Quantum Force in Superconductor
  Transitions between states with continuous (called as classical state) and discrete (called as quantum state) spectrum of permitted momentum values is considered. The persistent current can exist along the ring circumference in the quantum state in contrast to the classical state. Therefore the average momentum can changes at the considered transitions. In order to describe the reiterated switching into and out the quantum state an additional term is introduced in the classical Boltzmann transport equation. The force inducing the momentum change at the appearance of the persistent current is called as quantum force. It is shown that dc potential difference is induced on ring segments by the reiterated switching if the dissipation force is not homogeneous along the ring circumference. The closing of the superconducting state in the ring is considered as real example of the transition from classical to quantum state 
A.V.Nikulov