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arXiv:1905.04591

Forced quantum inverted oscillator

Pavel A. Golovinski

Published May 11, 2019• 0 citations
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Abstract

New exact and asymptotic results for a quantum inverted oscillator, driven by the variable external force, are presented. To illustrate the advantages of our approach, we applied the obtained propagator to the descriptions of evolution the initial Gaussian wave packet under arbitrary time-dependent force or a δ-pulse action. The alternative problem of tunneling a particle through a parabolic barrier under the influence of a low-frequency harmonic force we solve in the quasistatic approximation. Going to the Heisenberg picture in the Caldeira-Leggett model, we describe the influence of a time-dependent force on an open inverted oscillator. The resulting dynamics is presented in the form of combination the evolution of the average value of a coordinate operator and the stochastic diffusion, being induced the wave packet spreading and the Brownian motion.

DOI
10.48550/arxiv.1905.04591

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Using the evolution operator method, we derive the exact propagator of the generalized parametric oscillator in its more general form. This result is exploited to obtain the exact wavefunction of a damped and driven, inverted harmonic oscillator of the Caldirola-Kanai type, taking a Gaussian wavepacket as the initial state. We discuss the tunnelling process of such a system. The probability density and the persistence probability are evaluated. The expression for the sojourn time is derived for a small external force, and is the sum of two terms, whose explicit forms are obtained in the case of an extended wavepacket. The first term is an increasing function of the dissipation parameter gamma , whereas the second one is strictly due to the presence of the driving force.
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