Off-Diagonal Long-Range Order and Persistent Currents in a Hollow Cylinder

Some properties of the reduced density matrix are considered in their general relation to the current produced by a system of charged particles in a thin-walled long cylinder. The common connection of persistent currents and off-diagonal long-range order to the velocity distribution function will be particularly stressed. Essential features of this function, characteristic for the superconducting state, are discussed and exemplified by applying an analogous procedure to the case of boson and fermion systems.