2021/08/15 by Andreas Fring, Rebecca Tenney
Engineering · Mathematics · Physics and Astronomy · #Engineering #Hamiltonian (control theory) #Hermitian matrix #Mathematical analysis #Mathematical optimization #Mathematics #Metric (unit) #Nonlinear Photonic Systems #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Scheme (mathematics) #Series (stratigraphy) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8121/ac31a0
published as Journal of Physics A: Mathematical and Theoretical 54(2021) 485201 · 16 pages
arxiv created 2021/08/15 · openalex publication_date 2021/10/20 · arxiv updated 2021/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract We propose and explore a scheme that leads to an infinite series of time-dependent Dyson maps which associate different Hermitian Hamiltonians to a uniquely specified time-dependent non-Hermitian Hamiltonian. We identify the underlying symmetries responsible for this feature respected by various Lewis–Riesenfeld invariants. The latter are used to facilitate the explicit construction of the Dyson maps and metric operators. As a concrete example for which the scheme is worked out in detail we present a two-dimensional system of oscillators that are coupled to each other in a non-Hermitian <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">PT</mml:mi> </mml:math> -symmetrical fashion.