Open quantum systems integrable by partial commutativity

TL;DR

This paper introduces a framework based on partial commutativity and the Fedorov theorem to solve linear differential equations in open quantum systems, enabling analysis of time-dependent dissipative dynamics.

Contribution

It presents a novel method leveraging partial commutativity and the Fedorov theorem for solving dynamical maps in open quantum systems with time-dependent generators.

Findings

Efficient solution framework for specific quantum systems.

Applicable to systems with time-dependent relaxation rates.

Demonstrated on three-level and four-level quantum systems.

Abstract

The article provides a framework to solve linear differential equations based on partial commutativity which is introduced by means of the Fedorov theorem. The framework is applied to specific types of three-level and four-level quantum systems. The efficiency of the method is evaluated and discussed. The Fedorov theorem appears to answer the need for methods which allow to study dynamical maps corresponding with time-dependent generators. By applying this method, one can investigate countless examples of dissipative systems such that the relaxation rates depend on time.