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Universal structure of computing moments for exact quantum dynamics: Application to arbitrary system-bath couplings
Rui-Hao Bi1, Wei Liu1, Wenjie Dou1,2,3
1Department of Chemistry, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, Zhejiang 310024, China.
The Journal of Chemical Physics
|June 11, 2025
Summary
We present a new method for calculating higher-order moments in open quantum systems using Memory Kernel Coupling Theory (MKCT). This approach accurately models complex system-bath interactions, advancing quantum dynamics simulations.
Area of Science:
- Quantum Mechanics
- Theoretical Physics
- Chemical Physics
Background:
- Open quantum systems are crucial for understanding complex phenomena.
- Calculating higher-order moments of correlation functions is computationally challenging.
- Existing methods struggle with arbitrary system-bath couplings.
Purpose of the Study:
- To introduce a general procedure for computing higher-order moments in open quantum systems.
- To extend the Memory Kernel Coupling Theory (MKCT) for broader applicability.
- To demonstrate the method for polynomial system-bath couplings.
Main Methods:
- Developed a general procedure based on Memory Kernel Coupling Theory (MKCT).
- Analyzed recursive commutators of system operators, revealing a universal hierarchy.
- Evaluated system and bath operators separately, using a generating function for bath expectation values.
- Applied the method to the spin-boson model with linear and quadratic coupling.
Main Results:
- The recursive commutators of system operators follow a universal hierarchy for polynomial couplings.
- Higher-order moments can be computed by evaluating separate system and bath expectation values.
- The dipole autocorrelation function for the spin-boson model was accurately reproduced.
- Achieved agreement with the hierarchical equations of motion approach.
Conclusions:
- The generalized MKCT provides an accurate and efficient method for open quantum systems.
- The universal hierarchy of commutators simplifies calculations for complex couplings.
- This work offers a promising path for accurate dynamics in intricate quantum systems.
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