Coherent states and their generalizations for a charged particle in a magnetic field. (English) Zbl 1398.81118
Antoine, Jean-Pierre (ed.) et al., Coherent states and their applications. A contemporary panorama. Cham: Springer (ISBN 978-3-319-76731-4/hbk; 978-3-319-76732-1/ebook). Springer Proceedings in Physics 205, 311-338 (2018).
Summary: This is a brief review of various families of coherent and squeezed states (and their generalizations) for a charged particle in a magnetic field, that have been constructed for the past 50 years. Although the main attention is paid to the Gaussian states, various families of non-Gaussian states are also discussed, and the list of relevant references is provided.
For the entire collection see [Zbl 1398.81008].
For the entire collection see [Zbl 1398.81008].
MSC:
| 81R30 | Coherent states |
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
| 78A35 | Motion of charged particles |
References:
| [1] | 1.V. Fock, Bemerkung zur Quantelung des harmonischen Oszillators im Magnetfeld. Z. Phys. 47, 446-448 (1928) · JFM 54.0966.02 · doi:10.1007/BF01390750 |
| [2] | 2.C.G. Darwin, The diamagnetism of the free electron. Math. Proc. Cambridge Phil. Soc. 27, 86-90 (1931) · JFM 57.1591.01 · doi:10.1017/S0305004100009373 |
| [3] | 3.L. Page, Deflection of electrons by a magnetic field on the wave mechanics. Phys. Rev. 36, 444-456 (1930) · JFM 56.0756.02 · doi:10.1103/PhysRev.36.444 |
| [4] | 4.L. Landau, Diamagnetismus der Metalle. Z. Phys. 64, 629-637 (1930) · JFM 56.1318.10 · doi:10.1007/BF01397213 |
| [5] | 5.C.G. Darwin, Free motion in wave mechanics. Proc. R. Soc. Lond. A 117, 258-293 (1927) · JFM 53.0844.03 · doi:10.1098/rspa.1927.0179 |
| [6] | 6.E.H. Kennard, Zur quantenmechanik einfacher bewegungstypen. Z. Phys. 44, 326-352 (1927) · JFM 53.0853.02 · doi:10.1007/BF01391200 |
| [7] | 7.K. Husimi, Miscellanea in elementary quantum mechanics I. Prog. Theor. Phys. 9, 238-244 (1953) · Zbl 0050.22002 · doi:10.1143/ptp/9.3.238 |
| [8] | 8.M.H. Johnson, B.A. Lippmann, Motion in a constant magnetic field. Phys. Rev. 76, 828-832 (1949) · Zbl 0037.12402 · doi:10.1103/PhysRev.76.828 |
| [9] | 9.I.A. Malkin, V.I. Man’ko, Coherent states of a charged particle in a magnetic field. Zh. Eksp. Teor. Fiz 55, 1014-1025 (1968) [English translation: Sov. Phys. JETP 28, 527-532 (1969)] |
| [10] | 10.R.J. Glauber, Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766-2788 (1963) · Zbl 1371.81166 · doi:10.1103/PhysRev.131.2766 |
| [11] | 11.J.R. Klauder, Continuous representation theory. II. Generalized relation between quantum and classical dynamics. J. Math. Phys. 4, 1058-1073 (1963) · Zbl 0127.18701 · doi:10.1063/1.1704035 |
| [12] | 12.A.M. Perelomov, Coherent states for arbitrary Lie group. Commun. Math. Phys. 26, 222-236 (1972) · Zbl 0243.22016 · doi:10.1007/BF01645091 |
| [13] | 13.D.F. Walls, Squeezed states of light. Nature 306, 141-146 (1983) · doi:10.1038/306141a0 |
| [14] | 14.K.O. Friedrichs, \(Mathematical Aspects of the Quantum Theory of Fields\) (Interscience, New York, 1953) · Zbl 0052.44504 |
| [15] | 15.L. Infeld, J. Plebański, On a certain class of unitary transformations. Acta Phys. Polon. 14, 41-75 (1955) · Zbl 0068.22205 |
| [16] | 16.J. Plebański, Classical properties of oscillator wave packets. Bull. Acad. Pol. Sci. 2, 213-217 (1954) · Zbl 0057.43204 |
| [17] | 17.A.O. Barut, L. Girardello, New “coherent” states associated with noncompact groups. Commun. Math. Phys. 21, 41-55 (1971) · Zbl 0214.38203 · doi:10.1007/BF01646483 |
| [18] | 18.V.V. Dodonov, I.A. Malkin, V.I. Manko, Even and odd coherent states and excitations of a singular oscillator. Physica 72, 597-615 (1974) · doi:10.1016/0031-8914(74)90215-8 |
| [19] | 19.J.E. Avron, I.W. Herbst, B. Simon, Separaltion of center of mass in homogeneous magnetic fields. Ann. Phys. (NY) 114, 431-451 (1978) · Zbl 0409.35027 · doi:10.1016/0003-4916(78)90276-2 |
