On the Discretization Error of the Discrete Generalized Quantum Master Equation

• URL: http://arxiv.org/abs/2507.19323v1
• Date: Fri, 25 Jul 2025 14:34:53 GMT
• Title: On the Discretization Error of the Discrete Generalized Quantum Master Equation
• Authors: Ruojing Peng, Lachlan P. Lindoy, Joonho Lee,
• Abstract summary: The transfer tensor method (TTM) can be considered a discrete-time formulation of the Nakajima-Zwanzig quantum master equation (NZ-QME)<n>Recent paper raised concerns regarding the consistency of the TTM discretization.
• Score: 1.791016913040303
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The transfer tensor method (TTM) [Cerrillo and Cao, Phys. Rev. Lett. 2014, 112, 110401] can be considered a discrete-time formulation of the Nakajima-Zwanzig quantum master equation (NZ-QME) for modeling non-Markovian quantum dynamics. A recent paper [Makri, J. Chem. Theory Comput. 2025, 21, 5037] raised concerns regarding the consistency of the TTM discretization, particularly a spurious term at the initial time \( t=0 \). This Communication presents a detailed analysis of the discretization structure of TTM, clarifying the origin of the initial-time correction and establishing a consistent relationship between the TTM discrete-time memory kernel \( K_N \), and the continuous-time NZ-QME kernel \( \mathcal{K}(N\Delta t) \). This relationship is validated numerically using the spin-boson model, demonstrating convergence of reconstructed memory kernels and accurate dynamical evolution as \( \Delta t \to 0 \). While TTM provides a consistent discretization, we note that alternative schemes are also viable, such as the midpoint derivative/midpoint integral scheme proposed in Makri's work. The relative performance of various schemes for either computing accurate \( \mathcal{K}(N\Delta t) \) from exact dynamics, or obtaining accurate dynamics from exact \( \mathcal{K}(N\Delta t) \), warrants further investigation.

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