Description of zero field steps on the potential energy surface of a Frenkel-Kontorova model for annular Josephson junction arrays

Quapp, Wolfgang; Bofill, Josep María

doi:10.1140/epjb/s10051-021-00115-w

Cited by 3 publications

(4 citation statements)

References 54 publications

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“…The difference between this potential and the exact value (7) does not exceed 1.5%. Potential (8) coincides with Frenkel-Kontorova potential up to the constant and linear transformation of coordinates…”

Section: 𝑈(𝑥′ 𝑧′mentioning

confidence: 70%

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Simulation of Epitaxial Film–Substrate Interaction Potential

2022

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The formation of the substrate surface potential based on the Lennard-Jones two-particle potential is investigated in this paper. A simple atom’s square lattice on the substrate surface is considered. The periodic potential of the substrate atoms is decomposed into a Fourier series. The amplitude ratio for different frequencies has been examined numerically. The substrate potential is approximated with high accuracy by the Frenkel–Kontorova potential at most parameter values. There is a field of parameters in which the term plays a significant role, with a period half as long as the period of the substrate atoms. The ground state of the monoatomic film is modeled on the substrate potential. The film may be in both crystalline and amorphous phases. The transition to the amorphous phase is associated with a change in the landscape of the substrate potential. There are introduced order parameters for structural phase transition in the thin film. When changing the parameters of the substrate, the order parameter experiences a jump when changing the phase of the film.

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Section: 𝑈(𝑥′ 𝑧′mentioning

confidence: 70%

“…The cosine function specifies the periodic substrate potential. This simple approximation reveals a wide variety of ground states for the system [4][5][6] and different waves in the atoms chain [7][8][9]. Solitons are of the greatest interest.…”

Section: Introductionmentioning

confidence: 95%

Simulation of Epitaxial Film–Substrate Interaction Potential

2022

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“…one can determine an integer M such that the chain of length L o covers up M troughs of the site potential. If λ is set correctly, the FK chain will fit into the M troughs forming a structure of a minimum with an average separation ã, with Equation (7). It holds independently of whether the numbers, L o , a o , ã, and a s , are rational or irrational.…”

Section: The Disappearence Of Incommensurabilitiesmentioning

confidence: 99%

“…The latter acts on the extracted subsystem by a potential. Of special interest may be electronic applications [2][3][4][5][6][7] for Wigner electrons or Josephson junctions. Further models are chargedensity wave conductors [8][9][10], charge transport in solids and on crystal surfaces [11], magnetic or ferro-and antiferromagnetic domain walls [12], magnetic superlattices [13], superconductivity [14,15], and vortex matter [16][17][18], to name a few.…”

Section: Introductionmentioning

confidence: 99%