References & Citations
Quantum Physics
Title: Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach
(Submitted on 29 Jun 2022 (v1), last revised 19 Dec 2022 (this version, v2))
Abstract: Equivalent approaches to determine eigenfrequencies of the Liouvillians of open quantum systems are discussed using the solution of the Heisenberg-Langevin equations and the corresponding equations for operator moments. A simple damped two-level atom is analyzed to demonstrate the equivalence of both approaches. The suggested method is used to reveal the structure as well as eigenfrequencies of the dynamics matrices of the corresponding equations of motion and their degeneracies for interacting bosonic modes described by general quadratic Hamiltonians. Quantum Liouvillian exceptional and diabolical points and their degeneracies are explicitly discussed for the case of two modes. Quantum hybrid diabolical exceptional points (inherited, genuine, and induced) and hidden exceptional points, which are not recognized directly in amplitude spectra, are observed. The presented approach via the Heisenberg-Langevin equations paves the general way to a detailed analysis of quantum exceptional and diabolical points in infinitely dimensional open quantum systems.
Submission history
From: Jan Perina Jr. [view email][v1] Wed, 29 Jun 2022 16:16:01 GMT (232kb)
[v2] Mon, 19 Dec 2022 18:09:51 GMT (218kb,D)
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