A shortcut to adiabaticity is a finite-time process that produces the same
final state as would result from infinitely slow driving. We show that such
shortcuts can be found for weak perturbations from linear response theory. With
the help of phenomenological response functions a simple expression for the
excess work is found -- quantifying the nonequilibrium excitations. For two
specific examples, the quantum parametric oscillator and the spin-1/2 in a
time-dependent magnetic field, we show that finite-time zeros of the excess
work indicate the existence of shortcuts. Finally, we propose a degenerate
family of protocols, which facilitate shortcuts to adiabaticity for specific
and very short driving times.Comment: 9 pages, 8 figure; published versio
