On the Exponential Decay of Magnetic Stark Resonances

TL;DR

This paper investigates how magnetic Stark resonant states decay over time, demonstrating that for large times, the decay is exponential with a rate determined by the eigenvalues of a specific non-selfadjoint operator, using complex translation methods.

Contribution

It provides a rigorous proof of exponential decay of magnetic Stark resonances and links decay rates to eigenvalues of a non-selfadjoint operator.

Findings

Resonant states decay exponentially at large times.

Decay rates are given by the imaginary parts of eigenvalues.

The proof utilizes complex translation techniques.

Abstract

We study the time decay of magnetic Stark resonant states. As our main result we prove that for sufficiently large time these states decay exponentially with the rate given by the imaginary parts of eigenvalues of certain non-selfadjoint operator. The proof is based on the method of complex translations.