Fermi’s golden rule in tunneling models with quantum waveguides perturbed by Kato class measures
Year: 2024
Type: article
Abstract: In this paper we consider two dimensional quantum system with an infinite waveguide of the width d and a transversally invariant profile. Furthermore, we assume that at a distant ρ there is a perturbation defined by the Kato measure. We show that, under certain conditions, the resolvent of the Hamiltonian has the second sheet pole which reproduces the resonance at z ( ρ ) with the asymptotics z ( ρ ) = E β ; n + O ( exp ( − 2 | E β ; n | ρ ) ρ ) for ρ large and with the resonant energy E β ; n . Moreover, we show that the imaginary component of z ( ρ ) satisfies Fermi’s golden rule which we explicitly derive.
Authors: Sylwia Kondej, Kacper Ślipko
Institution: University of Zielona Góra
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403628548