Speaker
Description
Describing out-of-equilibrium quantum many-body dynamics remains a central challenge in condensed matter physics. While the time-dependent two-particle reduced density matrix (TD2RDM) formalism avoids the exponential scaling of exact wave-function methods, it requires closing the BBGKY hierarchy by reconstructing the three-particle cumulant. However, the validity of time-local reconstruction functionals - which ignore memory effects - remains unclear across different dynamical regimes.
In this work, we employ neural ordinary differential equations (ODEs) as a model-agnostic diagnostic tool to map the applicability of time-local cumulant expansion methods [1]. We show that neural ODEs trained on exact 2RDM data successfully extrapolate dynamics only when the correlation between two- and three-particle cumulants is high. In anti-correlated or uncorrelated regimes, the model’s failure indicates that no time-local functional can capture the evolution, highlighting the necessity of memory-dependent kernels. These findings establish neural ODEs as a powerful diagnostic tool for mapping the limits of time-local approximations and guiding the design of more robust, memory-dependent closure schemes.
[1] P. Egenlauf, I. Březinová, S. Andergassen, and M. Klopotek, arXiv:2512.13913 (2025).