| [20] | 20.B.R. Johnson, J.O. Hirschfelder, K.-H. Yang, Interaction of atoms, molecules, and ions with constant electric and magnetic fields. Rev. Mod. Phys. 55, 109-153 (1983) · doi:10.1103/RevModPhys.55.109 |
| [21] | 21.R. von Baltz, Guiding center motion of two interacting · doi:10.1016/0375-9601(84)90284-6 |
| [22] | 22.B. Mielnik, A. Ramírez, Magnetic operations: a little fuzzy mechanics? Phys. Scr. 84, 045008 (2011) · Zbl 1263.81172 · doi:10.1088/0031-8949/84/04/045008 |
| [23] | 23.K. Kowalski, J. Rembieliński, Coherent states of a charged particle in a uniform magnetic field. J. Phys. A Math. Gen. 38, 8247-8258 (2005) · Zbl 1081.81058 · doi:10.1088/0305-4470/38/38/006 |
| [24] | 24.V.V. Dodonov, V.I. Man’ko, Invariants and the evolution of nonstationary quantum systems, in \(Proceedings of the P.N. Lebedev Physical Institute\), ed. by M.A. Markov, vol. 183, (Nauka, Moscow, 1987). [English translation by Nova Science, Commack, New York (1989)] |
| [25] | 25.V.V. Dodonov, Parametric excitation and generation of nonclassical states in linear media, in \(Theory of Nonclassical States of Light\), ed. by V.V. Dodonov, V.I. Man’ko (Taylor & Francis, London, 2003), pp. 153-218 |
| [26] | 26.A. Feldman, A.H. Kahn, Landau diamagnetism from the coherent states of an electron in a uniform magnetic field. Phys. Rev. B 1, 4584-4589 (1970) · doi:10.1103/PhysRevB.1.4584 |
| [27] | 27.W.G. Tam, Coherent states and the invariance group of a charged particle in a uniform magnetic field. Physica 54, 557-572 (1971) · doi:10.1016/0031-8914(71)90090-5 |
| [28] | 28.V.V. Dodonov, I.A. Malkin, V.I. Man’ko, Coherent states of a charged particle in a time-dependent uniform electromagnetic field of a plane current. Physica 59, 241-256 (1972) · doi:10.1016/0031-8914(72)90082-1 |
| [29] | 29.M.H. Boon, Networks of coherent states for electron in magnetic field. Helv. Phys. Acta 48, 551-553 (1975) |
| [30] | 30.S. Varró, Coherent states of an electron in a homogeneous constant magnetic field and the zero magnetic field limit. J. Phys. A Math. Gen. 17, 1631-1638 (1984) · doi:10.1088/0305-4470/17/8/019 |
| [31] | 31.E.G.P. Rowe, Classical limit of quantum mechanics (electron in a magnetic field). Am. J. Phys. 59, 1111-1117 (1991) · doi:10.1119/1.16622 |
| [32] | 32.J.L. de Melo, I.A. Pedrosa, C. Furtado, Coherent states of Landau-Aharonov-Casher levels. Int. J. Mod. Phys. B 30, 1650022 (2016) · Zbl 1337.81076 · doi:10.1142/S0217979216500223 |
| [33] | 33.Y.I. Granovskii, Y.A. Dimashko, Coherent representation of Green’s functions and magnetism of free electrons. Ukr. Fiz. Zh. 19, 1456-1459 (1974) |
| [34] | 34.E.V. Ivanova, I.A. Malkin, V.I. Manko, Coherent states and radiation of a charged particle in stationary crossed fields. Yadernaya Fizika 21, 664-670 (1975). [English translation: Sov. J. Nucl. Phys. 21, 343-346 (1975)] |
| [35] | 35.D.F. Walls, Quantum statistics of the cyclotron resonance infrared detector. J. Phys. A Math. Gen. 8, 751-758 (1975) · doi:10.1088/0305-4470/8/5/010 |
| [36] | 36.A.A. Bobrov, O.F. Dorofeev, G.A. Chizhov, Synchrotron radiation of an electron in a coherent state. Teor. Mat. Fiz. 61, 293-300 (1984). [English translation: Theor. Math. Phys. 61, 1149-1154 (1984)] · doi:10.1007/BF01029117 |
| [37] | 37.R.G. Agayeva, Fluctuation of thermomagnetic current. J. Phys. C Solid State Phys. 18, 5841-5848 (1985) · doi:10.1088/0022-3719/18/31/016 |
| [38] | 38.S.T. Pavlov, A.V. Prokhorov, Density of electron states in metals and coherent states. Fiz. Tverd. Tela 32, 3451-3453 (1990) [English translation: Sov. Phys. Solid State 32, 2001-2002 (1990)] |
| [39] | 39.S.T. Pavlov, A.V. Prokhorov, Oscillation effects in metals in a magnetic field and macroscopic quantum interference. Zh. Eksp. Teor. Fiz. 100, 510-519 (1991). [English translation: Sov. Phys. JETP 73, 280-285 (1991)] |
| [40] | 40.S.T. Pavlov, I.S. Pivovarov, Dingle factor in the de Haas-van Alphen effect and the method of coherent states. Fiz. Tverd. Tela 33, 1615-1618 (1991) |
| [41] | 41.A. Jellal, Orbital magnetism of a two-dimensional noncommutative confined system. J. Phys. A Math. Gen. 34, 10159-10177 (2001) · Zbl 1017.81027 · doi:10.1088/0305-4470/34/47/319 |
