Semiclassical behavior of Stark resonances is studied. The complex distortion outside a cone is introduced to study resonances in any energy region for the Stark Hamiltonians with non-globally analytic potentials. The non-trapping resolvent estimate is proved by the escape function method. The Weyl law and the resonance expansion of the propagator are proved in the shape resonance model. To prove the resonance expansion theorem, the functional pseudodifferential calculus in the Stark effect is established, which is also useful in the study of the spectral shift function.

中文翻译：

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斯塔克效应中形状共振的半经典研究

研究了斯塔克共振的半经典行为。引入圆锥外的复杂变形来研究具有非全局解析势的斯塔克哈密顿量在任何能量区域的共振。非捕获解析解估计由逃逸函数方法证明。在形状共振模型中证明了外尔定律和传播子的共振扩展。为了证明共振展开定理，建立了斯塔克效应中的泛函赝微分，这对于谱移函数的研究也很有用。