Self-consistent dynamical maps for open quantum systems

TL;DR

This paper introduces self-consistent dynamical maps for open quantum systems that extend traditional master equations by incorporating non-perturbative environmental effects through the non-crossing approximation, demonstrated on the spin-boson model.

Contribution

It presents NCA and NCA-Markov dynamical maps that go beyond Born-Markov master equations using a self-consistent approximation, capturing strong-coupling effects.

Findings

Successfully applied to the spin-boson model at zero temperature.

Qualitatively captures strong-coupling behavior.

Quantitatively accurate beyond standard master equations.

Abstract

In several cases, open quantum systems can be successfully described using master equations relying on Born-Markov approximations, but going beyond these approaches has become often necessary. In this work, we introduce the NCA and NCA-Markov dynamical maps for open quantum systems, which go beyond these master equations replacing the Born approximation with a self-consistent approximation, known as non-crossing approximation (NCA). These maps are formally similar to master equations, but allow to capture non-perturbative effects of the environment at a moderate extra numerical cost. To demonstrate their capabilities, we apply them to the spin-boson model at zero temperature for both a Ohmic and a sub-Ohmic environment, showing that they can both qualitatively capture its strong-coupling behaviour, and be quantitatively correct beyond standard master equations.