| [42] | 42.G. Cristofano, D. Giuliano, G. Maiella, L. Valente, 2D electron in an external magnetic field in the presence of dissipation. Int. J. Mod. Phys. B 9, 707-718 (1995) · doi:10.1142/S0217979295000276 |
| [43] | 43.G. Cristofano, D. Giuliano, G. Maiella, 2D electron in a magnetic field with dissipation. J. Phys. I France 6, 861-872 (1996) · doi:10.1051/jp1:1996100 |
| [44] | 44.D. Schuch, M. Moshinsky, Coherent states and dissipation for the motion of a charged particle in a constant magnetic field. J. Phys. A Math. Gen. 36, 6571-6585 (2003) · Zbl 1069.81535 · doi:10.1088/0305-4470/36/23/320 |
| [45] | 45.F.T. Hadjioannou, N.V. Sarlis, Coherent states for the two-dimensional magnetic-electric Euclidean group MEE(2). Phys. Rev. B 56, 9406-9413 (1997) · doi:10.1103/PhysRevB.56.9406 |
| [46] | 46.S.T. Ali, F. Bagarello, Some physical appearances of vector coherent states and coherent states related to degenerate Hamiltonians. J. Math. Phys. 46, 053518 (2005) · Zbl 1110.81106 · doi:10.1063/1.1901343 |
| [47] | 47.S.T. Ali, F. Bagarello, G. Honnouvo, Modular structures on trace class operators and applications to Landau levels. J. Phys. A Math. Theor. 43, 105202 (2010) · Zbl 1190.81141 · doi:10.1088/1751-8113/43/10/105202 |
| [48] | 48.E. Drigho-Filho, S. Kuru, J. Negro, L.M. Nieto, Superintegrability of the Fock-Darwin system. Ann. Phys. 383, 101-119 (2017) · Zbl 1373.81222 · doi:10.1016/j.aop.2017.05.003 |
| [49] | 49.H.R. Lewis Jr., W.B. Riesenfeld, An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field. J. Math. Phys. 10, 1458-1473 (1969) · Zbl 1317.81109 · doi:10.1063/1.1664991 |
| [50] | 50.I.A. Malkin, V.I. Man’ko, D.A. Trifonov, Invariants and evolution of coherent states for charged particle in time-dependent magnetic field. Phys. Lett. A 30, 414-416 (1969) · doi:10.1016/0375-9601(69)90740-3 |
| [51] | 51.Malkin, I.A., Man’ko, V.I., Trifonov, D.A.: Evolution of coherent states of a charged particle in a variable magnetic field. Zh. Eksp. Teor. Fiz. 58, 721-729 (1970) [English translation: Sov. Phys. JETP 31, 386-390 (1970)] |
| [52] | 52.I.A. Malkin, V.I. Man’ko, D.A. Trifonov, Coherent states and transition probabilities in a time-dependent electromagnetic field. Phys. Rev. D 2, 1371-1385 (1970) · doi:10.1103/PhysRevD.2.1371 |
| [53] | 53.I.A. Malkin, V.I. Man’ko, Coherent states and Green’s function of a charged particle in variable electric and magnetic fields. Zh. Eksp. Teor. Fiz. 59, 1746-1754 (1970). [English translation: Sov. Phys. JETP 32, 949-953 (1971)] |
| [54] | 54.A. Holz, · doi:10.1007/BF02753775 |
| [55] | 55.I.A. Malkin, V.I. Man’ko, D.A. Trifonov, Linear adiabatic invariants and coherent states. J. Math. Phys. 14, 576-582 (1973) · doi:10.1063/1.1666360 |
| [56] | 56.V.V. Dodonov, I.A. Malkin, V.I. Man’ko, Integrals of the motion, Green functions and coherent states of dynamical systems. Int. J. Theor. Phys. 14, 37-54 (1975) · doi:10.1007/BF01807990 |
| [57] | 57.M.S. Abdalla, Charged harmonic oscillator in the presence of electric and magnetic fields. Nuovo Cim. B 101, 267-283 (1988) · doi:10.1007/BF02828709 |
| [58] | 58.I.A. Malkin, V.I. Man’ko, Coherent states and excitation of a charged particle in a constant magnetic field by means of an electric field. Teor. Mat. Fiz. 6, 71-77 (1971). [English translation: Theor. Math. Phys. 6, 51-55 (1971)] · doi:10.1007/BF01037578 |
| [59] | 59.R.G. Agayeva, Non-adiabatic parametric excitation of oscillator-type systems. J. Phys. A Math. Gen. 13, 1685-1699 (1980) · doi:10.1088/0305-4470/13/5/026 |
| [60] | 60.G. Fiore, L. Gouba, Class of invariants for the two-dimensional time-dependent Landau problem and harmonic oscillator in a magnetic field. J. Math. Phys. 52, 103509 (2011) · Zbl 1272.81226 · doi:10.1063/1.3653486 |
| [61] | 61.V.G. Bagrov, V.V. Belov, I.M. Ternov, Quasiclassical trajectory-coherent states of a particle in an arbitrary electromagnetic field. J. Math. Phys. 24, 2855-2859 (1983) · doi:10.1063/1.525666 |
