DIRT SOFTENS SOAP - ANOMALOUS ELASTICITY OF DISORDERED SMECTICS

We show that a smectic in a disordered medium (e.g., aerogel) exhibits anomalous elasticity, with the compression modulus B(k) vanishing and the bend modulus K(k) diverging as k --> 0. In addition, the effectiv e disorder develops long ranged correlations. These divergences are mu ch stronger than those driven by thermal fluctuations in pure smectics , and are controlled by a zero temperature glassy fixed point, which w e study in an epsilon = 5 - d expansion. We discuss the experimental i mplications of these theoretical predictions.