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Admittance of a long diffusive SNS junction

The dynamical properties of hybrid normal metal/superconductor structures have recently come into research focus both experimentally and theoretically. Recent experimental studies of the coherent admittance $% Y(ω)$ of SNS rings as function of the phase difference $ϕ_{0}$ are still not fully understood. Here we concentrate on the linear response regime, calculating $Y(ω)$ by solving Usadel equations, linearised in electric field. Although partially reproducing previously known results, we find qualitatively different behaviour in the collisionless regime of $τ_{in}^{-1}\ll ω\lesssim E_{Th}$ and high temperature $T\gg E_{Th}$ and low temperature $T\lesssim E_{Th}$ near the minigap closing $ϕ_{0}\sim π$. We find that the dissipative part $\mbox{Re}Y(ω)$ peaks when the minigap closes (at a phase difference of $π$) even at high temperatures, when the equilibrium supercurrent is fully suppressed.