Off-diagonal long-range order and superconducting particle density

Relations between the existence of ODLRO in the reduced density matrix ρn (for all n ≥ 1) and that of superconducting currents in a hollow cylinder is discussed. Some concrete behaviours of ρn, including the power lay decaying behaviour, in the coordinate space representation are considered and the corresponding effective superconducting particle densities are given. Some restraint conditions caused by the existence of the ODLRO (including quasi-ODLRO) have been found and discussions on the minimum unit of flux quantization are also included. (author). 3 refs