Limits of the non-Hermitian description of decay models

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.

💡 Research Summary

This paper investigates the relationship between two widely used frameworks for describing open quantum systems: non‑Hermitian Hamiltonian dynamics and the Lindblad master equation with purely dissipative (decay) terms. The authors first prove a general theorem (Result R1) stating that, for any Lindblad dynamics in which every jump operator L j reduces the particle number by one (i.e., all L j are annihilation operators), the quantum‑jump term Q