Vol. 44

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2013-12-19

Quantum Analysis of a Modified Caldirola-Kanai Oscillator Model for Electromagnetic Fields in Time-Varying Plasma

By Jeong Ryeol Choi, Samira Lakehal, Mustapha Maamache, and Salah Menouar
Progress In Electromagnetics Research Letters, Vol. 44, 71-79, 2014
doi:10.2528/PIERL13061601

Abstract

Quantum properties of a modified Caldirola-Kanai oscillator model for propagating electromagnetic fields in plasma medium are investigated using invariant operator method. As a modification, ordinary exponential function in the Hamiltonian is replaced with a modified exponential function, so-called the q-exponential function. The system described in terms of q-exponential function exhibits nonextensivity. Characteristics of the quantized fields, such as quantum electromagnetic energy, quadrature fluctuations, and uncertainty relations are analyzed in detail in the Fock state, regarding the q-exponential function. We confirmed, from their illustrations, that these quantities oscillate with time in some cases. It is shown from the expectation value of energy operator that quantum energy of radiation fields dissipates with time, like a classical energy, on account of the existence of non-negligible conductivity in media.

Citation


Jeong Ryeol Choi, Samira Lakehal, Mustapha Maamache, and Salah Menouar, "Quantum Analysis of a Modified Caldirola-Kanai Oscillator Model for Electromagnetic Fields in Time-Varying Plasma," Progress In Electromagnetics Research Letters, Vol. 44, 71-79, 2014.
doi:10.2528/PIERL13061601
http://jpier.org/PIERL/pier.php?paper=13061601

References


    1. Lewis, Jr., H. R. and 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., Vol. 10, No. 8, 1458-1473, 1969.
    doi:10.1063/1.1664991

    2. Choi, J. R., "Nonclassical properties of superpositions of coherent and squeezed states for electromagnetic fields in time-varying media," Quantum Optics and Laser Experiments, 25-48, 2012.

    3. Kalluri, D. K., "Electromagnetics of Time Varying Complex Media," CRC Press, 2010.

    4. Heald, M. A. and C. B. Wharton, "Plasma Diagnostics with Microwaves," Wiley, 1965.

    5. Caldirola, P., "Forze non conservative nella meccanica quantistica," Il Nuovo Cimento, Vol. 18, No. 9, 393-400, 1941.
    doi:10.1007/BF02960144

    6. Kanai, E., "On the quantization of the dissipative systems," Prog. Theor. Phys., Vol. 3, No. 4, 440-442, 1950.
    doi:10.1143/ptp/3.4.440

    7. Tsallis, C., "What are the numbers that experiments provide?," Quimica Nova, Vol. 17, 468-471, 1994.

    8. Ozeren, S. F., "The effect of nonextensivity on the time evolution of the SU(1,1) coherent states driven by a damped harmonic oscillator," Physica A, Vol. 337, No. 1--2, 81-88, 2004.
    doi:10.1016/j.physa.2004.01.038

    9. Liu, Z. P., L. N. Guo, and J. L. Du, "Nonextensivity and the q-distribution of a relativistic gas under an external electromagnetic field," Chin. Sci. Bull., Vol. 56, No. 34, 3689-3692, 2011.
    doi:10.1007/s11434-011-4750-2

    10. Pedrosa, I. A. and A. Rosas, "Electromagnetic field quantization in time-dependent linear media ," Phys. Rev. Lett., Vol. 103, No. 1, 010402, 2009.
    doi:10.1103/PhysRevLett.103.010402

    11. Maamache, M., J.-P. Provost, and G. Vallee, "Unitary equivalence and phase properties of the quantum parametric and generalized harmonic oscillators," Phys. Rev. A, Vol. 59, No. 3, 1777-1780, 1999.
    doi:10.1103/PhysRevA.59.1777

    12. Tsallis, C., "Possible generalization of Boltzmann-Gibbs statistics," J. Stat. Phys., Vol. 52, No. 1--2, 479-487, 1988.
    doi:10.1007/BF01016429

    13. Albuquerque, E. L. and M. G. Cottam, "Theory of elementary excitations in quasiperiodic structures ," Phys. Rep., Vol. 376, No. 4--5, 225-337, 2003.
    doi:10.1016/S0370-1573(02)00559-8

    14. Anastasiadis, A. D. and G. D. Magoulas, "Particle swarms and nonextensive statistics for nonlinear optimisation," The Open Cybernetics and Systemics Journal, Vol. 2, 173-179, 2008.
    doi:10.2174/1874110X00802010173

    15. McHarris, Wm. C., "Nonlinearities in quantum mechanics," Braz. J. Phys., Vol. 35, No. 2B, 380-384, 2005.
    doi:10.1590/S0103-97332005000300003

    16. Marchiolli, M. A. and S. S. Mizrahi, "Dissipative mass-accreting quantum oscillator," J. Phys. A: Math. Gen., Vol. 30, No. 8, 2619-2635, 1997.
    doi:10.1088/0305-4470/30/8/011

    17. Choi, J. R., "The decay properties of a single-photon in linear media," Chin. J. Phys., Vol. 41, No. 3, 257-266, 2003.

    18. Fujii, K. and T. Suzuki, "An approximate solution of the Jaynes-Cummings model with dissipation," Int. J. Geom. Methods Mod. Phys., Vol. 8, No. 8, 1799-1814, 2011.
    doi:10.1142/S0219887811005944

    19. Fujii, K. and T. Suzuki, "An approximate solution of the Jaynes-Cummings model with dissipation II: Another approach," Int. J. Geom. Methods Mod. Phys., Vol. 9, No. 4, 1250036, 2012.
    doi:10.1142/S0219887812500363

    20. Buzek, V., A. Vidiella-Barranco, and P. L. Knight, "Superpositions of coherent states: Squeezing and dissipation," Phys. Rev. A, Vol. 45, No. 9, 6570-6585, 1992.
    doi:10.1103/PhysRevA.45.6570

    21. Ji, Y.-H. and M.-S. Lei, "Squeezing e®ects of a mesoscopic dissipative coupled circuit," Int. J. Theor. Phys., Vol. 41, No. 7, 1346-1346, 2002.
    doi:10.1023/A:1019659101209

    22. Weiss, U., "Quantum Dissipative Systems," World Scientific, 2008.

    23. Garashchuk, S., V. Dixit, B. Gu, and J. Mazzuca, "The Schrodinger equation with friction from the quantum trajectory perspective ," J. Chem. Phys., Vol. 138, No. 5, 054107, 2013.
    doi:10.1063/1.4788832

    24. Stannigel, K., P. Rabl, and P. Zoller, "Driven-dissipative preparation of entangled states in cascaded quantum-optical networks," New J. Phys., Vol. 14, No. 6, 063014, 2012.
    doi:10.1088/1367-2630/14/6/063014

    25. Choi, J. R., "Quantum unitary transformation approach for the evolution of dark energy," Dark Energy --- Current Advances and Ideas, 117-134, 2009.

    26. Choi, J. R., "SU(1,1) Lie algebraic approach for the evolution of the quantum inflationary universe ," Phys. Dark Univ., Vol. 2, No. 1, 41-49, 2013.
    doi:10.1016/j.dark.2013.02.002