| [62] | 62.V.V. Dodonov, V.I. Man’ko, D.L. Ossipov, Quantum evolution of the localized states. Phys. A 168, 1055-1072 (1990) · doi:10.1016/0378-4371(90)90271-S |
| [63] | 63.V.V. Belov, D.V. Boltovskii, A.G. Karavayev, Quasi-classical trajectory-coherent states of a nonrelativistic particle in a uniform magnetic-field. Izv. Vyssh. Uchebn. Zaved. Fiz. 6, 113-117 (1990) |
| [64] | 64.M. Mǎntoiu, R. Purice, S. Richard, Coherent states and pure state quantization in the presence of a variable magnetic field. Int. J. Geom. Meth. Mod. Phys. 8, 187-202 (2011) · Zbl 1210.81055 · doi:10.1142/S0219887811005087 |
| [65] | 65.S. Ryu, M. Kataoka, H.S. Sim, Ultrafast emission and detection of a single-electron Gaussian wave packet: a theoretical study. Phys. Rev. Lett. 117, 146802 (2016) · doi:10.1103/PhysRevLett.117.146802 |
| [66] | 66.I.I. Rabi, Das freie Elektron im homogenen magnetfeld nach der Diracschen theorie. Z. Phys. 49, 507-511 (1928) · JFM 54.0975.01 · doi:10.1007/BF01333634 |
| [67] | 67.V.G. Bagrov, I.L. Bukhbinder, D.M. Gitman, Coherent states of relativistic particles. Izv. Vyssh. Uchebn. Zaved. Fiz., 8, 135-136 (1975). [English translation: Sov. Phys. J. 18, 1180-1181 (1975)] |
| [68] | 68.V.V. Dodonov, I.A. Malkin, V.I. Man’ko, Coherent states and Green functions of relativistic quadratic systems. Physica A 82, 113-133 (1976) · doi:10.1016/0378-4371(76)90094-7 |
| [69] | 69.V.G. Bagrov, I.L. Buchbinder, D.M. Gitman, Coherent states of a relativistic particle in an external electromagnetic field. J. Phys. A Math. Gen. 9, 1955-1965 (1976) · doi:10.1088/0305-4470/9/11/021 |
| [70] | 70.I.M. Ternov, V.G. Bagrov, On coherent states of relativistic particles. Ann. Physik 40, 2-9 (1983) |
| [71] | 71.E. Colavita, S. Hacyan, Coherent quantum states of a relativistic particle in an electromagnetic plane wave and a parallel magnetic field. Ann. Phys. (NY) 342, 205-213 (2014) · Zbl 1342.81195 · doi:10.1016/j.aop.2014.01.001 |
| [72] | 72.G.M. Filippov, Interaction of radiation and a relativistic electron in motion in a constant magnetic field. Zh. Eksp. Teor. Fiz. 113, 841-864 (1998). [English translation: Sov. Phys. JETP 86, 459-471 (1998)] |
| [73] | 73.V.G. Bagrov, V.V. Belov, Quasiclassical coherent trajectory states of a spinless relativistic particle in an arbitrary electromagnetic field. Izv. Vyssh. Uchebn. Zaved. Fiz. 4, 48-50 (1982). [English translation: Sov. Phys. J. 25, 333-335 (1982)] |
| [74] | 74.V.V. Belov, A.G. Karavayev, Quasi-classical trajectory-coherent states of relativistic spinless particle in a homogeneous magnetic field. Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 110-112 (1988) |
| [75] | 75.L.V. Gritsenko, I.P. Susak, A.Y. Trifonov, Trajectory-coherent states for the Klein-Gordon equation in its |
| [76] | 76.V.G. Bagrov, V.V. Belov, A.Y. Trifonov, Theory of spontaneous radiation by electrons in a trajectory-coherent approximation. J. Phys. A Math. Gen. 26, 6431-6449 (1993) · doi:10.1088/0305-4470/26/22/038 |
| [77] | 77.A. Mostafazadeh, F. Zamani, Quantum mechanics of Klein-Gordon fields II: relativistic coherent states. Ann. Phys. (NY) 321, 2210-2241 (2006) · Zbl 1104.81042 · doi:10.1016/j.aop.2006.02.008 |
| [78] | 78.A. Bermudez, M.A. Martin-Delgado, E. Solano, Mesoscopic superposition states in relativistic Landau levels. Phys. Rev. Lett. 99, 123602 (2007) |
| [79] | 79.V.Y. Demikhovskii, G.M. Maksimova, A.A. Perov, A.V. Telezhnikov, Long-term cyclotron dynamics of relativistic wave packets: spontaneous collapse and revival. Phys. Rev. A 85, 022105 (2012) · doi:10.1103/PhysRevA.85.022105 |
| [80] | 80.H.Y. Kim, J.H. Weiner, Gaussian-wave-packet dynamics in uniform magnetic and quadratic potential fields. Phys. Rev. B 7, 1353-1362 (1973) · doi:10.1103/PhysRevB.7.1353 |
| [81] | 81.A. Bechler, Generation of squeezed states in a homogeneous magnetic field. Phys. Lett. A 130, 481-482 (1988) · doi:10.1016/0375-9601(88)90712-8 |
