  Particles in space periodic potentials constitute standard models for
investigation of crystalline phenomena in solid state physics. Time periodicity
of periodically driven systems is a close analogue of space periodicity of
solid state crystals. There is an intriguing question if solid state phenomena
can be observed in the time domain. Here we show that wave-packets localized on
resonant classical trajectories of periodically driven systems are ideal
elements to realize Anderson localization or Mott insulator phase in the time
domain. Uniform superpositions of the wave-packets form stationary states of a
periodically driven particle. However, an additional perturbation that
fluctuates in time results in disorder in time and Anderson localization
effects emerge. Switching to many-particle systems we observe that depending on
how strong particle interactions are, stationary states can be Bose-Einstein
condensates or single Fock states where definite numbers of particles occupy
the periodically evolving wave-packets. Our study shows that non-trivial
crystal-like phenomena can be observed in the time domain.
