Effective Hamiltonian approach to the exact dynamics of open system by complex discretization approximation for environment

• URL: http://arxiv.org/abs/2303.06584v5
• Date: Sat, 08 Feb 2025 11:03:22 GMT
• Title: Effective Hamiltonian approach to the exact dynamics of open system by complex discretization approximation for environment
• Authors: H. T. Cui, Y. A. Yan, M. Qin, X. X. Yi,
• Abstract summary: We paper proposes a novel generalization of the discretization approximation method into the complex plane using complex Gauss quadratures. An effective Hamiltonian can be established by this way, which is non-Hermitian and demonstrates the complex energy modes with negative imaginary part.
• Score: 0.0
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• Abstract: The discretization approximation method in real configuration commonly used to simulate the open dynamics of system coupled to the environment in continuum often suffers from the recurrence. To address this issue, we paper proposes a novel generalization of the discretization approximation method into the complex plane using complex Gauss quadratures. An effective Hamiltonian can be established by this way, which is non-Hermitian and demonstrates the complex energy modes with negative imaginary part, describing accurately the dissipative dynamics of the system. This method is applied to examine the dynamics in two exactly solvable models, the dephasing model and the single-excitation open dynamics in the Aubry-Andr\'{e}-Harper model. By comparison with the exact numerics and analytical results, it is found that our approach not only significantly reduces recurrence and improve the effectiveness of calculation, but also provide a unique perspective into the dynamics of system based on the complex eigenvalues and corresponding eigenvectors. Furthermore, by analyzing the computational error, we establish a simple relationship between the parameters in computation and the effectiveness of simulation.

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