Quantum Parametric Resonance

Details Quantum Parametric Resonance Quantum Parametric Resonance

2001-06-25

arxiv.org/abs/quant-ph/0106138v1

J. Phys. A 35 (2002) 4669

Physics

Quantum Physics

10 pages, revtex

Scientific paper

10.1088/0305-4470/35/18/312

The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are shown to correspond to Floquet operators with qualitatively different properties. Their eigenfunctions, which are calculated exactly, exhibit a transition: for parameter values with classically stable solutions the eigenstates are normalizable while they cannot be normalized for parameter values with classically instable solutions. Similarly, the spectrum of quasi energies undergoes a specific transition. These observations remain valid qualitatively for arbitrary linear systems exhibiting classically parametric resonance such as the paradigm example of a frequency modulated pendulum described by Mathieu's equation.

Affiliated with

Also associated with

No associations

Rating

Quantum Parametric Resonance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum Parametric Resonance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Parametric Resonance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-194391