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arXiv · 1805.08165

Geometry and probability on the noncommutative 2-torus in a magnetic field

Mahouton Norbert Hounkonnou·Fridolin Melong
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Abstract

In this work, we describe the geometric and probabilistic properties of a noncommutative 2- torus in a magnetic field. We study the volume invariance, integrated scalar curvature and volume form by using the method of perturbation by inner derivation of the magnetic Laplacian in the noncommutative 2-torus. Then, we analyze the magnetic stochastic process describing the motion of a particle subject to a uniform magnetic field on the noncommutative 2-torus, derive and discuss the related main properties.

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Mahouton Norbert Hounkonnou, Fridolin Melong. 2018-05-21. Geometry and probability on the noncommutative 2-torus in a magnetic field. https://arxiv.org/abs/1805.08165

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