Unconventional quantum criticality in the kicked rotor

Abstract

The quantum kicked rotor (QKR) driven by $d$ incommensurate frequencies realizes the universality class of $d$-dimensional disordered metals. For $d>3$, the system exhibits an Anderson metal-insulator transition which has been observed within the framework of an atom optics realization. However, the absence of genuine randomness in the QKR reflects in critical phenomena beyond those of the Anderson universality class. Specifically, the system shows strong sensitivity to the algebraic properties of its effective Planck constant $\tilde h \equiv 4\pi /q$. For integer $q$, the system may be in a globally integrable state, in a `super-metallic' configuration characterized by diverging response coefficients, Anderson localized, metallic, or exhibit transitions between these phases. We present numerical data for different $q$-values and effective dimensionalities, with the focus being on parameter configurations which may be accessible to experimental investigations.