A Dirac-type variant of the xp-model and the Riemann zeros

Abstract

We propose a Dirac-type modification of the xp-model to a model on a semi-infinite cylinder. This model is inspired by recent work of Sierra et al. on the xp-model on the half-line. Our model realizes the Berry-Keating conjecture on the Riemann zeros. We indicate the connection of our model to that of gapped graphene with a supercritical Coulomb charge, which might provide a physical system for the study of the zeros of the Riemann Zeta function. © Copyright EPLA, 2013.