Counterdiabatic driving for Reversible and Irreversible Processes in 2D Systems

Counterdiabatic (CD) driving has been demonstrated to be an effective protocol for suppressing transitions in quantum and classical systems subject to fast driving. Previous work has found that the protocol performs equivalently for classical and quantum 1D non-linear oscillators. We study the efficacy of CD driving in 2D non-linear classical systems. Specifically, we evaluate the performance of the protocol in systems that (i) remain within an integrable regime, (ii) transition from integrable to non-integrable regime and (iii)  remain within an ergodic regime. Despite the some subtleties about the presence of an adiabatic limit, we see that the protocol performs efficiently in (i) and (ii) while having limited effectiveness in (iii). These findings have implications for the efficacy of CD driving in quantum many-body systems such as the Bose Hubbard model.