  A mesoscopic system of cylindrical geometry made of a metal or a
semiconductor is shown to exhibit features of a quantum coherent state. It is
shown that magnetostatic interaction can play an important role in mesoscopic
systems leading to an ordered ground state. The temperature $T^{*}$ below the
system exhibits long-range order is determined. The self-consistent mean field
approximation of the magnetostatic interaction is performed giving the
effective Hamiltonian from which the self-sustaining currents can be obtained.
  The relation of quantum coherent state in mesoscopic cylinders to other
coherent systems like superconductors is discussed.
