Current, conduction, and localization in quantum many-body systems

A representation of current is presented which can account for ideal conduction and distinguish superconductors, superfluids, ideal, and non-ideal conductors. The idea of the scheme is that different current operators and transport weights can be constructed based on the number of charge carriers in basic units of conduction. Ideal conductors with basic units of $p$ charge carriers exhibit a flux quantization rule of $\Phi_B=nhc/(pe)$ (for example $p=2$ for BCS). Extension of the current operators to lattice systems is also presented. A full diagonalization calculation for an interacting model of spinless fermions of all the transport coefficients is carried out. It is shown that in a number of strongly correlated models ideal conduction involving the simultaneous motion of all charge carriers is possible.