Quantum Mpemba Effect in Random Circuits

Abstract: The essence of the Mpemba effect is that non-equilibrium systems may relax faster the further they are from their equilibrium configuration. In the quantum realm, this phenomenon arises in the dynamics of closed systems, where it is witnessed by fundamental features such as symmetry and entanglement. Here, we study the quantum Mpemba effect in charge-preserving random circuits on qudits combining extensive numerical simulations and analytical arguments. We show that the more asymmetric certain classes of initial states (tilted ferromagnets) are, the faster they restore symmetry and reach the grand-canonical ensemble. Conversely, other classes of states (tilted antiferromagnets) do not show the Mpemba effect. We provide a simple and general mechanism underlying the effect, based on the spreading of nonconserved operators in terms of conserved densities. Our analysis is based on minimal principles -- locality, unitarity, and symmetry. Consequently, our results represent a significant advancement in clarifying the emergence of Mpemba physics in chaotic systems.