| [82] | 82.A. Jannussis, E. Vlahos, D. Skaltsas, G. Kliros, V. Bartzis, Squeezed states in the presence of a time-dependent magnetic field. Nuovo Cim. B 104, 53-66 (1989) · doi:10.1007/BF02742825 |
| [83] | 83.M.S. Abdalla, Statistical properties of a charged oscillator in the presence of a constant magnetic field. Phys. Rev. A 44, 2040-2047 (1991) · doi:10.1103/PhysRevA.44.2040 |
| [84] | 84.V.A. Kovarskiy, Coherent and squeezed states of Landau oscillators in a solid. Emission of nonclassical light. Fiz. Tverd. Tela 34, 3549-3553 (1992) [English translation: Sov. Phys. - Solid State 34, 1900-1902 (1992)] |
| [85] | 85.B. Baseia, On the generation of squeezing for a charged oscillator in a magnetic field. Phys. Lett. A 170, 311-314 (1992) · doi:10.1016/0375-9601(92)90260-S |
| [86] | 86.B. Baseia, S.S. Mizrahi, M.H.Y. Moussa, Generation of squeezing for a charged oscillator and a charged particle in a time dependent electromagnetic field. Phys. Rev. A 46, 5885-5889 (1992) · doi:10.1103/PhysRevA.46.5885 |
| [87] | 87.F.C. Delgado, B. Mielnik, Magnetic control of squeezing effects. J. Phys. A Math. Gen. 31, 309-320 (1998) · Zbl 0956.81024 · doi:10.1088/0305-4470/31/1/027 |
| [88] | 88.J.E. Santos, N.M.R. Peres, J.M.B. Lopes dos Santos, Evolution of squeezed states under the Fock-Darwin Hamiltonian. Phys. Rev. A 80, 053401 (2009) · doi:10.1103/PhysRevA.80.053401 |
| [89] | 89.V.V. Dodonov, E.V. Kurmyshev, V.I. Man’ko, Correlated coherent states, in \(Classical And Quantum Effects In Electrodynamics, Proceedings of the P.N. Lebedev Physical Institute\), ed. by A.A. Komar, vol. 176 (Nauka, Moscow, 1986), pp. 128-150 [English translation by Nova Science, Commack, New York (1988), pp. 169-199] |
| [90] | 90.A. Dehghani, H. Fakhri, B. Mojaveri, The minimum-uncertainty coherent states for Landau levels. J. Math. Phys. 53, 123527 (2012) · Zbl 1278.81167 · doi:10.1063/1.4770258 |
| [91] | 91.C. Aragone, New squeezed Landau states. Phys. Lett. A 175, 377-381 (1993) · doi:10.1016/0375-9601(93)90985-9 |
| [92] | 92.V.V. Dodonov, V.I. Man’ko, P.G. Polynkin, Geometrical squeezed states of a charged particle in a time-dependent magnetic field. Phys. Lett. A 188, 232-238 (1994) · doi:10.1016/0375-9601(94)90444-8 |
| [93] | 93.M. Ozana, A.L. Shelankov, Squeezed states of a particle in magnetic field. Fiz. Tverd. Tela 40, 1405-1412 (1998). [English translation: Phys. Solid State 40, 1276-1282 (1998)] · doi:10.1134/1.1130543 |
| [94] | 94.A.B. Dzyubenko, Charged two-dimensional magnetoexciton and two-mode squeezed vacuum states. Pis’ma v Zh. Eksp. Teor. Fiz. 74, 352-356 (2001). [English translation: JETP Lett. 74, 318-322 (2001)] · doi:10.1134/1.1421407 |
| [95] | 95.A.B. Dzyubenko, Charged hydrogenic problem in a magnetic field: Noncommutative translations, unitary transformations, and coherent states. Phys. Rev. B 65, 035318 (2001) · doi:10.1103/PhysRevB.65.035318 |
| [96] | 96.H. Takahasi, Information theory of quantum mechanical channels, in \(Advances in Communication Systems\), vol. l, Theory and Applications, ed. by A.V. Balakrishnan (Academic Press, New York, 1965), pp. 227-310 |
| [97] | 97.V.V. Dodonov, Man’ko, V.I.: Correlated and squeezed coherent states of time-dependent quantum systems, in \(Advances in Chemical Physics Modern Nonlinear Optics\), eds. by M. Evans, S. Kielich, vol. LXXXV, part 3. (Wiley, New York, 1994), pp. 499-530 |
| [98] | 98.A. Lukš, V. Peřinová, Z. Hradil, Principal squeezing. Acta Phys. Polon. A 74, 713-721 (1988) |
| [99] | 99.V.V. Dodonov, “Nonclassical” states in quantum optics: a “squeezed” review of the first 75 years. J. Opt. B Quantum Semiclass. Opt. 4, R1-R33 (2002) · doi:10.1088/1464-4266/4/1/201 |
| [100] | 100.V.V. Dodonov, Universal integrals of motion and universal invariants of quantum systems. J. Phys. A Math. Gen. 33, 7721-7738 (2000) · Zbl 1032.81509 · doi:10.1088/0305-4470/33/43/305 |
