The Hamiltonian describing the anomalous Zeeman effect for the hydrogen atom on noncommutative (NC) phase space is studied using the nonrelativistic limit of the Dirac equation. To preserve gauge invariance, space noncommutativity must be dropped. By using first-order perturbation theory, the correction to the energy is calculated for the case of a weak external magnetic field. We also obtained the orbital and spin g-factors on the NC phase space. We show that the experimental value for the spin g-factor puts an upper bound on the magnitude of the momentum NC parameter of the order of √ η 0, 34 µeV/c. On the other hand, the experimental value for the spin g-factor was used to establish a correction introduced by NC phase space to the presently accepted value of Planck's constant with an uncertainty of 2 part in 10 35 .
We investigate the classical Brownian motion of a particle in a
two-dimensional noncommutative (NC) space. Using the standard NC algebra
embodied by the sympletic Weyl-Moyal formalism we find that noncommutativity
induces a non-vanishing correlation between both coordinates at different
times. The effect stands out as a signature of spatial noncommutativity and
thus could offer a way to experimentally detect the phenomena. We further
discuss some limiting scenarios and the trade-off between the scale imposed by
the NC structure and the parameters of the Brownian motion itself.Comment: 9 page
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