Rescaled time, shortcuts to adiabaticity, and Dirac dynamics

Shortcuts to adiabaticity are a prominent tool-kit from quantum control to achieve effectively adiabatic dynamics in finite time. In this work, we explore both classical and quantum variants of shortcuts from so-called time-rescaled dynamics. We prove that time-rescaled Schrodinger systems and its classical variants with scale-invariant potentials can be reduced to time-independent problems with a modified scale-invariant potential. We also show that Hamiltonians, containing time-dependent kinetic terms in multi-dimensional Dirac systems like ultracold atoms, graphene and Weyl semi-metals, can be controlled and have their time-dependence modified by using external parameters in additional driving potentials. Our work opens up new avenues to realize shortcuts to adiabaticity in systems where the dynamics may have complicated dependence on time.