Lack of Reversibility for Adiabatic Annealing Protocols starting from Integrable Systems 

Counterdiabatic (CD) driving has proven to be a powerful annealing tool for minimizing disturbances in a system during rapid driving, both in quantum and classical contexts. While previous works have focused on applications of CD to quantum systems, CD driving has also been effectively generalized to both the classical and quantum 1D nonlinear oscillator. We now study the 2D nonlinear oscillator to bridge the gap between single-particle and many-body systems. We find that even under slow driving, the integrable system evolves irreversibly, indicating the absence of an adiabatic limit. From this point, we explore the long-time limit of dynamics in three different regimes for the nonlinear oscillator: integrable to integrable, integrable to nonintegrable, and ergodic to ergodic transitions. These findings have implications for the efficacy of CD driving when applied to semiclassical many-body systems such as Bose-Hubbard models.