Limits of the Lindblad and non-Hermitian description of open systems

Abstract: While it is well established that the dynamics of an open system is described accurately by the Lindblad master equation if the coupling to the bath is either in the weak or in the singular limit, it is not known whether this also extends to other coupling strengths. Here we use the exact solution of a microscopic system coupled to baths to gauge the validity of the Lindblad dynamics during a finite time evolution, and show that for a pure decay system, Lindbladian dynamics generally only holds in the weak and singular coupling limits. We also prove that Lindblad and non-Hermitian dynamics are equivalent in the highest particle subspace of such systems with pure decay. Using this equivalence, we rule out the possibility of obtaining non-Hermitian dynamics for any other couplings. Furthermore, we argue that exceptional points of the effective non-Hermitian Hamiltonian can only occur in the singular coupling limit, never in the weak coupling limit. Physically, this means that exceptional points can occur when the intrinsic time evolution of the isolated system is comparable to the relaxation time scale.