Eur. Phys. J. B 10, 563-571 (1999)
https://doi.org/10.1007/s100510050887

Resonance and non-recurrent rotationally ordered configuration in Frenkel-Kontorova models

¹ Institute of Physics, Academia Sinica, Taipei, Taiwan 115, ROC
² National Center for Theoretical Sciences, PO Box 2-131, Hsinchu, Taiwan 300, ROC

Corresponding author: ^a wjtzeng@phys.nthu.edu.tw

Received: 14 October 1998
Published online: 15 August 1999

Abstract

We demonstrate, with a class of exactly solvable Frenkel-Kontorova models, the emergence of the non-recurrent rotationally ordered configurations whenever certain resonance conditions are satisfied among the openings in the hull function in both the commensurate and the incommensurate cases. If one insists on depicting them with hull functions, suitably defined extended numbers must be employed. The defect-mediated transition in the incommensurate case is also discussed.