Decoherence under many-body system-environment interactions: a stroboscopic representation based on a fictitiously homogenized interaction rate

TL;DR

This paper introduces a stroboscopic approach to model many-body system-environment interactions by homogenizing decay rates, enabling efficient numerical simulation and analysis of decoherence processes.

Contribution

It presents a novel fictitious homogenization technique within the Keldysh formalism that simplifies the evaluation of system-environment propagators and is applicable to complex quantum systems.

Findings

The method accurately models multiexponential decay rates.

It facilitates numerical simulation of decoherence in many-body systems.

Application to a fermionic two-level system demonstrates effectiveness.

Abstract

An environment interacting with portions of a system leads to multiexponential interaction rates. Within the Keldysh formalism, we fictitiously homogenize the system-environment interaction yielding a uniform decay rate facilitating the evaluation of the propagators. Through an injection procedure we neutralize the fictitious interactions. This technique justifies a stroboscopic representation of the system-environment interaction which is useful for numerical implementation and converges to the natural continuous process. We apply this procedure to a fermionic two-level system and use the Jordan-Wigner transformation to solve a two-spin swapping gate in the presence of a spin environment.