On the controllability of transitions between equilibrium states in small inductively coupled arrays of Josephson junctions: A computational approach

Roland GLOWINSKI, Jorge López*, Héctor Juárez, Yehuda Braiman

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)

Abstract

In this article, we investigate computationally some controllability properties of a physical system consisting of three inductively coupled Josephson junctions. This system is modeled by nonlinear ordinary differential equations. A particular attention is given to the optimal control of the transition between equilibrium states, possibly unstable. After defining the control problem cost function, we use a perturbation analysis to compute its differential and formulate an optimality system. After appropriate time discretization of the control problem, we use a conjugate gradient algorithm to solve the discrete analogue of the above optimality system. The methodology we briefly described above has been applied successfully to the current pulse driven transition between two stable equilibrium states. This type of transitions was used in [1–5], to study Read/Write cryogenic memory cell operations based on the dynamics of small Josephson junction arrays. In order to show the robustness of our control-based approach we apply it also to the transitions from a stable equilibrium state to an unstable one.

Original languageEnglish
Article number109023
JournalJournal of Computational Physics
Volume403
DOIs
Publication statusPublished - 15 Feb 2020

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Conjugate gradient algorithms
  • Cryogenic memory
  • Josephson junction
  • Memory operators
  • Optimal control

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