Interaction-induced multivaluedness and topological change between quantum current and its variance

The variance of a quantum observable has been an important quantity in quantum mechanics, and it can reveal additional information beyond the average. By analyzing the parametric curves of the quantum current versus its variance, we found a general change of topology due to the interactions . We consider a benzene-like lattice with fermions driven by a magnetic flux for the isolated system and a three-site lattice connected driven by two particle reservoirs for the open system. In both systems, there is a one-to-one correspondence between the current and its variance in absence of interactions. When the interactions are introduced, the parametric curves exhibit loop structures and show multivalued correspondence between the current and its variance. The phenomena could be realizable using available cold-atom technology.
Reference: arXiv: 1805.06443.