Trajectory-based multi-configuration approaches to interacting many-body quantum dynamics

We give a brief review of trajectory-based methods to solve the time-dependent Schrödinger equation for Bose-Hubbard (BH) models and other model systems of interest in chemical physics. In order of increasing accuracy these are the truncated Wigner approximation [1], the Herman-Kluk propagator [2], the coupled coherent states approach [3] and a fully variational multi-configuration Gaussian method [4] that has recently been extended by the use of generalized coherent states [5]. The first three methods are based on classical trajectories, while the last method employs "quantum" trajectories.

We then discuss the results of benchmark calculations for BH model systems with increasing well numbers and highlight the fact that the more advanced methods are well suited to reveal genuine quantum effects beyond initial state preparation [6]. Furthermore, in the Mott insulator regime, a surprising quantum enhancement of thermalization is found [7].

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[5] Y. Qiao and F. Grossmann, Phys. Rev. A 103, 042209 (2021)
[6] Y. Qiao and F. Grossmann, Front. Phys. 11, 1221614 (2023)
[7] Y. Qiao et al., Phys. Rev. Lett. 135, 060404 (2025)