Generalized energy and time-translation invariance in a driven, dissipative system

TL;DR

This paper explores how energy and time-translation invariance manifest in a driven, dissipative system, revealing a continuous symmetry linked to Floquet quasi-energies and connecting it to equilibrium statistical mechanics.

Contribution

It demonstrates that Floquet quasi-energies correspond to a continuous symmetry in a driven system, providing a new understanding of energy invariance and equilibrium concepts.

Findings

Floquet quasi-energies relate to a continuous symmetry.

Gauge equivalence to a time-independent problem.

Noether charge recovers equilibrium statistical mechanics.

Abstract

Driven condensed matter systems consistently pose substantial challenges to theoretical understanding. Progress in the study of such systems has been achieved using the Floquet formalism, but certain aspects of this approach are not well understood. In this paper, we consider the exceptionally simple case of the rotating Kekul\'e mass in graphene through the lens of Floquet theory. We show that the fact that this problem is gauge-equivalent to a time-independent problem implies that the "quasi-energies" of Floquet theory correspond to a continuous symmetry of the full time-dependent Lagrangian. We use the conserved Noether charge associated with this symmetry to recover notions of equilibrium statistical mechanics.