Quantum force in a superconductor

Abstract

In order to account for a contradiction of the Little-Parks experiment with Ohm's law and other fundamental laws, the thermal fluctuation is considered as a dynamic phenomenon and an extra force, called the quantum force, is introduced. A persistent current can exist at zero voltage and nonzero resistance because of the quantum force induced by the thermal fluctuation. Not only the persistent current but also a persistent voltage ͑a direct voltage in the equilibrium state͒ can exist in an inhomogeneous superconducting ring. The directions of the persistent current and the persistent voltage coincide in a ring segment with lower critical temperature and are opposite in other ring segments with higher T c . Consideration of a superconducting ring interrupted by Josephson junction shows a connection of the quantum force with a real mechanical force.

The Meissner effect puzzle and the quantum force in superconductor

“…The energy difference between permitted states ∆E n,n+1 ≈ I p,A Φ 0 ≈ 4 10 −21 J (5) at the real amplitude I p,A ≈ 2 µA of the persistent current of a real ring measured even near superconducting transition T ≈ 0.99T c ≈ 1.24 K [11] corresponds to the value ∆E n,n+1 /k B ≈ 300 K exceeding strongly the temperature of measurements T ≈ 1.24 K. According to (4) and (5) the persistent current and the spectrum discreteness diminish ∆E n,n+1 ≈ I p,A Φ 0 = Φ 0 q /mr(sn s ) −1 → 0 with pair density decrease 1/(sn s ) −1 → 0. Both the persistent current I p,A = q /2mr(sn s ) −1 and the energy difference ∆E n,n+1 equal zero when pair density is zero n s,A = 0 at least in a ring segment l A , Fig.1, because 1/(sn s ) −1 ≈ sln s,A n s,0 /(ln s,A + l A n s,0 − l A n s,A ) = 0.…”

“…Other question, which can puzzle any theorist, may be connected with possibilities to close the wave function Ψ GL = |Ψ GL | exp iϕ in a ring segment l A , Fig.1. The quantum theory predicts even a mechanical force, which can be measured, at a mechanical closing of the superconducting ring, see the end of [4]. The force should act because of the energy difference between superconducting states of the ring with zero and non-zero velocity of pairs [4].…”

“…Here h and w are the height and width of ring or cylinder wall; (sn s ) −1 = l −1 l dl(sn s ) −1 is the value determining the amplitude I p,A = q /2mr(sn s ) −1 of the persistent current in a ring with section s and density n s which may vary along the ring circumference l [4].…”

“…The azimuthal quantum force, which J.E. Hirsch mentioned, was introduced [4] in order to explain some paradoxical phenomena observed in superconducting rings but it can not explain the Meissner effect. Its essence and the region of application will be clarified in the present paper.…”

“…J.E. Hirsch expresses fairly astonishment [2] that this puzzle is ignored: "Strangely, the question of what is the 'force' propelling the mobile charge carriers and the ions in the superconductor to move in direction opposite to the electromagnetic force in the Meissner effect was essentially never raised nor answered to my knowledge, except for the following instances: [3] (H. London states: "The generation of current in the part which becomes supraconductive takes place without any assistance of an electrical field and is only due to forces which come from the decrease of the free energy caused by the phase transformation," but does not discuss the nature of these forces), [4] (A.V. Nikulov introduces a "quantum force" to explain the Little-Parks effect in superconductors and proposes that it also explains the Meissner effect)".…”