Localization of electrons in internal frame

Abstract

Localization of electrons in the internal frame of reference is well established in one dimension in the presence and absence of Coulomb interaction. We start from quasi-one-dimensional (Q1D) ring and show the possibility of such a transition by going to a regime where it can be shown for electrons that just interact via Fermi statistics. We then give a proof that when the Q1D ring is made infinitely wide, then there will be such a localization even when Coulomb interaction is included. Finally, we also comment on dimensions greater than two.