Equilibrium frame reveals hidden PT symmetry of passive systems

TL;DR

This paper introduces an equilibrium frame approach to uncover hidden PT symmetry in passive, dissipative systems, revealing symmetries and exceptional point behaviors not apparent in the original Hamiltonian.

Contribution

It demonstrates that non-Hermitian Hamiltonians with certain decompositions possess hidden PT symmetries that become visible in an equilibrium frame.

Findings

Hidden PT symmetries are revealed in the equilibrium frame.

Passive systems can exhibit exceptional points similar to PT-symmetric systems.

Eigenstate degeneracies are more apparent in the equilibrium frame.

Abstract

We discuss how introducing an equilibrium frame, in which a given Hamiltonian has balanced loss and gain terms, can reveal PT symmetry hidden in non-Hermitian Hamiltonians of dissipative systems. Passive PT-symmetric Hamiltonians, in which only loss is present and gain is absent, can also display exceptional points, just like PT-symmetric systems, and therefore are extensively investigated. We demonstrate that non-Hermitian Hamiltonians, which can be divided into a PT-symmetric term and a term commuting with the Hamiltonian, possess hidden PT symmetries. These symmetries become apparent in the equilibrium frame. We also show that the number of eigenstates having the same value in an exceptional point is usually smaller in the initial frame than in the equilibrium frame. This property is associated with the second part of the Hamiltonian.