UPPER-BOUNDS ON THE SUPERFLUID STIFFNESS OF DISORDERED-SYSTEMS

We derive several upper bounds for the superfluid stiffness D-s for Bo se and Fermi systems in terms of expectation values of local operators using linear response theory and variational methods. These give insi ght into the nontrivial dependence of D-s on parameters such as disord er and interaction in systems with broken continuous translational inv ariance. Our best variational bound for disordered systems is obtained by allowing the phase twist applied at the boundary to be distributed inhomogeneously within the system. Path integral quantum Monte Carlo simulations are used to quantitatively compare the bounds and D-s for disordered interacting Bose systems.