Time-dependent PT-symmetric quantum mechanics in generic non-Hermitian systems

A conceptual framework extending (time-independent) PT-symmetric quantum mechanics into the time-dependent domain is presented. It is built upon a nontrivial time-dependent metric operator identified here and works for generic finite-dimensional non-Hermitian systems. All the ingredients of our framework, such as the time-dependent Hilbert space, the observable, and the measurement postulate, can be "realized" by means of dilating and reinterpreting the non-Hermitian system in question as a part of a larger Hermitian system. Aided by our metric operator, we formulate the concepts of stable and unstable phases for generic non-Hermitian systems and argue that they, respectively, generalize the notions of unbroken and broken phases in time-independent PT-symmetric systems. Possible applications of our framework are illustrated with well-known examples in quantum thermodynamics.