# Maximizing Time Delays for Toy Models of Quantum Scattering

## TL;DR

This paper models quantum scattering using toy systems of harmonic oscillators to analyze how coupling strengths influence time delays, revealing potential for arbitrarily large delays due to interference effects.

## Contribution

Introduces a simplified oscillator model to study quantum scattering time delays and explores how coupling variations affect these delays, including the possibility of arbitrarily large delays.

## Key findings

- Small wavenumber wavepackets exhibit a calculable time delay based on coupling strengths.
- For a single-site cluster, time delays have a minimum and maximum; for two sites, delays can become arbitrarily large.
- Large delays are likely caused by interference within the target region.

## Abstract

We model a particle entering a complicated system from free space using an infinite chain of simple harmonic oscillators coupled to a finite, $n$-site cluster. For a particle wavepacket with small wavenumber, an expression for the time delay in terms of the coupling strengths of the cluster is found. When the coupling strengths are varied, a minimum and maximum time delay can be found for $n=1$. When $n=2$, we can obtain seemingly arbitrarily large time delays. In both cases, the time delays share similarities with the time delays for the scattering from an analogous quantum well target. We conclude that this could mean that large time delays are caused by interference within the wavefunction in the target's region of space.