Simon Lieu
Time-reversal symmetry (TRS) plays an important role in closed quantum systems, highlighted by developments in symmetry-protected topological phases of matter. By contrast, the role of TRS in open systems remains less thoroughly understood, since such systems propagate irreversibly in time. For example, different symmetry-based classification schemes have been proposed to understand open generalizations of topological band insulators. Here, we prove a generalization of Kramers' degeneracy theorem which applies to open systems described by a Lindblad master equation. We find that a system needs to be coupled to a thermal environment via TRS-respecting terms for spectral degeneracies to survive. We provide simple examples of this phenomenon and show that the degeneracy is reflected in the standard Green's functions, which can be experimentally detected using spectroscopic techniques. While open quantum systems propagate irreversibly in time, our work points to TRS-protected features which survive coupling to a thermal environment.