Anomalous Threshold Laws in Quantum Sticking

TL;DR

This paper investigates deviations from the universal low-energy threshold law for quantum sticking, revealing anomalous laws caused by a soft gap in the density of states, using integral equation theory.

Contribution

It derives conditions for anomalous threshold laws in quantum sticking, extending the understanding beyond the universal linear behavior at low energies.

Findings

Anomalous threshold laws where sticking probability scales as $k^{1+eta}$ with $eta > 0$.

Zero-energy resonance leads to deviations from the universal threshold law.

Soft gaps in the density of states cause these anomalous behaviors.

Abstract

It has been stated that for a short-ranged surface interaction, the probability of a low-energy particle sticking to a surface always vanishes as $s\sim k$ with $k\to 0$ where $k=\sqrt{E}$. Deviations from this so-called universal threshold law are derived using a linear model of particle-surface scattering. The Fredholm theory of integral equations is used to find the global conditions necessary for a convergent solution. The exceptional case of a zero-energy resonance is considered in detail. Anomalous threshold laws, where $s\sim k^{1+\alpha}, \alpha > 0$ as $k\to 0$, are shown to arise from a soft gap in the weighted density of states of excitations; $\alpha$ is determined by the behavior of the weighted density of states near the binding energy.