Asymptotic TCL4 Generator for the Spin-Boson Model: Analytical Derivation and Benchmarking

• URL: http://arxiv.org/abs/2506.17009v1
• Date: Fri, 20 Jun 2025 14:06:19 GMT
• Title: Asymptotic TCL4 Generator for the Spin-Boson Model: Analytical Derivation and Benchmarking
• Authors: Prem Kumar, K. P. Athulya, Sibasish Ghosh,
• Abstract summary: This work presents the derivation of the complete fourth-order time-convolutionless (TCL) generator for a generic spin-boson model.<n>In the case of a semiconductor double-quantum-dot system, our results reveal corrections to the dynamics that may become physically significant.
• Score: 3.1406146587437904
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: The spin-boson model is a widely used model for understanding the properties of a two-level open quantum system. Accurately describing its dynamics often requires going beyond the weak system-environment coupling approximation. However, calculating the higher-order generators of such a dynamics, with a system-environment coupling that is not too weak, has been known to be challenging, both numerically and analytically. This work presents the analytical derivation of the complete fourth-order time-convolutionless (TCL) generator for a generic spin-boson model, accurate up to 4th order in the system-environment coupling parameter, under the assumption that the environmental spectral density is an odd function of frequency. In the case of a semiconductor double-quantum-dot system, our results reveal corrections to the dynamics that may become physically significant in some parameter regimes. Furthermore, we report that the widely used second-order TCL master equation tends to overestimate the non-Markovianity of a dynamics over a large parameter regime. Within the regime of its applicability, our results provide a computational advantage over numerically exact techniques. The accuracy of the fourth-order TCL generator is rigorously benchmarked against specialized analytical calculations done for the Ohmic spectral density with Drude cutoff and against the numerically exact Hierarchical Equations of Motion technique.

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