Abstract
A vibrational analog of the superradiant quantum transition (SQT) in a classical system of weakly bound oscillators of van der Pole-Duffing (self-generators), in which the coupling element is a linear oscillator, is described. Such an analog is a strongly modulated oscillatory process of almost complete periodic energy exchange between the generators. This type of mode is alternative to nonlinear normal modes (NNM) and close in its character to limiting phase trajectories (LPTs), which have been introduced recently as applied to conservative systems, but in contrast to them, as the attractor. It is shown that the necessary condition of the transition to intense energy exchange in the classical system is the instability of one of the NNMs similarly to that when the condition of the superradiant transition is the instability of the ground state in a quantum model.
Similar content being viewed by others
References
B. M. Garraway, Phil. Trans. Roy. Soc. A, No. 369, 1137 (2011).
R. H. Dicke, Phys. Rev. A, No. 93, 99 (1954).
F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, Phys. Rev. A No. 75, 013804 (2007).
Yu. A. Il’inskii and N. S. Maslova, Zh. Eksp. Teor. Fiz. 94(1), 171 (1988).
C. L. Pando Lambruschini, Europhys. Lett., No. 11, 391 (1990).
G. Preparata, in QED Coherence in Matter (World Sci., Singapore, 1995), pp. 41–50.
A. F. Vakakis, L. I. Manevitch, Yu. V. Mlkhlin, V. N. Pilipchuk, and A. A. Zevin, Normal Modes and Localization in Nonlinear Systems (New York, Wiley, 1996).
Y. Starosvetsky and L. I. Manevitch, Phys. Rev. E, No. 83, 046211 (2011).
L. I. Manevitch, Arch. Appl. Mech. 77(5), 301 (2007).
L. I. Manevitch and V. V. Smirnov, Phys. Rev. E, No. 82, 036602 (2010).
Kadji H. G. Enjieu and R. Yamapi, Physica A 370(2), 316 (2006).
A. P. Kuznetsov, N. V. Stankevich, and L. V. Turukina, Phys. D 238(14), 1203 (2009).
A. Maccari, J. Comput. Nonlinear Dyn. 6(1), 011016 (2011).
I. Semenov, Yu. Mitrishkin, A. Subbotin, A. Vertinski, and N. Marusov, Plasma Phys. Repts. 32(2), 1 (2006).
R. FitzHugh, Biophysics J., No. 1, 445 (1961).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © L.I. Manevitch, M.A. Kovaleva, 2013, published in Doklady Akademii Nauk, 2013, Vol. 452, No. 5, pp. 514–517.
Rights and permissions
About this article
Cite this article
Manevitch, L.I., Kovaleva, M.A. Vibration analog of a superradiant quantum transition. Dokl. Phys. 58, 428–432 (2013). https://doi.org/10.1134/S1028335813100078
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1028335813100078