Level curvatures, spectral statistics and scaling for interacting particles

The mobility of two interacting particles in a random potential is studied, using the sensitivity of their levels to a change of boundary conditions. The delocalization in Hilbert space induced by the interaction of the two particle Pock states is shown to decrease the mobility in metals and to increase it in insulators. In contrast to the single particle case, the spectral rigidity is not directly related to the level curvature. Therefore, another curvature of topological origin is introduced, which defines the energy scale below which the spectrum has the universal Wigner-Dyson rigidity.