Geodesic
Calculating the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 73-87 
V. V. Borzov; E. V. Damaskinskiy. Calculating the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 73-87. http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a5/
@article{ZNSL_2020_493_a5,
     author = {V. V. Borzov and E. V. Damaskinskiy},
     title = {Calculating the {Mandel} parameter for an oscillator-like system generated by generalized {Chebyshev} polynomials},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {73--87},
     year = {2020},
     volume = {493},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a5/}
}
TY  - JOUR
AU  - V. V. Borzov
AU  - E. V. Damaskinskiy
TI  - Calculating the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2020
SP  - 73
EP  - 87
VL  - 493
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a5/
LA  - ru
ID  - ZNSL_2020_493_a5
ER  - 
%0 Journal Article
%A V. V. Borzov
%A E. V. Damaskinskiy
%T Calculating the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials
%J Zapiski Nauchnykh Seminarov POMI
%D 2020
%P 73-87
%V 493
%U http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a5/
%G ru
%F ZNSL_2020_493_a5

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this paper, we calculate the Mandel parameter $Q_M$ for an oscillator-like system generated by generalized Chebyshev polynomials [1–3]. The sign of the Mandel parameter $Q_M$ characterizes the deviation of the excitation statistics from the Poisson one. This work is a continuation of our works [4, 5].

[1] V. V. Borzov, E. V. Damaskinskii, “Lokalnoe vozmuschenie diskretnogo uravneniya Shredingera i obobschennyi ostsillyator Chebysheva”, TMF, 200:3 (2019), 494–506 | MR | Zbl

[2] V. V. Borzov, E. V. Damaskinsky, “Generalized Chebychev polynomials conected with a point interaction for the discrete Schrödinger equation”, Proc. of the International Conference DAYS on DIFFRACTION'2018, 2018 | Zbl

[3] D. R. Yafaev, “A point interaction for the discrete Schrödinger operator and generalized Chebyshev polynomials”, J. Math. Phys., 58 (2017), 063511 | DOI | MR | Zbl

[4] V. V. Borzov, E. V. Damaskinsky, “Coherent states and uncertainty relations for generalized oscillators connected with the given families of orthogonal polynomials”, Proceedings of the International Conference “Days on Diffraction-2005”, IEEE, 2005, 40–49 | DOI | MR

[5] V. V. Borzov, E. V. Damaskinskii, Vychislenie parametra Mandelya dlya obobschennykh kogerentnykh sostoyanii deformirovannykh ostsillyatorov, svyazannykh s ortogonalnymi polinomami, Preprint POMI RAN, No 21, 2005

[6] L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence”, Optics Letters, 4:7 (1979), 205–207 | DOI

[7] M. C. Teich, B. E. A. Saleh, “Photon Bunching and Antibunching”, Chapter 1, Progress in Optics, XXVI, North Holland, 1988, 2–104

[8] V. V. Dodonov, ““Nonclassical” states in quantum optics: a “squeezed” review of the first 75 years”, J. Opt. B, 4:1 (2002), R1–R33 | DOI | MR

[9] V. V. Borzov, E. V. Damaskinskii, “Polinomy Sharle i ostsilyator Sharle kak diskretnaya realizatsiya garmonicheskogo ostsillyatora”, Probl. matem. analiza, 30 (2005), 3–15 | Zbl

[10] A. O. Barut, L. Girardello, “New “Coherent States” Associated with Non-Compact Groups”, Commun. Math. Phys., 21:1 (1072), 41–55 | DOI | MR

[11] J-P. Gazeau, J. R. Klauder, “Coherent states for systems with discrete and continuous spectrum”, J. Phys. A, 32:1 (1999), 123–132 | DOI | MR | Zbl

[12] V. V. Borzov, “Orthogonal polynomials and generalized oscillator algebras”, Integral Transforms and Special Functions, 12 (2001), 115–138 | DOI | MR | Zbl