dorsal/arxiv
View SchemaGeneralized coherent states associated with the C_{\lambda}-extended oscillator
| Authors | C. Quesne |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108126 |
| URL | https://arxiv.org/abs/quant-ph/0108126 |
| DOI | 10.1006/aphy.2001.6184 |
| Journal | Ann. Phys. (N.Y.) 293 (2001) 147-188 |
Abstract
Two new types of coherent states associated with the C_{\lambda}-extended oscillator, where C_{\lambda} is the cyclic group of order \lambda, are introduced. The first ones include as special cases both the Barut-Girardello and the Perelomov su(1,1) coherent states for \lambda=2, as well as the annihilation-operator coherent states of the C_{\lambda}-extended oscillator spectrum generating algebra for higher \lambda values. The second ones, which are eigenstates of the C_{\lambda}-extended oscillator annihilation operator, extend to higher \lambda values the paraboson coherent states, to which they reduce for \lambda=2. All these states satisfy a unity resolution relation in the C_{\lambda}-extended oscillator Fock space (or in some subspace thereof). They give rise to Bargmann representations of the latter, wherein the generators of the C_{\lambda}-extended oscillator algebra are realized as differential-operator-valued 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.
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"abstract": "Two new types of coherent states associated with the C_{\\lambda}-extended\noscillator, where C_{\\lambda} is the cyclic group of order \\lambda, are\nintroduced. The first ones include as special cases both the Barut-Girardello\nand the Perelomov su(1,1) coherent states for \\lambda=2, as well as the\nannihilation-operator coherent states of the C_{\\lambda}-extended oscillator\nspectrum generating algebra for higher \\lambda values. The second ones, which\nare eigenstates of the C_{\\lambda}-extended oscillator annihilation operator,\nextend to higher \\lambda values the paraboson coherent states, to which they\nreduce for \\lambda=2. All these states satisfy a unity resolution relation in\nthe C_{\\lambda}-extended oscillator Fock space (or in some subspace thereof).\nThey give rise to Bargmann representations of the latter, wherein the\ngenerators of the C_{\\lambda}-extended oscillator algebra are realized as\ndifferential-operator-valued matrices (or differential operators). The\nstatistical and squeezing properties of the new coherent states are\ninvestigated over a wide range of parameters and some interesting nonclassical\nfeatures are exhibited.",
"arxiv_id": "quant-ph/0108126",
"authors": [
"C. Quesne"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"physics.optics"
],
"doi": "10.1006/aphy.2001.6184",
"journal_ref": "Ann. Phys. (N.Y.) 293 (2001) 147-188",
"title": "Generalized coherent states associated with the C_{\\lambda}-extended oscillator",
"url": "https://arxiv.org/abs/quant-ph/0108126"
},
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