Landau operator on the quaternionic field
Azzouz Zinoun (PhLAM), Dominique Kazmierowski (PhLAM), Ahmed Intissar, (PhLAM)
TL;DR
This paper defines the Landau operator on the quaternionic field as a Fourier transform of the sub-Laplacian on the quaternionic Heisenberg group, linking it to harmonic oscillators in a magnetic field.
Contribution
It introduces a new formulation of the Landau operator on quaternionic fields via Fourier transform, connecting it to harmonic oscillators with magnetic effects.
Findings
Defines the Landau operator on quaternionic fields.
Establishes the operator as a Hamiltonian of harmonic oscillators.
Links the operator to magnetic field effects in quaternionic analysis.
Abstract
The Landau operator on the quaternionic field is defined as the partial Fourier transform of the sub-Laplacian on the quaternionic Heisenberg group. This operator is viewed as the Hamiltonian of two harmonic oscillators on the two dimensional complex space with a uniform magnetic field.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Biofield Effects and Biophysics · Spectral Theory in Mathematical Physics