Research PaperNo Access

Resonance free domain for a system of Schrödinger operators with energy-level crossings

Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu, 525-8577, Japan

E-mail Address: ra0039vv@ed.ritsumei.ac.jp

https://doi.org/10.1142/S0129055X21500070Cited by:4 (Source: Crossref)

Abstract

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

Keywords:

AMSC: 35P15, 35C20, 35S99, 47A75

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