Generalized Binomial Probability Distributions attached to Landau levels on the Riemann sphere

A family of generalized binomial probability distributions attached to Landau levels on the Riemann sphere is introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained explicitly. As application, photon number statistics related to coherent states under consideration are discussed.Comment: 12 pages, 1 figure. This is a revised and improved exposition. Typos corrected and references adde

Discrete coherent states for higher Landau levels

We consider the quantum dynamics of a charged particle evolving under the action of a constant homogeneous magnetic field, with emphasis on the discrete subgroups of the Heisenberg group (in the Euclidean case) and of the SL(2, R) group (in the Hyperbolic case). We investigate completeness properties of discrete coherent states associated with higher order Euclidean and hyperbolic Landau levels, partially extending classic results of Perelomov and of Bargmann, Butera, Girardello and Klauder. In the Euclidean case, our results follow from identifying the completeness problem with known results from the theory of Gabor frames. The results for the hyperbolic setting follow by using a combination of methods from coherent states, time-scale analysis and the theory of Fuchsian groups and their associated automorphic forms.Comment: Revised for Annals of Physic

Generalized second Bargmann transforms associated with the hyperbolic Landau levels on the Poincar\'e disk

We deal with a family of generalized coherent states associated to the hyperbolic Landau levels of the Schr\"odinger operator with uniform magnetic field on the Poincar\'e disk. Their associated coherent state transforms constitute a class of generalized second Bargmann transforms.Comment: 7 page

The polyanalytic Ginibre ensembles

We consider a polyanalytic generalization of the Ginibre ensemble. This models allowing higher Landau levels (the Ginibre ensemble corresponds to the lowest Landau level). We study the local behavior of this point process under blow-ups.Comment: 31 page