Zener tunneling and dissipation in small loops

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Abstract
Small and one-dimensional metallic loops, without leads, and only with elastic scattering, have been shown to have Josephson-like behavior, and should not exhibit a resistance, when excited by a time-dependent magnetic flux. Electrons in this loop behave like electrons in a superlattice whose potential variation, within a superlattice period, matches that found in the circuit around the ring. The earlier work neglected the Zener tunneling in this effective superlattice band structure. It is shown that transitions to higher-lying bands, arising from this Zener tunneling, can be undone, and represent energy storage, not dissipation.,