Work

Superintegrable classical Zernike system

Year: 2017

Type: article

Abstract: We consider the differential equation that Zernike proposed to classify aberrations of wavefronts in a circular pupil, as if it were a classical Hamiltonian with a non-standard potential. The trajectories turn out to be closed ellipses. We show that this is due to the existence of higher-order invariants that close into a cubic Higgs algebra. The Zernike classical system thus belongs to the class of superintegrable systems. Its Hamilton-Jacobi action separates into three vertical projections of polar coordinates of sphere, polar, and equidistant coordinates on half-hyperboloids, and also in elliptic coordinates on the sphere.

Source: Journal of Mathematical Physics

DOI: 10.1063/1.4990793

Authors: George S. Pogosyan, Kurt Bernardo Wolf, Alexander Yakhno

Institutions: Universidad de Guadalajara, Yerevan State University, Joint Institute for Nuclear Research, Universidad Nacional Autónoma de México

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Universidad de Guadalajara

Award: G3178141677