| [101] | 101.V.V. Dodonov, V.I. Man’ko, Density matrices and Wigner functions of quasiclassical quantum systems, in \(Group Theory, Gravitation and Elementary Particle Physics, Proceedings of the P.N. Lebedev Physical Institute\), ed. by A.A. Komar, vol. 167(Nauka, Moscow, 1986), pp. 7-79. [English translation by Nova Science, Commack, New York (1987), pp. 7-101] |
| [102] | 102.L.D. Landau, E.M. Lifshitz, \(Mechanics\) (Pergamon, Oxford, 1969) · Zbl 0081.22207 |
| [103] | 103.V.V. Dodonov, A.B. Klimov, D.E. Nikonov, Quantum phenomena in nonstationary media. Phys. Rev. A 47, 4422-4429 (1993) · doi:10.1103/PhysRevA.47.4422 |
| [104] | 104.P. Gulshani, A.B. Volkov, Heisenberg-symplectic angular-momentum coherent states in two dimensions. J. Phys. A Math. Gen. 13, 3195-3204 (1980) · doi:10.1088/0305-4470/13/10/016 |
| [105] | 105.P. Gulshani, A.B. Volkov, The cranked oscillator coherent states. J. Phys. G Nucl. Phys. 6, 1335-46 (1980) · doi:10.1088/0305-4616/6/11/006 |
| [106] | 106.S. Hacyan, Squeezed states and uncertainty relations in rotating frames and Penning trap. Phys. Rev. A 53, 4481-4487 (1996) · doi:10.1103/PhysRevA.53.4481 |
| [107] | 107.A. Wünsche, The quantum-mechanical inhomogeneous symplectic group. J. Opt. B Quantum Semiclass. Opt. 4, 1-14 (2002) · doi:10.1088/1464-4266/4/1/301 |
| [108] | 108.C. Bracher, Uncertainty relations for angular momentum eigenstates in two and three spatial dimensions. Am. J. Phys. 79, 313-319 (2011) · doi:10.1119/1.3534840 |
| [109] | 109.L. Rebón, R. Rossignoli, Entanglement of two harmonic modes coupled by angular momentum. Phys. Rev. A 84, 052320 (2011) · doi:10.1103/PhysRevA.84.052320 |
| [110] | 110.L. Rebón, N. Canosa, R. Rossignoli, Dynamics of entanglement between two harmonic modes in stable and unstable regimes. Phys. Rev. A 89, 042312 (2014) · doi:10.1103/PhysRevA.89.042312 |
| [111] | 111.D.V. Karlovets, Gaussian and Airy wave packets of massive particles with orbital angular momentum. Phys. Rev. A 91, 013847 (2015) · doi:10.1103/PhysRevA.91.013847 |
| [112] | 112.V.V. Dodonov, Rotating quantum Gaussian packets. J. Phys. A Math. Theor. 48, 435303 (2015) · Zbl 1326.81098 · doi:10.1088/1751-8113/48/43/435303 |
| [113] | 113.V.V. Dodonov, Rotating highly mixed Gaussian packets with minimal energy. Phys. Rev. A 93, 022106 (2016) · doi:10.1103/PhysRevA.93.022106 |
| [114] | 114.A. Goussev, Rotating Gaussian wave packets in weak external potentials. Phys. Rev. A 96, 013617 (2017) · doi:10.1103/PhysRevA.96.013617 |
| [115] | 115.G. Loyola, M. Moshinsky, A. Szczepaniak, Coherent states and accidental degeneracy for a charged particle in a magnetic field. Am. J. Phys. 57, 811-814 (1989) · doi:10.1119/1.15898 |
| [116] | 116.R. Ferrari, Two-dimensional electrons in a strong magnetic field: a basis for single-particle states. Phys. Rev. B 42, 4598-4609 (1990) · doi:10.1103/PhysRevB.42.4598 |
| [117] | 117.Z. Mouayn, Characterization of two-dimensional Euclidean Landau states by coherent state transforms. J. Phys. A Math. Gen. 37, 4813-4819 (2004) · Zbl 1050.81080 · doi:10.1088/0305-4470/37/17/011 |
| [118] | 118.W.-L. Yang, J.-L. Chen, Berry’s phase for coherent states of Landau levels. Phys. Rev. A 75, 024101 (2007) · doi:10.1103/PhysRevA.75.024101 |
| [119] | 119.M.N. Rhimi, R. El-Bahi, Geometric phases for wave packets of the Landau problem. Int. J. Theor. Phys. 47, 1095-1111 (2008) · Zbl 1140.81469 · doi:10.1007/s10773-007-9538-4 |
| [120] | 120.L.D. Abreu, P. Balazs, M. de Gosson, Z. Mouayn, Discrete coherent states for higher Landau levels. Ann. Phys. (NY) 363, 337-353 (2015) · Zbl 1360.81204 · doi:10.1016/j.aop.2015.09.009 |
| [121] | 121.H.-Y. Fan, H. Zou, Y. Fan, Angular momentum conserved coherent state for an electron in a uniform magnetic field. Chin. Phys. Lett. 16, 706-708 (1999) · doi:10.1088/0256-307X/16/10/002 |
| [122] | 122.D. Bhaumik, K. Bhaumik, B. Dutta-Roy, Charged bosons and the coherent state. J. Phys. A Math. Gen. 9, 1507-1512 (1976) · doi:10.1088/0305-4470/9/9/011 |
| [123] | 123.H. Fakhri, · Zbl 1054.81023 · doi:10.1088/0305-4470/37/19/007 |
