| A Random Matrix Model with explicitly broken U(N) invariance has been proposed and studied by means of effective-field theory. The effective action is constructed as a functional of the eigenvalue and eigenvector distributions. Using this effective action, the entire N-level distribution function is obtained in the mean-field approximation. This distribution was shown to be dependent on the choice of the basis. In the basis close to the diagonal, we show a smooth transition from the Gaussian Unitary Ensemble to the Poisson level distribution.;It was shown that the known analytical results on Density of States in the Impurity Band Tails in 1D problem can be reproduced by using the Random Matrix Theory approach combined with the recursion procedure.;It is shown that the Nernst coefficient in thin superconducting films is greatly enhanced (almost two orders of magnitude) due to the long-range vortex-vortex interactions. |
