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On the numerical stability and transitional stages of time-dependent Ginzburg–Landau model of superconductivity

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  • Coskun, Erhan

Abstract

We consider Semi-Discretized Time-Dependent Ginzburg–Landau model of superconductivity(SDTDGL), a nonlinear system of ordinary differential equations, and at first numerically investigate stability of minimizers of Ginzburg–Landau free energy with respect to variations in initial conditions and show computationally that the system may lead to unstable minimizers for certain range of initial conditions via comparative results of several high-order ODE solvers of MATLAB. In particular, we observe that MATLAB’s explicit solvers implemented with a vectorized code are very effective for obtaining equilibrium state and that all the solvers lead to same geometric alignment of vortices in a mixed state through indistinguishable GL energy dependence of time variable. Finally, we show that temporal evolution of a mixed state in zero-field cooling can be classified as of five substages based on qualitative properties of condensation, kinetic and field energy components of Ginzburg–Landau Energy functional.

Suggested Citation

  • Coskun, Erhan, 2023. "On the numerical stability and transitional stages of time-dependent Ginzburg–Landau model of superconductivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    • Handle: RePEc:eee:phsmap:v:626:y:2023:i:c:s0378437123005915
    DOI: 10.1016/j.physa.2023.129036
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    1. Coskun, Erhan, 2021. "On the properties of a single vortex solution of Ginzburg–Landau model of superconductivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
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