Zero absolute vorticity plane Couette flow as an hydrodynamic
representation of quantum energy states under perpendicular magnetic field
- URL: http://arxiv.org/abs/2204.01013v1
- Date: Sun, 3 Apr 2022 07:27:41 GMT
- Title: Zero absolute vorticity plane Couette flow as an hydrodynamic
representation of quantum energy states under perpendicular magnetic field
- Authors: Eyal Heifetz, Leo R. M. Maas, Julian Mak
- Abstract summary: We show how the Landau levels and the extended modes in the integer quantum Hall effect are all mapped into such zero absolute vorticity-like plane Couette flows.
We show how the Landau levels and the extended modes in the integer quantum Hall effect are all mapped into such zero absolute vorticity-like plane Couette flows.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Here we extend the Madelung transformation of the Schr\"{o}dinger equation
into a fluid-like form to include the influence of an external electromagnetic
field on a charged particle. The vorticity of the Madelung fluid is then in the
opposite direction to the imposed magnetic field and equal in magnitude to the
cyclotron angular frequency. When the particle motion is confined to a plane,
perpendicular to an imposed magnetic field, the equivalent flow dynamics is
that of zero absolute vorticity obtained in a quasi 2D rotating frame, where
the cyclotron frequency plays a role equivalent to that of the Coriolis
frequency in a rotating frame. We show how the Landau levels and the extended
modes in the integer quantum Hall effect are all mapped into such zero absolute
vorticity-like plane Couette flows, where the latter exhibit a geostrophic-like
balance between the magnetic force and the gradients of the quantum (Bohm)
potential and the electric force.
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