Exceptional point in a coupled Swanson system

Abstract

We propose an interacting nonhermitian model described by a two-mode quadratic Hamiltonian along with an interaction term to locate and analyze the presence of an exceptional point in the system. Each mode is guided by a Swanson-like quadratic Hamiltonian and a suitable choice is made for the interaction term. The parity-time symmetric transformation is adopted in the standard way relevant for a coupled system.

11 pages, 2 figures; Accepted in Europhysics Letters

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• A reappraisal of Lagrangians with non-quadratic velocity dependence and branched Hamiltonians
• Pseudo-Hermitian extensions of the harmonic and isotonic oscillators
• Artificial Hawking radiation, weak pseudo-Hermiticity and Weyl semimetal blackhole analogy
• Features, paradoxes and amendments of perturbative non-Hermitian quantum mechanics
• Phase transitions in quasi-Hermitian quantum models at exceptional points of order four
• Emergence and localization of exceptional points in an exactly solvable toy model
• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics