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

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.

35 Pages. References, corrections and improvements added. Accepted version for publication in EPJP

References in corpus (11)

• Motion of charged particles near weakly magnetized Schwarzschild black hole
• Testing Gravity with Cold-Atom Interferometers
• Possible signature of magnetic fields related to quasi-periodic oscillation observed in microquasars
• The Kerr spacetime: A brief introduction
• Off-equatorial orbits in strong gravitational fields near compact objects -- II: halo motion around magnetic compact stars and magnetized black holes
• Electrically charged matter in rigid rotation around magnetized black hole
• Acoustic Rabi oscillations between gravitational quantum states and impact on symmetron dark energy
• Charged particle motion around a quasi-Kerr compact object immersed in an external magnetic field
• Quasinormal modes of magnetized black hole
• Landau quantization and neutron emissions by nuclei in the crust of a magnetar
• Possible altitudinal, latitudinal and directional dependence of relativistic Sagnac effect in Chern-Simons modified gravity

Cited by in corpus (8)

• A fresh look at the influence of gravity on the quantum Hall effect
• A simple superconductor quantum interference device for testing gravity
• Scalar Field Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity
• Teleparallel Minkowski Spacetime with Perturbative Approach for Teleparallel Gravity on a Proper Frame
• Spin-1/2 particles under the influence of a uniform magnetic field in the interior Schwarzschild solution
• Fresh look at the effects of gravitational tidal forces on a freely-falling quantum particle
• The quantum Hall effect under the influence of gravity and inertia: A unified approach
• What can we learn from the conformal noninvariance of the Klein-Gordon equation?