Asymptotic TCL4 Generator for the Spin-Boson Model: Analytical Derivation and Benchmarking
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909654274015232 |
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| author | Kumar, Prem Athulya, K. P. Ghosh, Sibasish |
| author_facet | Kumar, Prem Athulya, K. P. Ghosh, Sibasish |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic TCL4 Generator for the Spin-Boson Model: Analytical Derivation and Benchmarking Kumar, Prem Athulya, K. P. Ghosh, Sibasish Quantum Physics 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. |
| title | Asymptotic TCL4 Generator for the Spin-Boson Model: Analytical Derivation and Benchmarking |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.17009 |