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arXiv · 2508.18385

Quantum Markovian master equation in the high-temperature limit

Ricardo C. Zamar·J. Agustín Taboada
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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.

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Ricardo C. Zamar, J. Agustín Taboada. 2025-08-25. Quantum Markovian master equation in the high-temperature limit. https://arxiv.org/abs/2508.18385

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