Reducing Spatial and Temporal Dimensionality in the Multidimensional Caldeira-Leggett Model
arXiv:2509.24525
The paper develops an efficient algorithm for simulating the real-time dynamics of the reduced density matrix in the multidimensional Caldeira‑Leggett model by using low‑rank spatial approximations and frozen Gaussian temporal approximations to cut down the dimensionality of the required integrals.
Abstract
Focusing on the real-time dynamics of the reduced density matrix of the multidimensional Caldeira-Leggett model, several techniques are adopted in this paper to reduce the spatial and temporal dimensionality, combined into an efficient algorithm. From a spatial perspective, an equivalent formulation of the Dyson series is presented. With the aid of a low-rank approximation, the spatial dimensionality of open quantum system simulations is halved. From a temporal perspective, the frozen Gaussian approximation is used to approximate both the evolution operator and the interaction operator in the multidimensional Caldeira-Leggett model. This reduces the high-dimensional integrals to one- and two-dimensional integrals independent of the truncation level of the Dyson series. Through these techniques, we design an efficient algorithm whose validity is verified through several numerical experiments, including a two-dimensional double slit simulation.