  We use the dynamical algebra of a quantum system and its dynamical invariants
to inverse engineer feasible Hamiltonians for implementing shortcuts to
adiabaticity. These are speeded up processes that end up with the same
populations than slow, adiabatic ones. As application examples we design
families of shortcut Hamiltonians that drive two and a three-level systems
between initial and final configurations imposing physically motivated
constraints on the terms (generators) allowed in the Hamiltonian.

Quantum Physics