Generalized Coherent States Associated with the Cλ-Extended Oscillator

Abstract

Two new types of coherent states associated with the C λ -extended oscillator, where C λ is the cyclic group of order λ, are introduced. The first ones include as special cases both the Barut-Girardello and the Perelomov su(1,1) coherent states for λ = 2, as well as the annihilation-operator coherent states of the C λ -extended oscillator spectrum generating algebra for higher λ values. The second ones, which are eigenstates of the C λ -extended oscillator annihilation operator, extend to higher λ values the paraboson coherent states, to which they reduce for λ = 2. All these states satisfy a unity resolution relation in the C λ -extended oscillator Fock space (or in some subspace thereof). They give rise to Bargmann representations of the latter, wherein the generators of the C λ -extended oscillator algebra are realized as differential-operatorvalued matrices (or differential operators). The statistical and squeezing properties of the new coherent states are investigated over a wide range of parameters and some interesting nonclassical features are exhibited.

Newq-deformed coherent states with an explicitly known resolution of unity

“…Determining the existence of a unity resolution relation is indeed a difficult task, which has not been solved for many of the putative GCS known in the literature. Recent progress in this domain has been achieved by using some properties of the inverse Mellin transform [10,11].…”

Structural transitions in GaAs during irradiation by a 100-fs laser pulse

“….). If we take the value of λ k to be unity in the expression (33), together with the property (5), in the expansion (34) we obtain…”

“…Keeping in mind the ladder character of the operatorsB ± we can recognize (57) as the shape-invariant generalization of the eigenvalue equation which defines purely squeezed states for harmonic oscillator systems [32,33]. Taking the null value of w k in expressions (33) and using it, together with property (5), in expansion (34), we obtain…”

Painlevé IV coherent states

“…With this interest in mind, he found quantum states with the right classical behavior in phase space [2]. Since these states can be used to examine the behavior of several systems at the border between quantum and semi-classical regimes [3][4][5][6][7][8], its study has taken an important place in quantum physics during the last fifty years. These are the coherent states (CS), a term which was coined by Glauber when studying electromagnetic correlation functions [9,10].…”