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Parametric instability of quantum oscillator

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