2018/05/21 by Hounkonnou, Mahouton Norbert, Melong, Fridolin
#2010: 46L87 #47L90 #81S25 #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1805.08165
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.