Temporal Scattering at Irremovable Exceptional Points in Lossless Drude Media

We investigate temporal scattering in lossless Drude media and reveal an overlooked role of the zero-frequency flat band associated with static polarization charge. This flat band forms an exceptional line spanning all wavenumbers and can be directly excited during temporal scattering at photonic time interfaces, generating non-propagating static fields alongside the usual reflected and transmitted waves. Eigenvector coalescence at the corresponding exceptional points leads to two distinctive features absent in previously studied systems: a static mode whose amplitude increases linearly with time, and an additional static component arising from the system's generalized eigenvector. Remarkably, these effects occur without violating total energy conservation, underscoring the Hermitian nature of the dynamics. Our findings present a new physical picture of temporal scattering, sharply distinct from that in dispersionless and Lorentz-dispersive media.