Little-Parks oscillations are observed in a system of 110 series-connected aluminum rings 2 µm in diameter with the use of measuring currents from 10 nA to 1 µA. The measurements show that the amplitude and character of the oscillations are independent of the relation between the measuring current and the amplitude of the persistent current. By using asymmetric rings, it is demonstrated that the persistent current has clockwise or contra-clockwise direction. This means that the total current in one of the semi-rings may be directed against the electric field at measurement of the Little-Parks oscillations. The measurements at zero and low measuring current have revealed that the persistent current, like the conventional circulating current, causes a potential difference on the semi-rings with different cross sections in spite of the absence of the Faraday's voltage.

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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 obtained periodic magnetic-field dependencies of the critical current Ic+(Φ/Φ0), Ic−(Φ/Φ0), measured in opposite directions on asymmetric superconducting aluminum rings, allow to explain observed earlier quantum oscillations of a dc voltage as a result of alternating current rectification. It is found, that the high efficiency of the rectification of both individual rings and ring systems is connected to a hysteresis of the current-voltage characteristics. The asymmetry of the currentvoltage characteristics providing the rectification effect is due to the relative shifts of the magnetic dependencies Ic−(Φ/Φ0) = Ic+(Φ/Φ0 + ∆φ) of the critical current measured in opposite directions. This shift means that position of Ic+(Φ/Φ0) and Ic−(Φ/Φ0) minimums does not correspond to n+0.5 magnetic flux quantum Φ0 which is in the direct contradiction with measurement results of the Little-Parks resistance oscillations. Despite of this contradiction the amplitude of the critical current anisotropy oscillations Ic,an(Φ/Φ0) = Ic+(Φ/Φ0) − Ic−(Φ/Φ0) and its variations with temperature correspond to expected amplitude of the persistent current oscillations and to its variations with temperature.

A dc voltage changed periodically with magnetic field is observed on segments of asymmetric aluminum loop without any external dc current at temperatures corresponded to superconducting transition. According to this experimental result a segment of the loop is a dc power source. A possibility of a persistent voltage on segments of an inhomogeneous normal metal mesoscopic loop follows from this result.