Effect of a Coulombic dot-lead coupling on the dynamics of a quantum dot

We investigate the effect of a Coulombic coupling on the dynamics of a quantum dot coupled to leads. Two cases are studied: a dot coupled to a Luttinger liquid and a dot coupled to a three-dimensional metallic lead. The leading divergences arising from the long-ranged Coulomb interaction are found to cancel, resulting in a slow decay of electronic correlations, controlled by subleading divergences. Explicit results are given for the short-time dynamics.