Ultra-Large Scale Simulations for Superconductor MgB2 Device toward Nuclear Application and Fundamental Issues in Nano-superconductivity and Atomic Fermi Gas Loaded on Optical Lattice

We performed large-scale numerical simulations on non-equilibrium superconducting dynamics after a neutron capture at the superconducting transition edge in MgB2 by solving the time-dependent Ginzburg-Landau equation coupled with the Maxwell and the heat diffusion equations. The simulations were executed under the current-biased condition in order to explain experimental results carried out in JRR-3, JAEA and the temperature and the current dependences of the experimentally observed signals were successfully reproduced. On the other hand, we investigated issues about microscopic matter-density inhomogeneities through the attractive Hubbard model with confinement potential, which is a model for nano-size domain of strongly-coupled superconductors and atomic Fermi gas loaded on an optical lattice. The calculations revealed that microscopic density inhomogeneities, whose characteristic variation length is the lattice constant, universally appear in the presence of strong attractive interaction and confinement potential breaking the translational symmetry. This type of inhomogeneity is easily observable for the optical lattice systems in atomic Fermi gases.