Superfluid density and stiffness of two-dimensional weakly interacting Boson system at zero temperature are calculated by one-loop renormalization group method using Holzmann-Baym formula. The result shows that when the contributions of high energy fluctuations dominate, both superfluid density and superfluid stiffness exhibit scaling behavior with respect to chemical potential. This result is qualitatively consistent with other researchers’result.

The properties of the single-particle distribution function in nanometer scale systems are rigorously studied. First, by using the variational principle, it is shown that this function is nonincreasing with respect to the single-particle energy levels at zero temperature. Then, by applying the Klein inequality, the same conclusion can be also established in the case of nonzero temperature. These results show clearly how the behavior of the single-particle distribution function is determined by the stability condition of the systems.