2022/01/13 by Kaustubh S. Agarwal, Jacob Muldoon, Yogesh N. Joglekar
Chemistry · Mathematics · Physics and Astronomy · #Conserved quantity #Exponential function #Floquet theory #Hermitian function #Hermitian matrix #Mathematical analysis #Mathematical physics #Mathematics #Parity (physics) #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Simple (philosophy) #Statistical physics #Synthesis and Properties of Aromatic Compounds #Time evolution #quant-ph
paper · pdf · doi:10.14311/ap.2022.62.0001
published as Acta Polytechnica 62, 1 (2022) · 7 pages, 2 figure: Proceedings of AAMP XVIII (Prague 2021)
arxiv created 2022/01/13 · openalex publication_date 2022/02/28 · arxiv updated 2022/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time (PT) symmetry that are best understood as systems with balanced, separated gain and loss. Here, we present an alternative way to characterize and derive conserved quantities, or intertwining operators, in such open systems. As a consequence, we also obtain non-Hermitian or Hermitian operators whose expectations values show single exponential time dependence. By using a simple example of a PT-symmetric dimer that arises in two distinct physical realizations, we demonstrate our procedure for static Hamiltonians and generalize it to time-periodic (Floquet) cases where intertwining operators are stroboscopically conserved. Inspired by the Lindblad density matrix equation, our approach provides a useful addition to the well-established methods for characterizing time-invariants in non-Hermitian systems.