Nontrivial Damping of Quantum Many-Body Dynamics in the Schr\"odinger Picture

Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of cases, the unperturbed dynamics is just damped by a simple function, e.g., exponentially as expected from Fermi's Golden Rule. While these predictions rely on random-matrix arguments and typicality, they can only be verified for a specific physical situation by comparing to the actual solution or measurement. Crucially, it also remains unclear how frequent and under which conditions counterexamples to the typical behavior occur. In this work, we discuss this question from the perspective of projection-operator techniques, where exponential damping occurs in the interaction picture but not necessarily in the Schrodinger picture. We suggest that a nontrivial damping in the Schrodinger picture can emerge if the dynamics in the unperturbed system possesses rich features. This suggestion is substantiated by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain, where the nearest-neighbor interactions are treated as a perturbation to the integrable reference system.