title: Geometry and dynamics in the fractional discrete Fourier transform.
abstract: The N x N Fourier matrix is one distinguished element within the group U(N) of all N x N unitary matrices. It has the geometric property of being a fourth root of unity and is close to the dynamics of harmonic oscillators. The dynamical correspondence is exact only in the N-->infinity contraction limit for the integral Fourier transform and its fractional powers. In the finite-N case, several options have been considered in the literature. We compare their fidelity in reproducing the classical harmonic motion of discrete coherent states.
authors.affiliation: Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, México. bwolf@fis.unam.mx
authors.forename: Kurt Bernardo
authors.initials: KB
authors.lastname: Wolf
authors.forename: Guillermo
authors.initials: G
authors.lastname: Krötzsch