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Impedance and parametric excitation of oscillators

 a, b
a University Academic Division of Nonlinear Optics, Institute of Electro-Physics of the Ural Division of the Russian Academy of Sciences, pr. Lenina 76, Chelyabinsk, 454010, Russian Federation
b College of Optics and Photonics/CREOL, University of Central Florida, 4000 Central Florida Blvd., Orlando, Florida, 32816-2700, USA

This article deals with the linear ordinary differential equations for one or several coupled oscillators. Emphasis is placed on the separate notions of the frequency matrix (as a kinematic entity) and the impedance matrix. The latter matrix is explicitly introduced in this article, and its time dependence is shown to be responsible for parametric excitation and for nonconservation of adiabatic invariants.

Fulltext is available at IOP
PACS: 05.45.Xt, 45.05.+x, 84.30.−r (all)
DOI: 10.1070/PU2008v051n05ABEH006498
URL: https://ufn.ru/en/articles/2008/5/d/
Citation: Zel’dovich B Ya "Impedance and parametric excitation of oscillators" Phys. Usp. 51 465–484 (2008)
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Оригинал: Зельдович Б Я «Импеданс и параметрическое возбуждение осцилляторов» УФН 178 489–510 (2008); DOI: 10.3367/UFNr.0178.200805d.0489

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  3. F.Ya. Khalili “Zero-point oscillations, zero-point fluctuations, and fluctuations of zero-point oscillations46 293–307 (2003)
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  7. L.N. Kaptsov “Four lecture demonstrations for courses on the theory of oscillations and radio engineering6 933–938 (1964)
  8. A.V. Shchagin “Fresnel coefficients for parametric X-ray (Cherenkov) radiation58 819–827 (2015)
  9. I.A. Sadovskyy “Reduction of the scattering matrix array58 872–876 (2015)
  10. Yu.L. Klimontovich “What are stochastic filtering and stochastic resonance?42 37–44 (1999)

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