Local and Global Master Equations through the Lens of Non-Hermitian Physics

TL;DR

This paper explores the connection between non-Hermitian physics and Lindblad dynamics in open quantum systems, revealing how exceptional points appear and differ in local versus global master equations, with implications for experimental realizations.

Contribution

It compares local and global master equations with non-Hermitian models, highlighting the emergence of exceptional points and proposing hybrid configurations for experimental study.

Findings

Exceptional points appear only in local master equations at strong nonequilibrium.

Hybrid models interpolate between Lindblad and non-Hermitian descriptions.

The study suggests circuit-QED platforms for experimental exploration.

Abstract

We investigate the relation between non-Hermitian Hamiltonian and Lindblad dynamics in nonequilibrium open quantum systems. Non-Hermitian models can extend phase diagrams and enable sensing advantages, but such effects often rely on postselection, raising questions about their relevance for unconditional dynamics. Using a minimal two-qubit setup mediating a heat current, we compare local and global Markovian master equations with their non-Hermitian counterparts. We observe that exceptional points emerge only in the local master equation and in the corresponding non-Hermitian Hamiltonian at sufficiently strong nonequilibrium. We further consider hybrid configurations, where one bath is treated with a Lindblad description and the other with a non-Hermitian approach, interpolating between the two extremes. Our results contribute understanding the role of quantum jumps and exceptional points in nonequilibrium open quantum systems and identify a simple, experimentally accessible architecture, realizable, for instance, in circuit-QED platforms, for their exploration.