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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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/

[1] V. L. Pokrovsky, A. L. Talap, “Phase transitions and vibrational spectra of nearly commensurate structures”, JETP, 75:9 (1978), 1151

[2] A. Filonov, “Development of the Hooke model”, Electronny Zhurnal “Issledovaniya v Rossii”, 22 (2008), 261–270 (in Russian) http://zhurnal.ape.relarn.ru/articles/2008/022.pdf

[3] A. Filonov, B. S. Dobronets, L. I. Kveglis, “The nature of the Portevin–Le Chatelier effect”, Electronny Zhurnal “Issledovaniya v Rossii”, 44 (2008), 511–517 (in Russian) http://zhurnal.ape.relarn.ru/articles/2008/044.pdf

[4] A. N. Filonov, “The ground state of $d$-dimensional elastic crystal in $d$-dimensional periodic potential with incommensurate crystal lattice periods and capacity”, JETP Lett., 57:9 (2012), 576–579

[5] A. Filonov, Exactly solvable models with applications, LAP LAMBERT Academic Publishing, 2012 (in Russian)

[6] L. D. Landau, E. M. Lifshitz, Theoretical Physics, v. 1, Mechanics, Nauka, M., 1973, in Russian pp. | MR

[7] L. D. Landau, E. M. Lifshitz, Theoretical Physics, v. 3, Quantum Mechanics, Nauka, M., 1974 (in Russian) | MR