Non-local tuning of quantum current fluctuations in multi-connected lattices with and without external reservoirs

Fluctuations arising from non-commutative operators in Heisenberg's uncertainty relation are fundamental in quantum mechanics. The current operator J_i,i+1 measures current between two lattice sites and does not commute with the interconnected current operator J_i+1,i+2. This means the current fluctuations are correlated and proportional to J_i,i+2. Quantum fluctuations of current are affected by the tunneling strength between the conjoining next-nearest-neighbor lattice sites. Open system and closed system methods are used to determine how the tunneling coefficient affects fluctuations for non-interacting and interacting fermions. Investigations illustrate a pure quantum current effect since the wave nature of quantum particles leads to non-local correlations.