The single-particle states of helium within a bundle of carbon nanotubes can range from nearly free-particle dispersion to localization, even within a single bundle. At intermediate effective masses, the corrugation in the external potential can be comparable to the intrasite He-He hard-core interaction. This results in a commensurate/incommensurate transition, where the mobility of the doubly occupied domain-wall solitons at high density greatly exceeds the corresponding hole mobility below the transition.
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Boninsegni et al. (2001) studied this question.
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