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Time-evolution operator for a forced parametric oscillator

✍ Scribed by José Récamier A.; Rocío Jáuregui

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
283 KB
Volume
62
Category
Article
ISSN
0020-7608

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✦ Synopsis

We apply an algebraic technique to describe the evolution of a parametric harmonic oscillator forced by a constant quartic potential. As the first step, we make use of iterative Ž . Bogolubov transformations IBT to incorporate information from the anharmonic part of the interaction in a nonperturbative form, yielding a unitary time-evolution operator. Later on, we make use of first-order perturbation theory to deal with that part of the interaction which was not incorporated previously. We show numerically that the resulting time-evolution operator is closer to unitarity than is the one obtained if no IBT is applied. The quantum fluctuations of position and momentum are evaluated for ''the ground'' state. Squeezing and correlation effects are observed.

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