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

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

From this effective free energy we can derive various formulae analytically for the critical temperature, the critical chemical potentials and the quark number density $\rho$, which are useful to have physical 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 is clarified in the $T$-$\mu$-$m$ space. Although our results are limited in the strong coupling, the behavior of $\sigma$, $\Delta$, and $\rho$ in the $T$-$\mu$-$m$ space has remarkable qualitative agreement with the recent results of Monte-Carlo simulations. Since we do not have to rely on any assumption of small $\mu$ nor small $m$ in our approach, the strong coupling analysis presented here is complementary to the chiral perturbation theory and provides a useful guide to the future lattice 2color-QCD simulations.