N-electron train effect on the enhancement of persistent current

We describe a train effect which may exist in small metallic and semiconductor rings. It is associated with the cooperative motion of a “train” of N electrons on the ring. It may be related to the long-standing problem of the persistent current enhancement. The train arises via an excitation or a back flow of spin waves or of interchannel charge density sound modes in a multichannel ring. Disorder has little influence on the “train” current. We calculated the persisent current for the Hubbard model by the Bethe ansatz. The fractional {M}/{N} periodicities of the persistent current serve as an indication of the electron “train”, where M is the number of spin-up electrons or electrons in a single channel.