Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation

• URL: http://arxiv.org/abs/2304.06677v2
• Date: Wed, 23 Aug 2023 16:21:00 GMT
• Title: Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation
• Authors: Andrey Alcala and Mikhail S. Plyushchay
• Abstract summary: A correspondence is established between the dynamics of the two-vortex system and the non-commutative Landau problem. We show that quantum two-vortex systems with non-zero total vorticity can be generated by applying conformal bridge transformation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A correspondence is established between the dynamics of the two-vortex system and the non-commutative Landau problem (NCLP) in its sub- (non-chiral), super- (chiral) and critical phases. As a result, a trivial permutation symmetry of the point vortices induces a weak-strong coupling duality in the NCLP. We show that quantum two-vortex systems with non-zero total vorticity can be generated by applying conformal bridge transformation to a two-dimensional quantum free particle or to a quantum vortex-antivortex system of zero total vorticity. The sub- and super-critical phases of the quantum NCLP are generated in a similar way from the 2D quantum free particle in a commutative or non-commutative plane. The composition of the inverse and direct transformations of the conformal bridge also makes it possible to link the non-chiral and chiral phases in each of these two systems.

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