Time-local Heisenberg-Langevin equations and the driven qubit

TL;DR

This paper derives a time-local master equation for driven boson systems, highlights the failure of extending this to driven qubits beyond weak excitation, and reveals unusual asymptotic behavior in driven systems far from equilibrium.

Contribution

It demonstrates the limitations of existing time-local equations for driven qubits and uncovers novel asymptotic dynamics in far-from-equilibrium driven systems.

Findings

Derived a time-local master equation for driven boson systems.

Showed the failure of extending this to driven qubits beyond weak excitation.

Identified persistent oscillations and singularities in the asymptotic dynamics of driven systems.

Abstract

The time-local master equation for a driven boson system interacting with a boson environment is derived by way of a time-local Heisenberg--Langevin equation. Extension to the driven qubit fails---except for weak excitation---due to the lost linearity of the system-environment interaction. We show that a reported time-local master equation for the driven qubit is incorrect. As a corollary to our demonstration, we also uncover odd asymptotic behavior in the "repackaged" time-local dynamics of a system driven to a far-from-equilibrium steady state: the density operator becomes steady while time-dependent coefficients oscillate (with periodic singularities) forever.