(Received July 19, 1961)
The production and persistence of ring currents is investigated in a simple model, consisting of Bose-Einstein particles contained in a ring-shaped volume; the particles do not interact with each other, but interact with randomly distributed scattering centres, and carry a test charge through which they respond to external fields. Except for the Bose-Einstein statistics, this model is identical with the model of Kohn and Luttinger, for which a normal, non-zero resistivity has been shown to exist. Furthermore, our model is known to give a qualitatively correct insight into the Meissner effect in actual superconductors, where the “bosons” are attractively correlated electron pairs.
We are able to elucidate the mechanism by which ring currents are generated, and to prove that these ring currents, within our model, have infinite lifetime. There are similarities to the ideas of London, but also significant differences. Our model has no energy gap, and thus our explanation of persistent ring currents is qualitatively dissimilar to the two-fluid model of Bardeen, in which the energy gap is essential. The model is a simple example of a strictly non-ergodic system, and therefore has some interest for the foundations of non-equilibrium statistical mechanics.
The model predicts a new, experimentally observable effect: If the ring is maintained between the poles of the magnet, and cooled well below the transition temperature, small ring currents are generated during this cooling. The effect of these ring currents is to force the flux through the ring very close to an integral number of flux “units” introduced by London. This approximate quantization of flux is destroyed when the ring is moved out of the external field.
URL : http://ptp.ipap.jp/link?PTP/26/761/
DOI : 10.1143/PTP.26.761