Resonances Width in Crossed Electric and Magnetic Fields

TL;DR

This paper investigates how electric and magnetic fields affect the spectral properties of a charged particle in 2D, showing that electric field-induced resonances have at least Gaussian long lifetimes as the electric field diminishes.

Contribution

It introduces a method to analyze the lifetime of resonances in a 2D charged particle system under crossed fields, demonstrating Gaussian long lifetimes as electric field approaches zero.

Findings

Resonance lifetimes are at least Gaussian long as electric field tends to zero.

Method of complex translations effectively analyzes spectral properties.

Electric field influences the spectral resonance behavior.

Abstract

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.