Testing bath correlation functions for open quantum dynamics simulations

Dissipative quantum systems are often investigated using the bath oscillator model, where the bath correlation function characterizes the reduced dynamics. Common simulation methods, including the hierarchical equations of motion [1] and the pseudomode representation [2], require an approximation of the bath correlation functions.

In this presentation, we address the challenge of assessing simulation accuracy for a given bath correlation function. A direct approach is to benchmark against exact solutions, with the harmonic oscillator system being particularly useful for evaluating the accuracy regarding thermalization [3]. However, simulating such a system requires additional approximations, such as truncating the infinite-dimensional oscillator system space.

We propose a method to facilitate this benchmark test. The idea is to use a moment-based state representation [4], where truncations can be performed exactly at a finite order due to the Gaussian nature of the system. This allows for robust and efficient testing, even in cases with complex bath correlation functions. We apply this method to test existing algorithms for fitting the bath correlation function.

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

[2] D. Tamascelli, et al., Phys. Rev. Lett. 120, 030402 (2018).

[3] Y. Tanimura, J. Chem. Phys. 142, 144110 (2015).

[4] M. Tokieda, Phys. Rev. A 109, 062228 (2024).