English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We report an infinite number of orthonormal wave functions bases for thequantum problem of a free particle in presence of an applied external magneticfield. Each set of orthonormal wave functions (basis) is labeled by an integer$p$, which is the number of magnetic fluxons trapped in the unit cell. Thesebases are suitable to describe particles whose probability density is periodicand defines a lattice in position space. The present bases of orthonormal wavefunctions unveils fractional effects since the number of particles in the unitcell is independent of the number of trapped fluxons. For a single particleunder $p$ fluxes in the unit cell, and confined to the lowest Landau level, theprobability density vanishes in $p$ points, thus each zero is associated to afraction $1/p$ of the particle. Remarkably the case of $n+1$ filled Landaulevels, hence with a total of $N=(n+1)p$ fermions, $n$ being the highest filledLandau level, the density displays an egg-box pattern with $p^2$ maxima(minima) which means that a $(n+1)/p$ fraction of flux is associated to everyone of these maxima (minima). We also consider the case of particlesinteracting through the magnetic field energy created by their own motion andfind an attractive interaction among them in case they are confined to thelowest Landau level ($n=0$). The well-known de Haas-van Alphen oscillations areretrieved within the present orthonormal basis of wave functions thus providingevidence of its correctness.

Orthonormal wave functions for periodic fermionic states under an applied magnetic field