$(q;l,\lambda)$-deformed Heisenberg algebra: coherent states, their statistics and geometry

TL;DR

This paper introduces a new three-parameter deformed Heisenberg algebra, constructs coherent states, analyzes their statistical properties, and explores the resulting geometric structure, expanding understanding of quantum deformation effects.

Contribution

It develops a novel $(q;l,mbda)$-deformed Heisenberg algebra, constructs associated coherent states, and investigates their statistical and geometric properties, which was not previously studied.

Findings

Deformed coherent states satisfy Klauder criteria.

Main states exhibit sub-Poissonian statistics.

Derived a generalized metric from the state statistics.

Abstract

The Heisenberg algebra is deformed with the set of parameters ${q, l,\lambda}$ to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly computed. Then, a proof on the sub-Poissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.