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Classical and Quantum Shortcuts to Adiabaticity in a Tilted Piston
journal contribution
posted on 2016-10-04, 00:00 authored by Ayoti Patra, Christopher JarzynskiAdiabatic quantum state evolution
can be accelerated through a
variety of shortcuts to adiabaticity. In one approach,
a counterdiabatic quantum Hamiltonian, ĤCD, is constructed to suppress nonadiabatic excitations. In
the analogous classical problem, a counterdiabatic classical Hamiltonian, HCD, 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, HCD(q, p, t), which we then quantize to obtain a Hermitian operator, ĤCD(t). Using numerical
simulations, we find that ĤCD effectively
suppresses nonadiabatic 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.