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Zouhair Mouayn

Publications and source records attributed to Zouhair Mouayn.

28 records · Page 2Linked to original sources
arXiv2011

A Family of Circular Bargmann Transforms

When considering a charged particle evolving in the Poincaré disk under influence of a uniform magnetic field with a strength proportional to +1, we construct for all hyperbolic Landau level ε^γ_$m$ m = 4m(-m), m 2 Z+ \[0, /2] a family of coherent states transforms labeled by (,m) and mapping isometrically square integrable functions on the unit circle with respect to the measure sin^γ-2m (θ/2) dθonto spaces of bound states of the particle. These transforms are called circular Bargmann transforms.

math-ph↗
arXiv2011

An index 2F2 hypergeometric transform

We construct a new one-parameter family of index hypergeometric transforms associated with the relativistic pseudoharmonic oscillator by using coherent states analysis.

math-ph↗
arXiv2011

Phase coherent states with circular Jacobi polynomials for the pseudoharmonic oscillator

We construct a class of generalized phase coherent states indexed by points of the unit circle and depending on three positive parameters "gamma","alpha" and "epsilon" by replacing the labelling coefficients of the canonical coherent states by circular Jacobi polynomials with parameter "gamma". The special case "gamma" = 0 corresponds to well known phase coherent phase states. The constructed states are superposition of eigenstates of a one-parameter pseudoharmonic oscillator depending on "alpha" and solve the identity of the state Hilbert space at the limit "epsilon"->0+. Closed form for their wavefunctions are obtained in the case "alpha" = "gamma" + 1 and their associated coherent states transform is defined.

math-ph↗
arXiv2010

A generating function for Hermite polynomials in connection with Euclidean Landau levels

We have formulated a generating function for the Hermite polynomials by comparing two expressions of the same coherent states attached to planar Landau levels. A first expression is obtained by generalizing the canonical coherent states when written as series expansion in the basis of number states. While the second expression is established by following a construction based on group representation theory.

math-ph↗
arXiv2010

Coherent state transforms attached to generalized Bargmann spaces on the complex plane

We construct a family of coherent states transforms attached to generalized Bargmann spaces [C.R. Acad.Sci.Paris, t.325,1997] in the complex plane. This constitutes another way of obtaining the kernel of an isometric operator linking the space of square integrable functions on the real line with the true-poly-Fock spaces [Oper.Theory. Adv.Appl.,v.117,2000].

math-ph↗
arXiv2010

Probability Distributions attached to generalised Bergman Spaces on the Poincaré Disk

A family of probability distributions attached to a class of generalized weighted Bergman spaces on the Poincaré disk are introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained explicitly. As application, photon number statistics related to coherent states under consideration are discussed.

math-ph↗