Year: 2025
Type: article
Abstract: Perelomov coherent states for equally spaced, infinite homogeneous waveguide arrays with Euclidean [Formula: see text] symmetry are defined and a new resolution of the identity is obtained. The key point to construct this novel resolution of the identity is the fact that coherent states satisfy the Helmholtz equation (in coherent states labels), and thus every coherent state belongs to a one-parameter family uniquely determined by the Cauchy initial data of the coherent state in a one-dimensional Cauchy set. For this reason we call Cauchy coherent states to these initial data. The novel, nonlocal resolution of the identity in terms of Cauchy coherent states is provided using frame theory. It is also shown that Perelomov coherent states for the Euclidean [Formula: see text] group have a simple and natural physical realization in these waveguide arrays.
Authors: Julio Guerrero, Francisco F. López-Ruiz
Institutions: Universidad de Granada, Universidad de Jaén, Universidad de Cádiz
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G5151083941, G8920660035
OpenAlex ID: W4415296599