Minimizing Losses in Classical Nonlinear Oscillators

Shortcuts to adiabaticity (STAs) have been used to make rapid changes to a system while eliminating or minimizing disturbances to the system's state. Especially in quantum systems, these shortcuts allow us to minimize inefficiencies and heating in experiments and quantum computing, but the theory of STAs can also be generalized to classical systems. We focus on one such STA, approximate counter-diabatic (ACD) driving, and numerically compare its performance in two classical systems: a quartic anharmonic oscillator and the β Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. In particular, we modify an existing variational technique to optimize the approximate driving and then develop classical figures of merit to quantify the performance of the driving. We find that relatively simple driving terms can dramatically suppress excitations regardless of system size. ACD driving in classical oscillators could have many applications, from minimizing heating in bosonic gases to investigating other classical nonlinear systems with many degrees of freedom.