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VishalSharma
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How are Hofstader's Butterfly and Landau Levels in 2-Dimesnions related to each other, if at all ?
Thanks for your help!atyy said:I googled your keywords and found http://online.kitp.ucsb.edu/online/colloq/kim1/
I'm currently writing a paper about Quantum Hall Effect, and I've run into these two concepts during my research. And as far as I am concerned, Landau level doesn't fully explain QHE and the "butterfly" is only remotely related. Quantum Hall effect is more of the result of mathematics than physics. The formulation of the resulting current in y direction under a weak electric filed in x direction, just so happens to consists of an integration that is mathematically proven to be an integer.VishalSharma said:Thanks for your help!
The Harper-Hofstader Model is a mathematical model that describes the behavior of electrons in a two-dimensional lattice structure under the influence of both a magnetic field and a periodic potential.
The Butterfly and Landau Levels are two distinct but interrelated phenomena that arise in the Harper-Hofstader Model. The Butterfly Levels refer to the fractal-like energy spectrum of the electrons, while the Landau Levels refer to the quantization of the electrons' motion in the presence of a magnetic field.
The Harper-Hofstader Model takes into account both the magnetic field and the periodic potential, while other models may only consider one or the other. This allows for a more complete understanding of the behavior of electrons in a lattice structure.
The Harper-Hofstader Model has been used to study various physical phenomena, such as the quantum Hall effect and superconductivity. It has also been applied in the design of electronic devices, such as quantum dots and topological insulators.
Current research is focused on exploring the behavior of electrons in more complex lattice structures, as well as extending the model to include interactions between electrons. There is also ongoing research on using the Harper-Hofstader Model to study other systems, such as cold atoms in optical lattices.