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

¹ Saha Institute of Nuclear Physics, Theory Division - 1/AF Bidhannagar, Kolkata 700 064, India
² School of Physics, University of Hyderabad - Central University P O, Hyderabad, AP, PIN 500046, India
³ Instituto de Fisica, Universidade de Brasilia - Caixa Postal 04455, 70919-970, Brasilia, DF, Brazil

Received: 3 December 2012
Accepted: 22 March 2013

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.