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29 March 2024
 
  » arxiv » nlin.CD/0008005

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Stability of the Ground State of a Harmonic Oscillator in a Monochromatic Wave
Gennady P. Berman ; Daniel F.V. James ; Dimitry I. Kamenev ;
Date 4 Aug 2000
Subject Chaotic Dynamics | nlin.CD
AbstractClassical and quantum dynamics of a harmonic oscillator in a monochromatic wave is studied in the exact resonance and near resonance cases. This model describes, in particular, a dynamics of a cold ion trapped in a linear ion trap and interacting with two lasers fields with close frequencies. Analytically and numerically a stability of the ``classical ground state’’ (CGS) -- the vicinity of the point ($x=0, p=0$) -- is analyzed. In the quantum case, the method for studying a stability of the quantum ground state (QGS) is suggested, based on the quasienergy representation. The dynamics depends on four parameters: the detuning from the resonance, $delta=ell-Omega/omega$, where $Omega$ and $omega$ are, respectively, the wave and the oscillator’s frequencies; the positive integer (resonance) number, $ell$; the dimensionless Planck constant, $h$, and the dimensionless wave amplitude, $epsilon$. For $delta=0$, the CGS and the QGS are unstable for resonance numbers $ell=1, 2$. For small $epsilon$, the QGS becomes more stable with increasing $delta$ and decreasing $h$. When $epsilon$ increases, the influence of chaos on the stability of the QGS is analyzed for different parameters of the model, $ell$, $delta$ and $h$.
Source arXiv, nlin.CD/0008005
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