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The random phase hypothesis for random Schr\"odinger operators on stripsMathematical Physics & Probability
|Speaker: ||Christian Sadel, UC Irvine|
|Location: ||2112 MSB|
|Start time: ||Thu, May 27 2010, 4:30PM|
Random Schr\"odinger operators on strips can be described by transfer matrices.
Considering their action on a certain compact flag manifold one can obtain formulas
for the Lyapunov exponents in terms of the invariant measure. For a perturbative
analysis we are multiplying the random disorder by a coupling constant $\lambda$.
The random phase hypothesis is a statement about the convergence of the invariant
measure on the flag manifold for $\lambda\to 0$. It states that the limit of the
invariant measures converges to a natural Haar measure. If for $\lambda=0$ the
transfer matrix has only elliptic channels we obtain convergence to a measure with
smooth density w.r.t. this Haar measure. For the Wegner L-orbital model we obtain
exactly the Haar measure.