Note on a Floquet/Bloch-band fusion phenomenon in scattering by truncated periodic multi-well potentials

TL;DR

This paper investigates a quantum scattering phenomenon in a multi-well potential, revealing a band fusion process where transmission peaks combine as gaps close, leading to a single broader transmission band.

Contribution

It introduces the concept of band fusion in quantum scattering, showing how transmission bands merge as gaps vanish in a multi-well potential system.

Findings

Identification of multiple transmission bands with N-1 peaks

Discovery of band fusion resulting in 2N-1 peaks

Observation of gap collapse leading to a single broad band

Abstract

A transmission phenomenon for a quantal particle scattered through a multi-well potential in one dimension is observed by means of an amplitude-phase method. The potential model consists of $N$ identical potential cells, each containing a symmetric well. Typical transmission bands contain $N-1$ possible energies of total transmission. It is found that certain band types contain $n$ energies of total transmission. A fusion phenomenon of this type of band with a typical neigboring band is also found. As the transmission gap between them collapse and disappear, a resulting fused single band is seen to contain $2N-1$ energy peaks of total transmission.