Generalized second Bargmann transforms associated with the hyperbolic Landau levels on the Poincar\'e disk

TL;DR

This paper introduces a family of generalized coherent states linked to hyperbolic Landau levels on the Poincaré disk, leading to new generalized second Bargmann transforms with potential applications in quantum physics.

Contribution

It develops a novel class of generalized second Bargmann transforms based on hyperbolic Landau levels, expanding the mathematical framework for quantum states on the Poincaré disk.

Findings

Construction of generalized coherent states for hyperbolic Landau levels

Development of associated generalized second Bargmann transforms

Potential applications in quantum physics and signal analysis

Abstract

We deal with a family of generalized coherent states associated to the hyperbolic Landau levels of the Schr\"odinger operator with uniform magnetic field on the Poincar\'e disk. Their associated coherent state transforms constitute a class of generalized second Bargmann transforms.