantum turbulence in complex quantum phases.

## Key findings

- Prediction of a $k^{-13/3}$ scaling law in wave turbulence.
- Observation of a $k^{-1}$ scaling law in vortex turbulence.
- Numerical confirmation using Gross-Pitaevskii simulations.

## Abstract

We investigate quantum turbulence in a two-dimensional trapped supersolid and demonstrate that both the wave and vortex turbulence involve triple rather than dual cascades, as in a superfluid. Because of the presence of a second gapless mode associated with translation symmetry breaking, a new $k^{-13/3}$ scaling law is predicted to occur in the wave turbulence. Simultaneous fast vortex-antivortex creation and annihilation in the interior of the oscillating supersolid results in a $k^{-1}$ scaling law in the vortex turbulence. Numerical simulations based on the Gross-Pitaevskii equation confirmed the predictions.