Geometric effects of a quarter of corrugated torus

TL;DR

This paper investigates how corrugation affects the quantum properties of a particle on a quarter torus, revealing altered geometric potentials, modified tunneling behavior, and potential applications in particle filtering.

Contribution

It provides the effective Schrödinger equation for a particle on a corrugated torus and analyzes how corrugation influences geometric potential and quantum transport.

Findings

Corrugation significantly alters the geometric potential on the torus.

Resonant tunneling peaks are broadened and merged due to corrugation.

The quarter corrugated torus can act as a particle filter based on energy.

Abstract

In the spirit of the thin-layer quantization scheme, we give the effective Shr\"{o}dinger equation for a particle confined to a corrugated torus, in which the geometric potential is substantially changed by corrugation. We find the attractive wells reconstructed by the corrugation not being at identical depths, which is strikingly different from that of a corrugated nanotube, especially in the inner side of the torus. By numerically calculating the transmission probability, we find that the resonant tunneling peaks and the transmission gaps are merged and broadened by the corrugation of the inner side of torus. These results show that the quarter corrugated torus can be used not only to connect two tubes with different radiuses in different directions, but also to filter the particles with particular incident~energies.