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Two-dimensional electron systems beyond the diffusive regime

Transport properties of disordered electron system can be characterized by the conductance, Lyapunov exponent, or level spacing. Two additional parameters, $K_{11}$ and $γ$ were introduced recently which measure the non-homogeneity of the spatial distribution of the electron inside the sample. % [Phys. Rev. Lett. {\bf 82}, 4272 (1999)]. For the orthogonal, unitary and symplectic two dimensional disordered models, we investigate numerically the system size dependence of these parameters in the diffusive and localized regime. Obtained size and disorder dependence of $K_{11}$ and $γ$ is in agreement with with single parameter transport theory. In the localized regime, $γ\to 0$ independently on the physical symmetry of the model. In the diffusive regime, $γ$ equals to the symmetry parameter $β$. For the symplectic model we analyze the size dependence of $γ$ in the critical region of the metal-insulator transition and found the non-universal critical value $γ_c$.