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arXiv · 1912.10180

Resonance free domain for a system of Schr\"odinger operators with energy-level crossings

Kenta Higuchi
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Abstract

We consider a $2\times 2$ system of 1D semiclassical differential operators with two Schr\"odinger operators in the diagonal part and small interactions of order $h^\nu$ in the off-diagonal part, where $h$ is a semiclassical parameter and $\nu$ is a constant larger than $1/2$. We study the absence of resonance near a non-trapping energy for both Schr\"odinger operators in the presence of crossings of their potentials. The width of resonances is estimated from below by $Mh\log(1/h)$ and the coefficient $M$ is given in terms of the directed cycles of the generalized bicharacteristics induced by two Hamiltonians.

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Kenta Higuchi. 2019-12-21. Resonance free domain for a system of Schr\"odinger operators with energy-level crossings. https://doi.org/10.1142/s0129055x21500070

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