Limits of the non-Hermitian description of decay models

TL;DR

This paper proves the equivalence of non-Hermitian and Lindblad decay dynamics in the highest particle subspace, identifies limits of non-Hermitian accuracy, and discusses the absence of exceptional points in weak-coupling regimes.

Contribution

It provides a general proof of the equivalence between non-Hermitian and Lindblad decay models and introduces a method to assess non-Hermitian descriptions' validity.

Findings

Non-Hermitian and Lindblad dynamics are equivalent in the highest particle subspace.

Non-Hermitian approximation is accurate only in weak and singular coupling limits.

Exceptional points cannot occur in weak-coupling for nondegenerate Hamiltonians.

Abstract

We present a general proof that non-Hermitian dynamics and Lindblad dynamics with only decay terms are equivalent in the highest particle subspace. We then propose an unbiased method to determine if a system's dynamics in the highest-particle subspace is non-Hermitian. We exemplify this for a simple two-site decay system connected to two baths, and find that the exact solution is well approximated by non-Hermitian dynamics only in the weak-coupling and in the singular-coupling limits, where a Lindbladian description was already known to be accurate. The fact that an accurate non-Hermitian description is so limited, even for such a simple system, raises doubts about how valid such descriptions are for more complicated systems away from these asymptotic limits. Finally, we prove that for models with a nondegenerate system Hamiltonian, exceptional points cannot occur in the weak-coupling limit. This result is relevant for the design of experiments that aim to identify such exceptional points.