### Abstract

Original language | English |
---|---|

Pages (from-to) | 19 |

Number of pages | 11 |

Journal | Condensed Matter |

Volume | 3 |

Issue number | 2 |

DOIs | |

Publication status | Published - 13 Jun 2018 |

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### Cite this

*Condensed Matter*,

*3*(2), 19. https://doi.org/10.3390/condmat3020019

}

*Condensed Matter*, vol. 3, no. 2, pp. 19. https://doi.org/10.3390/condmat3020019

**Annealed Low Energy States in Frustrated Large Square Josephson Junction Arrays.** / Lankhorst, Martijn (Corresponding Author); Brinkman, Alexander ; Hilgenkamp, H.; Poccia, Nicola ; Golubov, Alexandre Avraamovitch.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Annealed Low Energy States in Frustrated Large Square Josephson Junction Arrays

AU - Lankhorst, Martijn

AU - Brinkman, Alexander

AU - Hilgenkamp, H.

AU - Poccia, Nicola

AU - Golubov, Alexandre Avraamovitch

PY - 2018/6/13

Y1 - 2018/6/13

N2 - Numerical simulations were done to find low energy states in frustrated large square Josephson Junction arrays in a perpendicular magnetic field using simulated annealing on the coupled RSJ model. These simulations were made possible by a new algorithm suitable for parallel gpu computing and reduced complexity. Free boundary conditions were used so that values of the frustration factor f that are incommensurate with the array size are permitted. The resulting energy as a function of f is continuous with logarithmic discontinuities in the derivative dE/df at rational frustration factors f=p/q with small q, substantiating the mathematical proof that this curve is continuous and further showing that the staircase state hypothesis is incorrect. The solution shows qualitative similarities with the lowest energy branch of the Hofstadter butterfly, which is a closely related problem. Furthermore, it is found that at the edge of an array there are either extra vortices or missing vortices depending the frustration factor, and the width of this region is independent of the array size.

AB - Numerical simulations were done to find low energy states in frustrated large square Josephson Junction arrays in a perpendicular magnetic field using simulated annealing on the coupled RSJ model. These simulations were made possible by a new algorithm suitable for parallel gpu computing and reduced complexity. Free boundary conditions were used so that values of the frustration factor f that are incommensurate with the array size are permitted. The resulting energy as a function of f is continuous with logarithmic discontinuities in the derivative dE/df at rational frustration factors f=p/q with small q, substantiating the mathematical proof that this curve is continuous and further showing that the staircase state hypothesis is incorrect. The solution shows qualitative similarities with the lowest energy branch of the Hofstadter butterfly, which is a closely related problem. Furthermore, it is found that at the edge of an array there are either extra vortices or missing vortices depending the frustration factor, and the width of this region is independent of the array size.

U2 - 10.3390/condmat3020019

DO - 10.3390/condmat3020019

M3 - Article

VL - 3

SP - 19

JO - Condensed Matter

JF - Condensed Matter

SN - 2410-3896

IS - 2

ER -