Landau problem in dynamical noncommutative space

Abstract

This paper aims to investigate the Landau problem in the framework of a two-dimensional dynamical noncommutative (DNC) space. We study the deformed Landau problem using time-independent perturbation theory, wherein the energy shift notably depends on the DNC parameter $\tau$. Using the accuracy of energy measurement, we put an upper bound on the parameter $\tau$. Moreover, we study magnetoconductivity by employing the Kubo formula. This approach has allowed us to test the effects of noncommutative and DNC spaces on the behavior of magnetoconductivity. We show that dynamical noncommutativity of space has no effects on the x-component of the magnetoconductivity, but has a direct effect on its y-component.