Quantum Markovian master equation in the high-temperature limit

TL;DR

This paper derives a high-temperature quantum Markovian master equation (HTME) that generalizes existing models, incorporates non-thermal initial states, and clarifies the conditions for its validity in open quantum systems.

Contribution

The authors provide a rigorous derivation of the HTME, extending previous models to include non-thermal states and analyzing spectral density symmetrization, thereby refining the theoretical framework for quantum dissipation.

Findings

Derivation of a generalized HTME including non-thermal initial states

Identification of a symmetrization condition for spectral densities at high temperatures

Demonstration of limitations of ARH-IME in strongly correlated spin systems

Abstract

We present a critical derivation of the high-temperature quantum Markovian master equation (HTME), examining its foundational assumptions, their quantum-mechanical implications, and its range of validity. Starting from the Born-Markov master equation, and combining the spin Hamiltonian eigenoperator formalism with a linear expansion in statistical coefficients, as the only assumption, we obtain a quantum dissipator that generalizes the Abragam-Redfield-Hubbard inhomogeneous master equation (ARH-IME). Our derivation naturally incorporates an additional term for non-thermal, high-order initial states, while reducing to ARH-IME for spin states evolving near thermal equilibrium (weak-order). Through an alternative operator-based derivation of the HTME, we confirm these results and reveal a symmetrization condition for the spectral densities in the linear thermal regime. We rigorously analyze the internal consistency of both approaches and compare them with prior literature. To illustrate these findings, we study: (i) A canonical spin-1/2 system interacting with a bosonic bath, demonstrating first-principles symmetrization of spectral densities at high temperatures. (ii) Singlet-triplet conversion in a correlated two-spin system, where the ARH-IME fails, exposing the limitations of the weak-order hypothesis in strongly correlated regimes. Our results challenge the traditional boundaries of NMR spin-lattice relaxation theory and provide a refined framework for modeling open quantum systems beyond weak order.