# Three-dimensional localized-delocalized Anderson transition in the time domain

## TL;DR

This paper demonstrates that a three-dimensional quantum system under disordered periodic driving can undergo an Anderson transition in the time domain, analogous to spatial Anderson localization, with potential experimental realization using ultra-cold atoms.

## Contribution

It introduces the concept of a three-dimensional time-domain Anderson transition in driven quantum systems, expanding the understanding of localization phenomena.

## Key findings

- Localization-delocalization transition in time observed in simulations
- Analogous behavior to spatial Anderson transition demonstrated
- Potential for experimental observation with ultra-cold atomic gases

## 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.