Fourth-Order Master Equation for a Charged Harmonic Oscillator Interacting with the Electromagnetic Field

TL;DR

This paper derives a detailed fourth-order master equation for a charged harmonic oscillator interacting with an electromagnetic field, revealing the significance of higher-order effects on system dynamics.

Contribution

It provides exact analytical expressions for higher-order corrections in the master equation, including mass renormalization and diffusion coefficients, for the first time in this context.

Findings

Third and fourth order contributions often oppose second order effects.

Higher-order terms significantly influence the oscillator's dissipation and diffusion.

Analytical results are obtained for a blackbody environment.

Abstract

The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth-order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form and includes a diamagnetic term. Exact analytical expressions for the second, the third, and the fourth-order contributions to mass renormalization, decay constant, normal and anomalous diffusion coefficients are obtained for the blackbody type environment. It is found that, generally, the third and the fourth order contributions have opposite sign when their magnitudes are comparable to that of the second order one.