Dynamical invariant formalism of shortcuts to adiabaticity

We give a pedagogical introduction to dynamical invariant formalism of shortcuts to adiabaticity. For a given operator form of the Hamiltonian with undetermined coefficients, the dynamical invariant is introduced to design the coefficients. We discuss how the method allows us to mimic adiabatic dynamics and describe a relation to the counterdiabatic formalism. The equation for the dynamical invariant takes a familiar form and is often used in various fields of physics. We introduce examples of Lax pair, quantum brachistochrone and flow equation. This article is part of the theme issue ‘Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives’.