Title: Three-dimensional localized-delocalized Anderson transition in the time domain,
Abstract: Systems which can spontaneously reveal periodic evolution are dubbed time
crystals. This is in analogy with space crystals that display periodic behavior
in configuration space. While space crystals are modelled with the help of
space periodic potentials, crystalline phenomena in time can be modelled by
periodically driven systems. Disorder in the periodic driving can lead to
Anderson localization in time: the probability for detecting a system at a
fixed point of configuration space becomes exponentially localized around a
certain moment in time. We here show that a three-dimensional system exposed to
a properly disordered pseudo-periodic driving may display a
localized-delocalized Anderson transition in the time domain, in strong analogy
with the usual three-dimensional Anderson transition in disordered systems.
Such a transition could be experimentally observed with ultra-cold atomic
gases.