Classical and quantum shortcuts to adiabaticity in a tilted piston

Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabaticity. In one approach, a counterdiabatic quantum Hamiltonian hat H_CD is constructed to suppress nonadiabatic excitations. In the analogous classical problem, a counterdiabatic classical Hamiltonian H_CD ensures that the classical action remains constant even under rapid driving. Both the quantum and classical versions of this problem have been solved for the special case of scale-invariant driving, characterized by linear expansions, contractions or translations of the system. Here we investigate an example of a non-scale-invariant system - a tilted piston. We solve exactly for the classical counterdiabatic Hamiltonian H_CD(q,p,t), which we then quantize to obtain a Hermitian operator hat H_CD(t). Using numerical simulations, we find that hat H_CD effectively suppresses non-adiabatic excitations under rapid driving. These results offer a proof of principle - beyond the special case of scale-invariant driving - that quantum shortcuts to adiabaticity can successfully be constructed from their classical counterparts.