$(q;l,\lambda)$-Deformed Heisenberg Algebra: Coherent States, Their Statistics and Geometry

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 subPoissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.