  Dynamical conductivity in a disordered one-dimensional model of interacting
fermions is studied numerically at high temperatures and in the
weak-interaction regime in order to find a signature of many-body localization
and vanishing d.c. transport coefficients. On the contrary, we find in the
regime of moderately strong local disorder that the d.c. conductivity sigma0
scales linearly with the interaction strength while being exponentially
dependent on the disorder. According to the behavior of the charge stiffness
evaluated at the fixed number of particles, the absence of the many-body
localization seems related to an increase of the effective localization length
with the interaction.

Strongly Correlated Electrons