Quantum mechanics on the noncommutative plane and sphere
V.P. Nair (CUNY), A.P. Polychronakos (CUNY & Ru)
TL;DR
This paper explores quantum mechanics on noncommutative geometries, solving the Landau problem on both the noncommutative plane and sphere, revealing a critical magnetic field where the density of states diverges.
Contribution
It provides exact solutions for the Landau problem on noncommutative geometries and identifies a critical magnetic field related to noncommutativity.
Findings
Critical magnetic field causes infinite density of states.
Exact solutions for Landau problem on noncommutative plane and sphere.
Comparison between plane and sphere geometries.
Abstract
We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density of states becomes infinite, for the value of the magnetic field equal to the inverse of the noncommutativity parameter. The Landau problem on the noncommutative two-sphere is also solved and compared to the plane problem.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.