UC San Diego

The quantum variance of an observable is a fundamental quantity in quantum mechanics and provides additional information other than the average itself. By examining the relation between the particle-current variance (δJ)2 and the average current J in both closed and open interacting fermionic systems, we show the emergence of a multivalued parametric curve between δJ and J due to interactions. As a closed system we consider the persistent current in a benzenelike lattice enclosing an effective magnetic flux and solve it by exact diagonalization. For the open system, the steady-state current flowing through a few lattice sites coupled to two particle reservoirs is investigated using a Lindblad equation. In both cases, interactions open a loop and change the topology of the corresponding δJ-J curve, showing that this effect is model independent. We finally discuss how the predicted phenomenon can be observed in ultracold atoms, thus offering an alternative way of probing the dynamics of many-body systems.