Some problems of low-dimensional physics

TL;DR

This paper addresses the limitations of traditional periodic boundary conditions in low-dimensional physics by proposing a self-consistent potential box model to accurately calculate Fermi and kinetic energies in confined systems, and derives conditions for effective dimensional reduction.

Contribution

It introduces a self-consistent potential box model for low-dimensional systems and derives conditions for when particles behave as effectively lower-dimensional.

Findings

Potential box model provides more logical calculations for confined particles.

Conditions for neglecting dimensions in low-dimensional systems are established.

The approach improves understanding of particle behavior in confined geometries.

Abstract

Fermi and kinetic energy are usually calculated in periodic boundary conditions model, which is not self-consistent for low-dimensional problems, where particles are confined. Thus for confined particles the potential box model was used self-consistently to calculate Fermi and kinetic energies in 3-, 2-, and 1-dimensional cases. This approach is much more logical and self-consistent. Then the conditions for neglecting dimensions, that is conditions under which the movement of particles in the box could be considered as 2- and 1- dimensional, were derived.