Quantum Walk and Quantum Rings. Effects of a Magnetic Field applied and construction of Quantum Walk by a Moire pattern

Quantum Rings have been simulated so far in many ways, but in this work a new aproximation is deemed. We use particles without angular momentum and several spectra, for different geometric settings, are gotten. These spectra depends on K, not on L. The application of a magnetic field is also analysed, and an Aharonov-Bohm kind of effect is observed. Some new math technique is introduced as well. We think that with this new approach the spectrum matrix can be treated in a distinct way, and in such a manner is how we get to handle the Moire pattern spectrum. Furthermore, we show that two electrons quantum walking by some kind of double concentric Quantum Rings and those very same electrons quantum walking by a Moire circunference could indeed have, if not for some parameters, the same spectrum. So they might somehow display similar behaviour and similar properties