@article{ZNSL_2006_335_a4,
author = {V. V. Borzov and E. V. Damaskinsky},
title = {Coherent states for generalized oscillator in finite-dimensional {Hilbert} space},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {75--99},
year = {2006},
volume = {335},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_335_a4/}
}
V. V. Borzov; E. V. Damaskinsky. Coherent states for generalized oscillator in finite-dimensional Hilbert space. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 19, Tome 335 (2006), pp. 75-99. http://geodesic.mathdoc.fr/item/ZNSL_2006_335_a4/
[1] V. V. Dodonov, “"Nonclassical" states in quantum optics: a 'squeezed' review of the first 75 years”, J. Opt. B, 4:1 (2002), R1–R33 | MR
[2] A. Miranowicz, W. Leonski, N. Imoto, “Quantum-optical states in finite-dimensional Hilbert space. I: General formalism”, Modern Nonlinear Optics, Advances in Chemical Physics, 119, ed. M. W. Evans, Wiley, New York, 2001, 155–193; ; W. Leonski, A. Miranowicz, “Quantum-optical states in finite-dimensional Hilbert space. II: State generation”, Modern Nonlinear Optics, Advances in Chemical Physics, 119, ed. M. W. Evans, Wiley, New York, 2001, 195–213; arXiv: /quant-ph/0108080arXiv: /quant-ph/0110146
[3] D. Galetti, M. A. Marchiolli, M. Ruzzi, Extended Cahill-Glauber formalism for finite dimensional spaces: I. Fundamentals, ; D. Galetti, M. A. Marchiolli, “Discrete coherent states and probability distributions in finite-dimensional spaces”, Ann. Phys., 249 (1996), 454–480 ; M. A. Marchiolli, “Nonclassical statistical properties of finite-coherent states in the framework of the Jaynes-Cummings model”, Physica A, 319 (2203), 331–354 arXiv: /quant-ph/0503054 | MR | DOI | MR | Zbl | DOI
[4] V. V. Borzov, “Orthogonal polynomials and generalized oscillator algebras”, Integral Transf. and Special Funct., 12:2, 2201 | MR
[5] V. V. Borzov, E. V. Damaskinsky, “Realization of the annihilation operator for an oscillator-like system by a differential operator and Hermite-Chihara polynomials”, Integral Transforms and Special Functions, 13:6 (2002), 547–554 ; arXiv: /math.QA/0101215 | DOI | MR | Zbl
[6] V. V. Borzov, E. V. Damaskinskii, “Kogerentnye sostoyaniya dlya ostsillyatora Lezhandra”, Zap. Nauchn. Semin. POMI, 285, 2002, 39–52 ; arXiv: /math.QA/0307187 | MR | Zbl
[7] V. V. Borzov, E. V. Damaskinskii, “Kogerentnye sostoyaniya i polinomy Chebysheva”, Matematicheskie idei P. L. Chebysheva i ikh prilozheniya k sovremennym problemam estestvoznaniya, Sb. trudov mezhdunarodnoi konferentsii (Obninsk, 14–18 maya 2002 g.)
[8] V. V. Borzov, E. V. Damaskinskii, “Kogerentnye sostoyaniya i ortogonalnye mnogochleny”, Trudy konferentsii “Den Difraktsii 2002”, SPb, 2002; arXiv: /math.QA/0209181
[9] V. V. Borzov, E. V. Damaskinskii, “Kogerentnye sostoyaniya Baruta–Zhirardello dlya ostsillyatora Gegenbauera”, Zap. Nauchn. Semin. POMI, 291, 2002, 43–63 | MR | Zbl
[10] V. V. Borzov, E. V. Damaskinsky, Generalized Coherent States for $q$-oscillator connected with $q-$Hermite Polynomials Day on Diffraction 2003, , 2003 arXiv: /math.QA/0307356
[11] V. V. Borzov, E. V. Damaskinskii, “Obobschennye kogerentnye sostoyaniya dlya $q$-ostsillyatora, assotsiirovannogo s diskretnymi $q$-polinomami Ermita”, Zap. nauchn. semin. POMI, 308, 2004, 48–66 | MR | Zbl
[12] V. V. Borzov, E. V. Damaskinskii, “Obobschennye kogerentnye sostoyaniya dlya ostsillyatorov, svyazannykh s polinomami Meiksnera i Meiksnera–Polacheka”, Zap. nauchn. semin. POMI, 317, 2004, 66–93 | MR | Zbl
[13] T. Opatrny, V. Buzek, J. Bajer, G. Drobny, “Propensities in discrete phase spaces: Q-function of a state in a finite-dimensional Hilbert-space”, Phys. Rev. A, 52:3 (1995), 2419–2428 | DOI
[14] R. Koekoek, R. F. Swarttouw, The Askey sheme of hypergeometric orthogonal polynomials and its $q$-analogue, Report No 94–05, Delft University of Technology, 1994 ; arXiv: /math.CA/9602214 | Zbl
[15] N. M. Atakishiev, S. K. Suslov, “Raznostnye analogi garmonicheskogo ostsillyatora”, TMF, 85:1 (1990), 64–73 | MR | Zbl
[16] N. M. Atakishiev, K. B. Wolf, “Fractional Fourier-Kravchuk transform”, J. Opt. Soc. Amer. A, 14:7 (1997), 1467–1477 | DOI | MR
[17] N. M. Atakishiyev, E. I. Jafarov, Sh. M. Nagiyev, K. B. Wolf, “Meixner oscillators”, Revista Mexicana de Fisica, 44:3 (1998), 235–244 ; arXiv: /math-ph/9807035 | MR
[18] V. Buzek, A. D. Wilson–Gordon, P. L. Knight, W. K. Lai, “Coherent states in a finite-dimensional basis: Their phase properties and relationship to coherent states of light”, Phys. Rev. A, 45 (1992), 8079–8094 | DOI
[19] A. Miranowicz, K. Piatek, R. Tanaś, “Coherent states in a finite dimensional Hilbert space”, Phys. Rev. A, 50:4 (1994), 3423 ; A. Miranowicz, K. Piatek, T. Opatrny, R. Tanaś, “Phase coherent states”, Acta Phys. Slovaca, 45 (1995), 391 | DOI
[20] R. J. Glauber, “The Quantum Theory of Optical Coherence”, Phys. Rev., 130 (1963), 2529–2539 | DOI | MR
[21] 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
[22] G. Sege, Ortogonalnye mnogochleny, FM, M., 1962
[23] N. I. Akhiezer, Klassicheskaya problema momentov i nekotorye voprosy analiza, svyazannye s neyu, FM, M., 1961
[24] B. Roy, P. Roy, “Coherent states, even and odd coherent states in a finite-dimensional Hilbert space and their properties”, J. Phys. A, 31 (1998), 1307–1317 ; B. Roy, P. Roy, Phase properties of a new nonlinear coherent state, arXiv: /quant-ph/0002043 | DOI | MR | Zbl