  We consider the quantum dynamics of a particle in a weakly rough billiard.
The Floquet operator for reflection at the boundary is obtained as a unitary
band matrix. The resulting dynamics in angular momentum space can be treated in
the framework of the one-dimensional supersymmetric nonlinear sigma model. We
find analytically localization and the corresponding localization length
$\xi=D_{cl}$ where $D_{cl}$ is the classical diffusion constant due to boundary
scattering.

Condensed Matter