Fluctuations in a mesoscopic superconducting ring: resonant behavior of conductivity and specific heat in two mode critical regime

The critical fluctuations in a mesoscopic superconducting ring are studied within the Ginzburg-Landau approach. The nonlocal conductivity as well as the specific heat are calculated as functions of the magnetic flux $\mathrm{\Phi }$ through the ring. At $\mathrm{\Phi }={\mathrm{\Phi }}_0\mathrm{/}2$ two low-energy eigenstates become degenerate and near this point the behavior of fluctuations-dependent quantities change dramatically: both the zero Fourier component ${\sigma }_0$ of the fluctuation conductivity and the specific heat become non-monotonic functions of $\mathrm{\mid }\mathrm{\Phi }-{\mathrm{\Phi }}_0\mathrm{/}2\mathrm{\mid }$ with rather special resonant structure.