  We investigate the universal dissipationless dynamics of Gaussian
continuous-variable systems in the presence of a band-gapped bosonic
environment. Our results show that environmental band gaps can induce localized
modes, which give rise to the dissipationless dynamics where the system behaves
as free oscillators instead of experiencing a full decay in the long time
limit. We present a complete characterization of localized modes, and show the
existence of the critical system-environment coupling. Beyond the critical
values, localized modes can be produced and the system dynamics become
dissipationless. This novel dynamics can be utilized to overcome the
environmental noises and protect the quantum resources in the
continuous-variable quantum information.
