Energy spectrum and persistent current in one-dimensional rings

Abstract

The correlations in the energy spectrum and persistent current of electrons in one-dimensional disordered rings threaded by an Aharonov-Bohm magnetic flux are shown to be so strong that the current of any level is sufficient to cancel the sum of the contributions of all previous levels. Hence, the sign of the sum of the n lowest single-level currents alternates as a function of n. A new relation between the real part of the inverse transmission coefficient and the energy spectrum is also derived.