In open quantum systems, reduced dynamics is commonly described by a master equation, whose Liouvillian gap closing (LGC) typically signals the emergence of decoherence-free subspace. By contrast, the dynamics of the full system-environment compound is governed by the underlying Hamiltonian spectrum, where bound states in the continuum (BICs) can protect long-lived quantum resources. Despite these parallel perspectives, the relation between LGC and BIC formation has remained largely unexplored. Here we bridge this gap in a paradigmatic giant-atom waveguide platform and show that the occurrence of LGC can act as an indicator for a BIC in the full Hamiltonian description in this specific model. By engineering the giant-atom geometry, we further demonstrate rich dynamical regimes, including Rabi oscillations, fractional decay, and complete exponential relaxation, depending on the number of supported BICs, which can be tuned from three to zero. Remarkably, when two BICs become frequency degenerate, the long-time dynamics approaches a steady state rather than exhibiting persistent oscillations. Our results indicate that there may exist a spectral-dynamical correlation between effective Markovian and full Hamiltonian descriptions and provide a route toward flexible control of open-system dynamics.

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• Open quantum systems
• Quantum engineering
• Waveguide arrays