Quantum Dynamics of Dissipative Polarizable Media

Classical polarizable approaches have become the gold standard for simulating complex systems and processes in the condensed phase. These methods describe intrinsically dissipative polarizable media, requiring a formal definition within the framework of open quantum systems. We present a Hamiltonian formulation for the quantum dynamics of polarizable sources based on a generalized theory of the damped harmonic oscillator, using pseudo-boson theory to characterize their coherent state dynamics. Through a phase space formulation, we derive analytical expressions for correlation functions over arbitrary Gaussian states. These results are then applied to describe the contribution of dissipation in polarizable media to the open dynamics of an interacting quantum system. Moreover, a self-consistent relation for the emitted electric field of the polarizable media is established in the semiclassical approximation, based on exact formulas for medium polarization