# Semiclassical study of shape resonances in the Stark effect

## TL;DR

This paper investigates the semiclassical behavior of Stark resonances using complex distortion and pseudodifferential calculus, establishing new estimates, Weyl law, and resonance expansion results for Stark Hamiltonians with non-analytic potentials.

## Contribution

It introduces a novel complex distortion method and functional pseudodifferential calculus to analyze Stark resonances across energy regions, advancing spectral analysis techniques.

## Key findings

- Proved non-trapping resolvent estimate using escape function method.
- Established Weyl law for Stark resonances.
- Derived resonance expansion of the propagator in the shape resonance model.

## Abstract

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.