Escape behaviour of a quantum particle in a loop coupled to a lead

TL;DR

This paper studies how a quantum particle escapes from a loop with magnetic flux when connected to a lead, analyzing the probability of the particle remaining in the loop over time.

Contribution

It provides a detailed analysis of the escape dynamics of a quantum particle in a magnetic flux loop coupled to a lead, considering initial confinement and coupling effects.

Findings

Derived expressions for nonescape probability over time

Identified influence of magnetic flux on escape behavior

Quantified the effect of coupling strength on particle retention

Abstract

We consider a one-dimensional loop of circumference $L$ crossed by a constant magnetic flux $\Phi$ and connected to an infinite lead with coupling parameter $\epsilon$. Assuming that the initial state $\psi_0$ of the particle is confined inside the loop and evolves freely, we analyse the time evolution of the nonescape probability $P(\psi_0,L,\Phi,\epsilon,t)$, which is the probability that the particle will still be inside the loop at some later time $t$.