Quantum Dynamics of Dissipative Polarizable Media

TL;DR

This paper develops a quantum Hamiltonian framework for dissipative polarizable media, enabling detailed analysis of their optical response and open quantum dynamics, with applications to plasmonic systems.

Contribution

It introduces a Hamiltonian formulation for quantum dissipative media using pseudo-boson theory and derives a master equation for their open quantum dynamics.

Findings

Derived a self-consistent relation for emitted electric fields.

Provided analytical expressions for correlation functions in Gaussian states.

Applied theory to study optical responses of plasmonic systems.

Abstract

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. We then apply our theory to the study of the optical response of two plasmonic systems. Furthermore, by exploiting the phase space formulation of quantum mechanics and the integrability of quadratic Hamiltonians, we derive a self-consistent relation for the emitted electric field of the polarizable medium under the semiclassical approximation, based on exact formulas for medium polarization. Finally, we derive the master equation describing the open dynamics of a quantum system interacting with the quantum polarizable medium, along with analytical expressions for correlation functions calculated over arbitrary Gaussian states.