Finite Drude weight for 1D low temperature conductors

We apply well established finite temperature Quantum Monte Carlo techniques to one dimensional Bose systems with soft and hardcore constraint, as well as to spinless fermion systems. We give clear and robust numerical evidence that, as expected, no superfluid density for Bosons or Meissner fraction for fermions. is possible at {\em any} non zero temperature in one dimensional interacting Bose or fermi lattice models, whereas a finite Drude weight is generally observed in gapless systems, in partial disagreement to previous expectations.