Ground state of the Frenkel–Kontorova model with a globally deformable substrate potential

2020 ◽  
Vol 406 ◽  
pp. 132298
Author(s):  
Andreas A. Buchheit ◽  
Sergej Rjasanow
Keyword(s):  
Ground State ◽  
Substrate Potential ◽  
Kontorova Model

The ground state of the Frenkel–Kontorova model

2016 ◽  
Vol 58 (9) ◽  
pp. 1834-1845
Author(s):  
A. Yu. Babushkin ◽  
A. K. Abkaryan ◽  
B. S. Dobronets ◽  
V. S. Krasikov ◽  
A. N. Filonov
Keyword(s):  
Ground State ◽  
Kontorova Model

On the ground state of commensurate overlayer lattices in a weak substrate potential

1989 ◽  
Vol 220 (1) ◽  
pp. A467-A468
Author(s):  
I. Lyuksyutov ◽  
E. Bauer
Keyword(s):  
Ground State ◽  
Substrate Potential

On the ground state of commensurate overlayer lattices in a weak substrate potential

1989 ◽  
Vol 220 (1) ◽  
pp. 29-42 ◽  
Author(s):  
I. Lyuksyutov ◽  
E. Bauer
Keyword(s):  
Ground State ◽  
Substrate Potential

Influence of the deformable substrate potential on Shapiro steps in the incommensurate structure

2014 ◽  
Vol 28 (28) ◽  
pp. 1450225
Author(s):  
Zhi-Gang Shao ◽  
Jia-Yu Li ◽  
Cang-Long Wang ◽  
Lei Yang
Keyword(s):  
Shape Parameter ◽  
Amplitude Dependence ◽  
Standard Potential ◽  
Shapiro Steps ◽  
Substrate Potential ◽  
Threshold Force ◽  
Incommensurate Structure ◽  
Kontorova Model

Influence of the deformable substrate potential on Shapiro steps is investigated in the overdamped Frenkel–Kontorova model with incommensurate structure. Both the number and size of Shapiro steps are strongly affected by the deformation of substrate potential. As substrate potential gets deformed, the oscillation of Shapiro steps reduces and the periodicity of oscillation significantly changes. For some value of shape parameter r, the odd and even maxima oscillation forms of harmonic steps still maintain the Bessel-like form. Compared with those in standard potential, the amplitude dependence of harmonic step exhibits obvious difference. The dynamical DC threshold force correspondingly increases with rising the value of r.

COMMENSURABILITY EFFECTS ON DIFFUSION PROCESS IN STEPPED STRUCTURES

2011 ◽  
Vol 25 (21) ◽  
pp. 1749-1760 ◽  
Author(s):  
Y. LACHTIOUI ◽  
M. MAZROUI ◽  
Y. BOUGHALEB
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Process ◽  
Ground State ◽  
Nearest Neighbor ◽  
Diffusion Rate ◽  
Dimensional System ◽  
One Dimensional ◽  
Substrate Potential ◽  
Numerical Studies

This study deals with the investigation of diffusion process of one-dimensional system with steps for adsorbates interacting via the nearest-neighbor harmonic forces. The results are obtained from numerical studies, utilizing the method of stochastic Langevin dynamics. To study commensurability effects and the role of steps in the behavior of the diffusing particles, we have computed the diffusion coefficient for large concentrations and several interaction strengths. Our numerical results show that the diffusive behavior is reduced for commensurate structure case when the ground state has only one particle per one period of the substrate potential and enhanced for incommensurate density. Furthermore, the dynamic is qualitatively similar to that obtained in the case of no steps but with a clear reduction of the diffusion rate. Implications of these findings are discussed.

Coherent structures in the ground state of the quantum Frenkel-Kontorova model

1994 ◽  
Vol 49 (12) ◽  
pp. 8212-8226 ◽  
Author(s):  
Gennady P. Berman ◽  
Evgeny N. Bulgakov ◽  
David K. Campbell
Keyword(s):  
Coherent Structures ◽  
Ground State ◽  
Kontorova Model

scholarly journals Exact ground state of the Frenkel-Kontorova model with repeated parabolic potential. I. Basic results

1997 ◽  
Vol 56 (14) ◽  
pp. 8623-8630 ◽  
Author(s):  
R. B. Griffiths ◽  
H. J. Schellnhuber ◽  
H. Urbschat
Keyword(s):  
Ground State ◽  
Parabolic Potential ◽  
Exact Ground State ◽  
Kontorova Model
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