Universal Structure of Computing Moments for Exact Quantum Dynamics: Application to Arbitrary System-Bath Couplings
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| Format: | Preprint |
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2025
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| _version_ | 1866912423840055296 |
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| author | Bi, Rui-Hao Liu, Wei Dou, Wenjie |
| author_facet | Bi, Rui-Hao Liu, Wei Dou, Wenjie |
| contents | We introduce a general procedure for computing higher-order moments of correlation functions in open quantum systems, extending the scope of our recent work on Memory Kernel Coupling Theory (MKCT) [W. Liu, Y. Su, Y. Wang, and W. Dou, arXiv:2407.01923 (2024)]. This approach is demonstrated for arbitrary system-bath coupling that can be expressed as polynomial, $H_{SB} = \hat{V} (α_0 + α_1 \hat{q} + α_2 \hat{q}^2+ \dots)$, where we show that the recursive commutators of a system operator obey a universal hierarchy. Exploiting this structure, the higher-order moments are obtained by evaluating the expectation values of the system and bath operators separately, with bath expectation values derived from the derivatives of a generating function. We further apply MKCT to compute the dipole autocorrelation function for the spin-boson model with both linear and quadratic coupling, achieving agreement with the hierarchical equations of motion approach. Our findings suggest a promising path toward accurate dynamics for complex open quantum systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00649 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Structure of Computing Moments for Exact Quantum Dynamics: Application to Arbitrary System-Bath Couplings Bi, Rui-Hao Liu, Wei Dou, Wenjie Quantum Physics Chemical Physics We introduce a general procedure for computing higher-order moments of correlation functions in open quantum systems, extending the scope of our recent work on Memory Kernel Coupling Theory (MKCT) [W. Liu, Y. Su, Y. Wang, and W. Dou, arXiv:2407.01923 (2024)]. This approach is demonstrated for arbitrary system-bath coupling that can be expressed as polynomial, $H_{SB} = \hat{V} (α_0 + α_1 \hat{q} + α_2 \hat{q}^2+ \dots)$, where we show that the recursive commutators of a system operator obey a universal hierarchy. Exploiting this structure, the higher-order moments are obtained by evaluating the expectation values of the system and bath operators separately, with bath expectation values derived from the derivatives of a generating function. We further apply MKCT to compute the dipole autocorrelation function for the spin-boson model with both linear and quadratic coupling, achieving agreement with the hierarchical equations of motion approach. Our findings suggest a promising path toward accurate dynamics for complex open quantum systems. |
| title | Universal Structure of Computing Moments for Exact Quantum Dynamics: Application to Arbitrary System-Bath Couplings |
| topic | Quantum Physics Chemical Physics |
| url | https://arxiv.org/abs/2504.00649 |