Non-Markovian dynamics of the giant atom beyond the rotating-wave approximation

We study the non-Markovian dynamics of a giant artificial atom coupled to a one-dimensional acoustic waveguide beyond the rotating-wave and weak-coupling approximations. By combining an optimized ESPRIT-based decomposition of the bath correlation function with the hierarchical equations of motion (HEOM), we achieve numerically exact simulations in regimes with long memory times, finite temperature, and strong system-bath coupling. Benchmarking against analytical results reveals the breakdown of perturbative non-Markovian approaches such as Redfield theory even at weak coupling in the presence of delay-induced memory. We further show that non-Markovian features, including excitation revivals, remain robust at finite temperature and can be enhanced by increasing the system-bath coupling strength. Our approach provides a versatile framework for studying non-Markovian quantum dynamics in structured environments relevant to giant-atom platforms.