A toy black hole model tracks information through Hawking radiation

Using a simplified matrix quantum mechanics inspired by Maldacena's recent proposal, the authors track Krylov complexity—a measure of how broadly a quantum state spreads through operator space—as a black hole radiates. Early-time growth matches expectations for chaotic systems; late-time behavior saturates to a plateau signaling equilibration between the black hole and its emitted radiation. The plateau is given a semiclassical explanation via Euclidean instanton contributions in an effective path integral. The model is deliberately minimal, trading full dynamical fidelity for analytic and numerical tractability.