Title: Résonances Semiclassiques Engendrées par des Croisements de Trajectoires Classiques Show Chinese title

Title: 半经典共振由经典轨迹交叉产生

Abstract: We consider a $2\times2$ system of one-dimensional semiclassical Schr\"odinger operators with small interactions with respect to the semiclassical parameter $h$. We study the asymptotics in the semiclassical limit of the resonances near a non-trapping energy for both corresponding classical Hamiltonians. We show the existence of resonances of width $T^{-1}h\log(1/h)$, contrary to the scalar case, under the condition that two classical trajectories cross and compose a periodic trajectory with period $T$. omposent une trajectoire p\'eriodique de p\'eriode $T$. Show Chinese abstract

Abstract: 我们考虑一个一维半经典薛定谔算子的$2\times2$系统，其与半经典参数$h$的相互作用很小。我们研究了在非陷阱能量附近，对应经典哈密顿量的共振在半经典极限下的渐进行为。我们证明了在两个经典轨迹交叉并组成周期为$T$的周期轨迹的条件下，存在宽度为$T^{-1}h\log(1/h)$的共振，这与标量情况相反。组成一条周期为$T$的轨迹。