# On time crystallinity in dissipative Floquet systems

## TL;DR

This paper explores how dissipative Floquet systems can maintain stable subharmonic responses, identifying conditions that preserve time-crystallinity despite noise and dissipation effects, and contrasting with disordered many-body localized systems.

## Contribution

It provides a framework for understanding stability of time-crystalline order in dissipative quantum systems, including examples of stable oscillations and distinctions from disordered systems.

## Key findings

- Short-ranged 2D system exhibits persistent subharmonic oscillations.
- Dissipation can stabilize time-crystalline order under certain conditions.
- Fully connected models show stability of subharmonics in the thermodynamic limit.

## Abstract

We investigate the conditions under which periodically driven quantum systems subject to dissipation exhibit a stable subharmonic response. Noting that coupling to a bath introduces not only cooling but also noise, we point out that a system subject to the latter for the entire cycle tends to lose coherence of the subharmonic oscillations, and thereby the long-time temporal symmetry breaking. We provide an example of a short-ranged two-dimensional system which does not suffer from this and therefore displays persistent subharmonic oscillations stabilised by the dissipation. We also show that this is fundamentally different from the disordered DTC previously found in closed systems, both conceptually and in its phenomenology. The framework we develop here clarifies how fully connected models constitute a special case where subharmonic oscillations are stable in the thermodynamic limit.