Geometry and dynamics in the fractional discrete Fourier transform.
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.
Wolf
Kurt Bernardo
KB
Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, México. bwolf@fis.unam.mx
Krötzsch
Guillermo
G