The quantum Hall effect under the influence of gravity and inertia: A
unified approach
- URL: http://arxiv.org/abs/2403.07069v1
- Date: Mon, 11 Mar 2024 18:01:55 GMT
- Title: The quantum Hall effect under the influence of gravity and inertia: A
unified approach
- Authors: Alexandre Landry, Fay\c{c}al Hammad and Reza Saadati
- Abstract summary: We examine how both the integer and the fractional quantum Hall effects behave under a combined influence of gravity and inertia.
The general Hamiltonian for describing the combined effect of gravity, rotation and inertia on the electrons of a Hall sample is then built and the eigenstates are obtained.
- Score: 44.99833362998488
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The quantum Hall effect under the influence of gravity and inertia is studied
in a unified way. We make use of an algebraic approach, as opposed to an
analytic approach. We examine how both the integer and the fractional quantum
Hall effects behave under a combined influence of gravity and inertia using a
unified Hamiltonian. For that purpose, we first re-derive, using the purely
algebraic method, the energy spectrum of charged particles moving in a plane
perpendicular to a constant and uniform magnetic field either (i) under the
influence of a nonlinear gravitational potential or (ii) under the influence of
a constant rotation. The general Hamiltonian for describing the combined effect
of gravity, rotation and inertia on the electrons of a Hall sample is then
built and the eigenstates are obtained. The electrons mutual Coulomb
interaction that gives rise to the familiar fractional quantum Hall effect is
also discussed within a such a combination.
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