Eur. Phys. J. Plus (2020) 135: 90
https://doi.org/10.1140/epjp/s13360-020-00108-1

Regular Article

Landau levels in a gravitational field: the Levi-Civita and Kerr spacetimes case

¹ Department of Physics and Astronomy, Bishop’s University, 2600 College Street, Sherbrooke, QC, J1M 1Z7, Canada
² Physics Department, Champlain College-Lennoxville, 2580 College Street, Sherbrooke, QC, J1M 0C8, Canada
³ Département de Physique, Université de Montréal, 2900 Boulevard Édouard-Montpetit, Montréal, QC, H3T 1J4, Canada

^* e-mail: fhammad@ubishops.ca

Received: 1 October 2019
Accepted: 3 January 2020
Published online: 17 January 2020

Abstract

We have recently found that the gravitational field of a static spherical mass removes the Landau degeneracy of the energy levels of a particle moving around the mass inside a magnetic field by splitting the energy of the Landau orbitals. In this paper, we present the second part of our investigation of the effect of gravity on Landau levels. We examine the effect of the gravitational fields created by an infinitely long massive cylinder and a rotating spherical mass. In both cases, we show that the degeneracy is again removed thanks to the splitting of the particle’s orbitals. The first case would constitute an experimental test—which is quantum mechanical in nature—of the gravitational field of a cylinder. The approach relies on the Newtonian approximation of the gravitational potential created by a cylinder but, in view of self-consistency and for future higher-order approximations, the formalism is based on the full Levi-Civita metric. The second case opens up the possibility for a novel quantum mechanical test of the well-known rotational frame-dragging effect of general relativity.