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2008

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May

  

Methodological notes


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.

Text can be downloaded in Russian. English translation is available on IOP Science.
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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