2-color QCD at finite density is interesting in the sense that itprovides an unique opportunity to compare various ideas at finitechemical potential with the lattice simulations. Also finite density2-color QCD may provide us a hint to understand physics of the colorsuperconductivity in 3-color QCD.

In this talk we report our recent study on the thermodynamics of 2-colorlattice QCD in the strong coupling limit defined on the lattice withstaggered fermions (*). Employing the $1/d$ expansion and the mean fieldapproximation, the effective free energy is obtained in a simple form interms of the chiral condensate $\sigma$ and the diquark condensate$\Delta$ with finite temperature $T$, chemical potential $\mu$ andcurrent quark mass $m$.

From this effective free energy we can derive various formulaeanalytically for the critical temperature, the critical chemicalpotentials and the quark number density $\rho$, which are useful to havephysical insight into the problem.

Also we studied numerically the interplay among the chiral condensate,the diquark condensate and the quark number density as functions of $T$,$\mu$ and $m$. The phase structure of strong coupling 2-color QCD isclarified in the $T$-$\mu$-$m$ space. Although our results are limitedin the strong coupling, the behavior of $\sigma$, $\Delta$, and $\rho$in the $T$-$\mu$-$m$ space has remarkable qualitative agreement withthe recent results of Monte-Carlo simulations. Since we do not have torely on any assumption of small $\mu$ nor small $m$ in our approach, thestrong coupling analysis presented here is complementary to the chiralperturbation theory and provides a useful guide to the future lattice2color-QCD simulations.