Local vs global dynamics in a dissipative qubit-impurity system

TL;DR

This paper compares local and global derivation schemes of GKSL master equations for a dissipative qubit-impurity system, showing the local approach better captures qubit coherence dynamics in relevant regimes.

Contribution

It clarifies the validity domains of local and global GKSL approaches and demonstrates the local scheme's superiority in certain parameter regimes.

Findings

Local approach captures qubit coherence crossover accurately.

Global approach's validity is limited to well-separated energy scales.

Local scheme provides a better GKSL description in experimental regimes.

Abstract

We analyse the dynamics of a qubit coupled to a dissipative impurity by comparing local and global derivation schemes of a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation within the Born-Markov and full secular (FS) approximations. We show that the local approach correctly captures a crossover in the dynamics of the qubit coherence, while the FS approximation restricts the validity of the global approach to regimes with well-separated energy scales. Our results clarify the domains of validity of the two approaches and show that the local scheme provides a better GKSL description of the qubit dynamics in the experimentally relevant parameter regime.