2026/07/28 by Christos Mystilidis, Christos Tserkezis, George Fikioris
Physics and Astronomy · #cond-mat.other
We explore the similarities and differences between the Gibbs phenomenon in partial Fourier representations of discontinuous signals and Friedel oscillations in the electron density of a solid near an anomaly. Inspired by the apparent similarities of the two phenomena, we perform a detailed exploration of both from the viewpoint of an engineer being introduced to a concept from solid-state physics. Focusing on the density of an one-dimensional electronic gas confined by a square potential, we show that, despite the similarities, Friedel oscillations cannot be attributed to the inability of a partial Fourier series to describe a discontinuity. Nevertheless, the two phenomena do exhibit similarities, which can be exploited to develop intuition. By adopting an educational style, we hope to establish some common language between electrical engineers and condensed-matter physicists, hoping that this can further inspire the two communities to seek intuition and further comprehension within neighbouring but different disciplines.