Open quantum systems with particle and bath driven by time-dependent fields

TL;DR

This paper derives a generalized quantum Langevin equation and fluctuation-dissipation relation for a particle interacting with a medium under time-dependent external fields, with applications in quantum noise and wireless technology.

Contribution

It introduces a new form of the quantum Langevin equation and fluctuation-dissipation relation accounting for external time-dependent fields, extending previous models to driven quantum systems.

Findings

Derived a generalized quantum Langevin equation for driven systems

Established a modified fluctuation-dissipation relation including external fields

Presented a new quantum Nyquist noise expression relevant for GHz-THz frequencies

Abstract

We derive a generalized quantum Langevin equation and its fluctuation-dissipation relation describing the quantum dynamics of a tagged particle interacting with a medium (environment), where both the particle and the environment are driven by an external time-dependent (e.g. oscillating) field. We specialize on the case of a charged tagged particle interacting with a bath of charged oscillators, under an external AC electric field, although the results are much more general and can be applied to any type of external time-dependent fields. We derive the corresponding quantum Langevin equation, which obeys a modified fluctuation-dissipation relation (FDR) where the AC field plays an explicit role. The modified FDR is non-Markovian even if the undriven particle-bath system is Markovian without the external field. We provide an illustration of the usefulness of these results and derive a new form of the quantum Nyquist noise for the voltage fluctuations in electrical circuits under AC conditions (finite frequency), which is the most general since it also accounts for the response of the heat bath (e.g. lattice ions) to the applied AC electric field in the GHz-THz region, of relevance for 5G/6G wireless technologies. This generalized quantum fluctuation-dissipation relation for driven systems can also find other applications ranging from quantum noise in quantum optics to quantum computing with trapped ions.