Geodesic
Numerical Simulation of the Ground-state of Elastic-periodic Chain of Atoms in Periodic Potential of Arbitrary Shape
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 3, pp. 279-282

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An elastic periodic chain of atoms in periodic potential has been considered. Numerical simulations revealed the existence of stepwise behavior of the ground state graph near the origin. Such behavior is not observed in the continuous medium approximation. The step height is equal to one-half the classical frequency.
Keywords: Frenkel–Kontorova model, periods incommensurate, discrete finite chain. 
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     author = {Boris S. Dobronets and Alexsandr N. Filonov},
     title = {Numerical {Simulation} of the {Ground-state} of {Elastic-periodic} {Chain} of {Atoms} in {Periodic} {Potential} of {Arbitrary} {Shape}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Boris S. Dobronets; Alexsandr N. Filonov. Numerical Simulation of the Ground-state of Elastic-periodic Chain of Atoms in Periodic Potential of Arbitrary Shape. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 3, pp. 279-282. http://geodesic.mathdoc.fr/item/JSFU_2013_6_3_a0/