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We have measured a diamagnetic persistent current with flux periodicities of both h/e and h/2e in an array of thirty diffusive mesoscopic gold rings. At the lowest temperatures, the magnitudes of the currents per ring corresponding to the h/e- and h/2e-periodic responses are both comparable to the Thouless energy Ecħ/τD, where τD is the diffusion time. Taken in conjunction with earlier experiments, our results strongly challenge the conventional theories of persistent current. We consider a new approach associated with the saturation of the phase coherence time τϕ.

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