Lindbladian approximation beyond ultra-weak coupling

TL;DR

This paper introduces a new Lindbladian approximation for open quantum systems that remains accurate beyond ultra-weak coupling, especially in nonequilibrium conditions, improving upon the traditional RWA-based methods.

Contribution

It presents an alternative derivation of Lindblad-type master equations that does not depend on ultra-weak coupling assumptions, extending applicability to broader regimes.

Findings

The new approximation performs well away from equilibrium.

It outperforms the RWA in large parameter regimes.

Effective for extended Hubbard models with Ohmic baths.

Abstract

Away from equilibrium, the properties of open quantum systems depend on the details of their environment. A microscopic derivation of a master equation (ME) is therefore crucial. Of particular interest are Lindblad-type equations, not only because they provide the most general class of Markovian MEs, but also since they are the starting point for efficient quantum trajectory simulations. Lindblad-type MEs are commonly derived from the Born-Markov-Redfield equation via a rotating-wave approximation (RWA). However the RWA is valid only for ultra-weak system bath coupling and often fails to accurately describe nonequilibrium processes. Here we derive an alternative Lindbladian approximation to the Redfield equation, which does not rely on ultra-weak system-bath coupling. Applying it to an extended Hubbard model coupled to Ohmic baths, we show that, especially away from equilibrium, it provides a good approximation in large parameter regimes where the RWA fails.