Instability Zones in the Dynamics of a Quantum Mechanical Quasiperiodic Parametric Oscillator

TL;DR

This paper investigates the instability zones in a quantum quasiperiodic parametric oscillator, revealing that the zones for mean position, variance, and energy are identical at the strongest resonance, regardless of the modulation type.

Contribution

It demonstrates that the instability zones for quasiperiodic and periodic modulations are identical at the strongest resonance, extending understanding of quantum oscillator dynamics.

Findings

Instability zones for mean position and variance are identical in quasiperiodic oscillators.

The zones are the same for quasiperiodic and periodic modulations at strongest resonance.

The result applies to the three-dimensional parameter space of quasiperiodic modulation.

Abstract

Quasi-periodically driven quantum parametric oscillators have been the subject of several recent investigations. Here we show that for such oscillators, the instability zones of the mean position and variance (alternatively the mean energy) for a time developing wave packet are identical for the strongest resonance in the three-dimensional parameter space of the quasi-periodic modulation as it is for the two-dimensional parameter space of the periodic modulations.