What's the cage size of an electron?

Start: 10/30/2013 - 4:15pm
End  : 10/30/2013 - 5:15pm


Chris Marx, California Institute of Technology


 The quantum Hall effect captures how the electrons of a crystal respond to an external magnetic field. Depending on the properties of the crystalline material, the magnetic field may enhance or reduce the movability of the electrons, thus making the crystal behave more like a metal or an insulator.
To describe this phenomenon mathematically, we will consider quasi-periodic Schrodinger operators: doubly-infinite band matrices with elements generated by irrational rotations on the circle. Insulator-like behavior amounts to exponentially decaying eigenvectors of such operators, representing electrons ``trapped'' in some finite region in the crystal.
In this talk we will derive criteria to detect presence or lack of such exponential decay thereby quantifying metal-insulator transitions.
The results presented in this talk are joint work with Juan Adame, a junior undergraduate student in Mathematics at Caltech.

Davidson Lecture Hall, Claremont McKenna College

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