Landau levels
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In quantum mechanics, the energies of cyclotron orbits of charged particles in a uniform magnetic field are quantized to discrete values, thus known as Landau levels. These levels are degenerate, with
Diagram of a cyclotron orbit of a particle with speed v, which is the classical trajectory of a charged particle (here positive charge) under a uniform magnetic field B. The Landau quantization refers to a quantum charged particle under a uniform magnetic field.
Hofstadter's butterfly
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In condensed matter physics, Hofstadter's butterfly is a graph of the spectral properties of non-interacting two-dimensional electrons in a perpendicular magnetic field in a lattice. The fractal, self
Landau levels
…tight binding energy spectrum of charged particles in a two dimensional infinite lattice is known to be self-similar and fractal, as demonstrated in Hofstadter's butterfly. For an integer ratio of the magnetic flux quantum and the magnetic flux through a lattice cell, one recovers the Landau levels for large integers. The…
Rendering of the butterfly by Hofstadter
Hofstadter's butterfly monochrome with axes en
Hofstadter 2002