Schrödinger operators

Spectrum of magnetic operator Determining the spectral type of discrete Schroedinger operators related to lattice gauge fields is open in many examples. Such operators exist because some ergodic cohomology groups are trivial. An example of this class of operators is obtained, when the magnetic flux on the plaquette are independent, identically distributed random variables and where the lattice gauge fields are in general not independent random variables.

An example, where the spectral properties are already not known is a two dimensional lattice with a IID magnetic field with uniform distribution on U(1). Experiments indicate that there are no eigenvalues in this case.

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