Gaussian decay of Harmonic Oscillators and related models

Biagio Cassano; Luca Fanelli

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arXiv · 1603.06738

Gaussian decay of Harmonic Oscillators and related models

Biagio Cassano·Luca Fanelli

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Abstract

We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can produce solutions to the evolutionary Schr\"odinger flows associated to the Hamiltonians, with a stronger Gaussian decay at two distinct times. We then characterize, in a quantitative way, the sharpest possible Gaussian decay of solutions as a function of the oscillation frequency or the strength of the field, depending on the Hamiltonian which is considered. This is connected to the Hardy's Uncertainty Principle for free Schr\"odinger evolutions.

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Biagio Cassano, Luca Fanelli. 2016-03-22. Gaussian decay of Harmonic Oscillators and related models. https://arxiv.org/abs/1603.06738

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