Constructing bath correlation functions aligned with the fluctuation-dissipation relation for efficient open quantum dynamics simulation

Dissipative quantum systems are commonly studied through the bath oscillator model, where the bath’s influence on the reduced dynamics is encapsulated in the bath correlation function (BCF). The BCF satisfies the fluctuation-dissipation relation (FDR), which leads to the thermalization of the reduced state.

The hierarchical equations of motion [1] enable efficient simulation of the bath oscillator model by expressing the BCF as a sum of exponential terms. Recently, several algorithms have been proposed to express complex BCF using a minimal set of exponential terms [2–5].

In this presentation, we explore an alternative approach that builds upon the methods in Refs. [4,5]. Similar to these methods, we treat the structural and Matsubara contributions separately. To accurately capture thermalization behavior, we fit the Matsubara contribution to closely align with the FDR. The efficiency of our method is assessed by directly comparing simulation results with exact solutions. Additionally, we identify a condition that guarantees complete positivity of the reduced dynamics and discuss the integration of this condition into our method.

[1] Y. Tanimura, J. Chem. Phys. 153, 020901 (2020).

[2] M. Xu, et al., Phys. Rev. Lett. 129, 230601 (2022).

[3] H. Takahashi, et al., J. Chem. Phys. 160, 204105 (2024).

[4] N. Lambert, et al., Nature Communications 10, 3721 (2019).

[5] B. L. Dé, et al., J. Chem. Phys. 160, 244102 (2024).