Fractional Moment Estimates for Random Unitary Operators

Details Fractional Moment Estimates for Random Unitary Operators Fractional Moment Estimates for Random Unitary Operators

2004-11-21

arxiv.org/abs/math-ph/0411068v1

Physics

Mathematical Physics

Scientific paper

10.1007/s11005-005-3256-8

We consider unitary analogs of $d-$dimensional Anderson models on $l^2(\Z^d)$ defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The operator $S$ is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman-Molchanov to get exponential estimates on fractional moments of the matrix elements of $U_\omega(U_\omega -z)^{-1}$, provided the distribution of phases is absolutely continuous and the parameters correspond to small off-diagonal elements of $S$. Such estimates imply almost sure localization for $U_\omega$.

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