| [124] | 124.I. Aremua, M.N. Hounkonnou, E. Baloïtcha, Coherent states for Landau levels: algebraic and thermodynamical properties. Rep. Math. Phys. 76, 247-269 (2015) · Zbl 1334.81051 · doi:10.1016/S0034-4877(15)30032-X |
| [125] | 125.A. Dehghani, B. Mojaveri, Generalized su(2) coherent states for the Landau levels and their nonclassical properties. Eur. Phys. J. D 67, 264 (2013) · Zbl 1275.81031 · doi:10.1140/epjd/e2013-40550-2 |
| [126] | 126.M. Novaes, J.P. Gazeau, Multidimensional generalized coherent states. J. Phys. A Math. Gen. 36, 199-212 (2003) · Zbl 1047.81039 · doi:10.1088/0305-4470/36/1/313 |
| [127] | 127.H. Fakhri, Generalized Klauder-Perelomov and Gazeau-Klauder coherent states for Landau levels. Phys. Lett. A 313, 243-251 (2003) · Zbl 1059.81191 · doi:10.1016/S0375-9601(03)00676-5 |
| [128] | 128.M.R. Setare, A. Fallahpour, Generalized coherent states for charged particle in uniform and variable magnetic field. Acta Phys. Polon. B 40, 217-228 (2009) |
| [129] | 129.P.M. Mathews, K. Eswaran, Semi-coherent states of the quantum harmonic oscillator. Nuovo Cim. B 17, 332-335 (1973) · doi:10.1007/BF02894677 |
| [130] | 130.V.V. Dodonov, M.B. Renó, Nonclassical properties of “semi-coherent” quantum states. J. Phys. A Math. Gen. 39, 7411-7422 (2006) · Zbl 1097.81037 · doi:10.1088/0305-4470/39/23/016 |
| [131] | 131.A. Dehghani, B. Mojaveri, New semi coherent states: nonclassical properties. Int. J. Theor. Phys. 54, 3507-3515 (2015) · Zbl 1325.81099 · doi:10.1007/s10773-015-2592-4 |
| [132] | 132.R.L. Matos Filho, W. Vogel, Nonlinear coherent states. Phys. Rev. A 54, 4560-4563 (1996) · doi:10.1103/PhysRevA.54.4560 |
| [133] | 133.V.I. Man’ko, G. Marmo, E.C.G. Sudarshan, F. Zaccaria, f-oscillators and nonlinear coherent states. Phys. Scr. 55, 528-541 (1997) · doi:10.1088/0031-8949/55/5/004 |
| [134] | 134.S. Sivakumar, Studies on nonlinear coherent states. J. Opt. B Quantum. Semiclass Opt. 2, R61-R75 (2000) · doi:10.1088/1464-4266/2/6/02 |
| [135] | 135.J.P. Gazeau, J.R. Klauder, Coherent states for systems with discrete and continuous spectrum. J. Phys. A Math. Gen. 32, 123-132 (1999) · Zbl 0919.47061 · doi:10.1088/0305-4470/32/1/013 |
| [136] | 136.D. Herrera, A.M. Valencia, F. Pennini, S. Curilef, A charged particle in a magnetic field: a review of two formalisms of coherent states and the Husimi function. Eur. J. Phys. 29, 439-449 (2008) · Zbl 1140.81410 · doi:10.1088/0143-0807/29/3/005 |
| [137] | 137.J.P. Gazeau, M.C. Baldiotti, D.M. Gitman, Coherent states of a particle in a magnetic field and the Stieltjes moment problem. Phys. Lett. A 373, 1916-1920 (2009) · Zbl 1229.81141 · doi:10.1016/j.physleta.2009.03.061 |
| [138] | 138.B.I. Lev, A.A. Semenov, C.V. Usenko, Behaviour of · doi:10.1016/S0375-9601(97)00242-9 |
| [139] | 139.B.I. Lev, A.A. Semenov, C.V. Usenko, J.R. Klauder, Relativistic coherent states and charge structure of the coordinate and momentum operators. Phys. Rev. A 66, 022115 (2002) · doi:10.1103/PhysRevA.66.022115 |
| [140] | 140.H. Feshbach, F. Villars, Elementary relativistic wave mechanics of spin 0 and spin 1/2 particles. Rev. Mod. Phys. 30, 24-45 (1958) · Zbl 0082.21905 · doi:10.1103/RevModPhys.30.24 |
| [141] | 141.H.-Y. Fan, Y. Fan, Angular momentum-phase coherent state for an electron in uniform magnetic field. Chin. Phys. Lett. 18, 319-321 (2001) · doi:10.1088/0256-307X/18/5/314 |
| [142] | 142.G.S. Agarwal, K. Tara, Nonclassical properties of states generated by the excitations of a coherent state. Phys. Rev. A 43, 492-497 (1991) · doi:10.1103/PhysRevA.43.492 |
| [143] | 143.B. Mojaveri, A. Dehghani, Generation of excited coherent states for a charged particle in a uniform magnetic field. J. Math. Phys. 56, 041704 (2015) · Zbl 1315.81054 · doi:10.1063/1.4917545 |
| [144] | 144.V.G. Bagrov, D.M. Gitman, V.D. Skarzhinsky, The Aharonov-Bohm effect for stationary and coherent states of an electron in a uniform magnetic field. in \(Classical and Quantum Effects in Electrodynamics Proceedings of the P.N. Lebedev Physical Institute\), ed. by A.A. Komar, vol. 176. (Nauka, Moscow, 1986), pp. 151-165. [English translation by Nova Science, Commack, New York (1988), pp. 201-219] |
