2019/06/08 by Da-Jian Zhang, Qinghai Wang, Qing-hai Wang +1 · 1 citation
Mathematics · Physics and Astronomy · #Eigenvalues and eigenvectors #Hermitian matrix #Hilbert space #Mathematical physics #Mathematics #Mechanical and Optical Resonators #Observable #Operator (biology) #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #quant-ph
paper · pdf · doi:10.1103/physreva.100.062121
published as Phys. Rev. A 100, 062121 (2019) · 9 pages, no figures
arxiv created 2019/06/08 · openalex created_date 2019/06/14 · openalex publication_date 2019/12/20 · arxiv updated 2019/12/25 · openalex updated_date 2026/08/05
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.