Regular Article

Edge states of a three dimensional kicked rotor

Technion – Israel Institute of Technology, Technion City, Haifa 3200004, Israel

^a e-mail: sasha.bakman@gmail.com

Received: 1 April 2019
Received in final form: 16 July 2019
Published online: 15 October 2019

Abstract

Edge localization is a fascinating quantum phenomenon. In this paper, the underlying mechanism generating it is presented analytically and verified numerically for a weakly kicked three-dimensional rotor. We expand the eigenstates of the one-kick propagator of the kicked rotor in the basis of the free rotor eigenstates, which are defined by the quantum number of angular momentum. Since this quantum number must be non-negative, there is an edge near zero angular momentum, and an edge state is created. Analogy to tight binding model in solid state physics is used.