Coupled systems subject to dissipation exhibit two different regimes known as weak coupling and
strong coupling. Two damped coupled harmonic oscillators (CHOs) constitute a model system where the
key features of weak and strong coupling can be identified. Several of these features are common to
classical and quantum systems, as a number of quantum-classical correspondences have shown. However,
the condition defining the boundary between weak and strong coupling is distinct in classical and
quantum formalisms. Here we describe the origin of two widely used definitions of strong coupling.
Using a classical CHO model, we show that energy exchange cycles and avoided resonance crossings
signal the onset of strong coupling according to one criterion. From the classical CHO model we
derive a non-Hermitian Hamiltonian describing open quantum systems. Based on the analytic properties
of the Hamiltonian, we identify the boundary between weak and strong coupling with a different
feature: a…