Quantum phase transitions in the quasi-periodic kicked rotor

TL;DR

This paper develops a microscopic theory for transport phenomena in quasi-periodic kicked rotors, revealing a transition from localized to super-metallic behavior depending on the rationality of Planck's constant.

Contribution

It introduces a detailed microscopic framework explaining localization and super-metallic phases in quasi-periodic kicked rotors based on Planck's constant values.

Findings

Irrational $ ilde h/(4\\pi)$ leads to localization similar to disordered systems.

Rational $ ilde h/(4\\pi)$ results in infinite static conductivity, creating a super-metal phase.

The paper discusses signatures of the metal/super-metal transition.

Abstract

We present a microscopic theory of transport in quasi-periodically driven environments (`kicked rotors'), as realized in recent atom optic experiments. We find that the behavior of these systems depends sensitively on the value of Planck's constant $\tilde h$: for irrational values of $\tilde h/(4\pi)$ they fall into the universality class of disordered electronic systems and we derive the microscopic theory of the ensuing localization phenomena. In contrast, for rational values the rotor-Anderson insulator acquires an infinite (static) conductivity and turns into a `super-metal'. Signatures of the corresponding metal/super-metal transition are discussed.