  An energy eigenfunction in a classically chaotic system is known to have
spatial correlations which (in the limit of small $\hbar$) are governed by a
microcanonical distribution in the classical phase space. This result is valid,
however, only over coordinate distances which are small compared to any
relevant classical distance scales (such as the cyclotron radius for a charged
particle in a magnetic field). We derive a modified formula for the correlation
function in the regime of large separation. This then permits a complete
description, over all length scales, of the statistical properties of chaotic
eigenfunctions in the $\hbar\to 0$ limit. Applications to quantum dots are
briefly discussed.
