Multicomponent dense electron gas as a model of Si MOSFET

We solve a 2D model of $N$-component dense electron gas in the limit $N\to \infty$ and in a range of the Coulomb interaction parameter: $N^{-3/2}\ll r_s\ll 1$. The quasiparticle interaction on the Fermi circle vanishes as $\hbar^2/Nm$. The ground state energy and the effective mass are found as series in powers of $r_s^{2/3}$. In the quantum Hall state on the lowest Landau level at integer filling: $1\ll\nu<N$, the charge activation energy gap and the exchange constant are: $\Delta=\log(r_s N^{3/2})\hbar\omega_H/\nu$ and $J=0.66 \hbar\omega_H/\nu$.