Many-body multi-valuedness of particle-current variance in closed and open cold-atom systems

TL;DR

This paper reveals that interactions in many-body fermionic systems cause the particle-current variance and average current to form multi-valued Lissajous curves, providing new insights into quantum fluctuations in closed and open cold-atom systems.

Contribution

It demonstrates the emergence of multi-valued Lissajous curves between current variance and average current due to interactions, in both closed and open fermionic systems, independent of specific models.

Findings

Interactions induce multi-valued Lissajous curves between current and variance.

The effect is observed in both closed and open systems.

Phenomena can be experimentally observed in ultracold atom setups.

Abstract

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