dorsal/arxiv
View SchemaUnifying the Construction of Various Types of Generalized Coherent States
| Authors | M. K. Tavassoly |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510118 |
| URL | https://arxiv.org/abs/quant-ph/0510118 |
Abstract
In this tutorial I intend to present some of the results I obtained through my PhD work in the "quantum optics group of the University of Isfahan" under consideration Dr. R. Roknizadeh and Prof. S. Twareque Ali as my supervisor and advisor, respectively. I will revisit some of the pioneering proposals recently developed the concept of generalized CSs. As it can be observed the customary three generalization methods {\it (symmetry, algebraic and dynamical)} have never been considered in neither of them. Our intention in this work is at first to investigate the lost ring between the customary three methods and the recently developed ones, as possible. For this purpose it has been devised general analytic descriptions, which successfully demonstrate how different varieties of CSs (which are nonlinear in nature) can be obtained by two processes, first the {\it "nonlinear CSs"} method and second by {\it "basis transformations on an underlying Hilbert spaces"}. As a result, I will systematize the recently introduced generalized CSs in a clear and concise way. It will be clear also, that how our results can be considered as a first step in the generation process of the mathematical physics CSs in the context of quantum optics. Besides this, some new results emerge from our studies. I introduce a large classes of generalized CSs, namely the {\it "dual family"} associated with each set of early known CSs. But, in this relation, the previous processes for constructing the dual pair of Gazeau-Klauder CSs fail to work well, so I outlined a rather different method based on the {\it "temporal stability"} requirement of generalized nonlinear CSs.
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"abstract": "In this tutorial I intend to present some of the results I obtained through\nmy PhD work in the \"quantum optics group of the University of Isfahan\" under\nconsideration Dr. R. Roknizadeh and Prof. S. Twareque Ali as my supervisor and\nadvisor, respectively. I will revisit some of the pioneering proposals recently\ndeveloped the concept of generalized CSs. As it can be observed the customary\nthree generalization methods {\\it (symmetry, algebraic and dynamical)} have\nnever been considered in neither of them. Our intention in this work is at\nfirst to investigate the lost ring between the customary three methods and the\nrecently developed ones, as possible. For this purpose it has been devised\ngeneral analytic descriptions, which successfully demonstrate how different\nvarieties of CSs (which are nonlinear in nature) can be obtained by two\nprocesses, first the {\\it \"nonlinear CSs\"} method and second by {\\it \"basis\ntransformations on an underlying Hilbert spaces\"}. As a result, I will\nsystematize the recently introduced generalized CSs in a clear and concise way.\nIt will be clear also, that how our results can be considered as a first step\nin the generation process of the mathematical physics CSs in the context of\nquantum optics. Besides this, some new results emerge from our studies. I\nintroduce a large classes of generalized CSs, namely the {\\it \"dual family\"}\nassociated with each set of early known CSs. But, in this relation, the\nprevious processes for constructing the dual pair of Gazeau-Klauder CSs fail to\nwork well, so I outlined a rather different method based on the {\\it \"temporal\nstability\"} requirement of generalized nonlinear CSs.",
"arxiv_id": "quant-ph/0510118",
"authors": [
"M. K. Tavassoly"
],
"categories": [
"quant-ph"
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"title": "Unifying the Construction of Various Types of Generalized Coherent States",
"url": "https://arxiv.org/abs/quant-ph/0510118"
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