Geometry and dynamics in the Fresnel transforms of discrete systems.
Free propagation in continuous optical and mechanical systems is generated by the momentum-squared operator and results in a shear of the phase space plane along the position coordinate. We examine three discrete versions of the Fresnel transform in periodic systems through their Wigner function on a toroidal phase space. But since it is topologically impossible to continuously and globally shear a torus, we examine a fourth version of the Fresnel transform on a spherical phase space, in a model based on the Lie algebra of angular momentum, where the corresponding Fresnel transform wrings the sphere.
Wolf
Kurt Bernardo
KB
Instituto de Ciencias Físicas, Universidad nacional Autónoma de México, Morelos, México. bwolf@fis.unam.mx
Krötzsch
Guillermo
G