| [145] | 145.V.G. Bagrov, S.P. Gavrilov, D.M. Gitman, D.P. Meira Filho, Coherent states of non-relativistic electron in the magneticsolenoid field. J. Phys. A Math. Theor. 43, 354016 (2010) · Zbl 1196.81145 · doi:10.1088/1751-8113/43/35/354016 |
| [146] | 146.V.G. Bagrov, S.P. Gavrilov, D.M. Gitman, D.P. Meira Filho, Coherent and semiclassical states in a magnetic field in the presence of the Aharonov-Bohm solenoid. J. Phys. A Math. Theor. 44, 055301 (2011) · Zbl 1208.81113 · doi:10.1088/1751-8113/44/5/055301 |
| [147] | 147.V.G. Bagrov, S.P. Gavrilov, D.M. Gitman, K. Gorska, Completeness for coherent states in a magnetic-solenoid field. J. Phys. A Math. Theor. 45, 244008 (2012) · Zbl 1250.81049 · doi:10.1088/1751-8113/45/24/244008 |
| [148] | 148.V.V. Belov, M.F. Kondrat’eva, The Aharonov-Bohm effect for nonstationary quasiclassical trajectory-coherent states in a uniform magnetic field. Izv. Vyssh. Uchebn. Zaved., Fiz. 10, 83-90 (1992). [English translation: Russ. Phys. J. 35, 961-968 (1993)] |
| [149] | 149.H. Fakhri, B. Mojaveri, M.A. Gomshi Nobary, Landau levels as a limiting case of a model with the Morse-like magnetic field. Rep. Math. Phys. 66, 299-310 (2010) · Zbl 1236.81126 · doi:10.1016/S0034-4877(11)00002-4 |
| [150] | 150.B. Mojaveri, Klauder-Perelomov and Gazeau-Klauder coherent states for an electron in the Morse-like magnetic field. Eur. Phys. J. D 67, 105 (2013) · doi:10.1140/epjd/e2013-40048-y |
| [151] | 151.J. Beckers, D. Dehin, V. Hussin, Dynamical and kinematical supersymmetries of the quantum harmonic oscillator and the motion in a constant magnetic field. J. Phys. A Math. Gen. 21, 651-667 (1988) · Zbl 0649.17002 · doi:10.1088/0305-4470/21/3/020 |
| [152] | 152.B.W. Fatyga, V.A. Kostelecký, M.M. Nieto, D.R. Truax, Supercoherent states. Phys. Rev. D 43, 1403-1412 (1991) · doi:10.1103/PhysRevD.43.1403 |
| [153] | 153.H. Fakhri, H. Motavali, Parasupersymmetric coherent states for Landau levels with dynamical symmetry group · Zbl 1041.81054 · doi:10.1142/S0217751X02010546 |
| [154] | 154.S.T. Ali, F. Bagarello, Supersymmetric associated vector coherent states and generalized Landau levels arising from two-dimensional supersymmetry. J. Math. Phys. 49, 032110 (2008) · Zbl 1153.81308 · doi:10.1063/1.2898117 |
| [155] | 155.V.A. Kostelecký, V.I. Man’ko, M.M. Nieto, D.R. Truax, Supersymmetry and a time-dependent Landau system. Phys. Rev. A 48, 951-963 (1993) · doi:10.1103/PhysRevA.48.951 |
| [156] | 156.M.C. Baldiotti, J.P. Gazeau, D.M. Gitman, Semiclassical and quantum motions on the non-commutative plane. Phys. Lett. A 373, 3937-3943 (2009) · Zbl 1234.81092 · doi:10.1016/j.physleta.2009.08.059 |
| [157] | 157.M.-L. Liang, Y. Jiang, Time-dependent harmonic oscillator in a magnetic field and an electric field on the non-commutative plane. Phys. Lett. A 375, 1-5 (2010) · Zbl 1241.81111 · doi:10.1016/j.physleta.2010.10.035 |
| [158] | 158.Z. Mouayn, Coherent states attached to Landau levels on the Poincare disc. J. Phys. A Math. Gen. 38, 9309-9316 (2005) · Zbl 1081.81060 · doi:10.1088/0305-4470/38/42/010 |
| [159] | 159.Z. Mouayn, Coherent states attached to Landau levels on the Riemann sphere. Rep. Math. Phys. 55, 269-276 (2005) · Zbl 1085.81048 · doi:10.1016/S0034-4877(05)80032-1 |
| [160] | 160.B.C. Hall, J.J. Mitchell, Coherent states for a 2-sphere with a magnetic field. J. Phys. A Math. Theor. 45, 244025 (2012) · Zbl 1250.81053 · doi:10.1088/1751-8113/45/24/244025 |
| [161] | 161.Y. Kurochkin, I. Rybak, D. Shoukavy, Coherent states on horospheric three-dimensional Lobachevsky space. J. Math. Phys. 57, 082111 (2016) · Zbl 1344.81097 · doi:10.1063/1.4960474 |
| [162] | 162.M. Salazar-Ramírez, D. Ojeda-Guillén, R.D. Mota, Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime. Ann. Phys. (NY) 372, 283-296 (2016) · Zbl 1380.83267 · doi:10.1016/j.aop.2016.05.011 |
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