Localized and extended states in a disordered trap

TL;DR

This paper investigates how disorder and trapping potentials influence the coexistence of localized and extended quantum states, revealing that trap confinement can produce extended states weakly affected by disorder, with implications for disordered quantum gases.

Contribution

It demonstrates the coexistence of localized and extended states in a disordered trap and explains their distinct physical origins, providing a basis for experimental observation.

Findings

Extended states result from trap confinement and are weakly affected by disorder.

Localized states are eigenstates of the disordered potential, influenced mainly by the trap.

Coexistence of localized and extended states can be observed in disordered quantum gases.

Abstract

We study Anderson localization in a disordered potential combined with an inhomogeneous trap. We show that the spectrum displays both localized and extended states, which coexist at intermediate energies. In the region of coexistence, we find that the extended states result from confinement by the trap and are weakly affected by the disorder. Conversely, the localized states correspond to eigenstates of the disordered potential, which are only affected by the trap via an inhomogeneous energy shift. These results are relevant to disordered quantum gases and we propose a realistic scheme to observe the coexistence of localized and extended states in these systems.