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Parametric instability of quantum oscillator

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Abstract

It is shown that the dynamic symmetry group of an oscillator with variable frequency is the line or group SL(2, R). Classical and quantum oscillators are described respectively by two-dimensional representations of this group. The conditions for the appearance of parametric resonance are investigated. For the case of periodic frequency modulation, nonspreading coherent states are constructed.

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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 7–12, May, 1979.

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Granovskii, Y.I., Dimashko, Y.A. Parametric instability of quantum oscillator. Soviet Physics Journal 22, 463–467 (1979). https://doi.org/10.1007/BF00893232

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Keywords

  • Frequency Modulation
  • Symmetry Group
  • Coherent State
  • Variable Frequency
  • Parametric Resonance