  Methods that are devised to achieve reversal of quantum dynamics in time have
been named "quatum time mirrors". Such a time mirror can be considered as a
generalization of Hahn's spin echo to systems with continuous degrees of
freedom. We extend the quantum time mirror protocol originally proposed for
Dirac dispersions to arbitrary two-band systems and establish the general
requirements for its efficient implementation. We further discuss its
sensitivity to various non- homogeneous perturbations including disorder
potentials and the effect of external static magnetic and electric fields. Our
general statements are verified for a number of exemplary Hamiltonians, whose
phase-coherent dynamics are studied both analytically and numerically. The
Hamiltonians considered can be used to describe the low-energy properties of
systems as diverse as cold atom- optics setups, direct band gap semiconductors
or (mono- or bilayer) graphene. We discuss the consequences of many-body
effects at a qualitative level, and consider the protocol feasibility in
state-of-the-art experimental setups.
