We consider force-induced unzipping transition for a heterogeneous DNA model with a correlated base sequence. Both finite-range and long-range correlated situations are considered. It is shown that finite-range correlations increase stability of DNA with respect to the external unzipping force. Due to long-range correlations the number of unzipped base pairs displays two widely different scenarios depending on the details of the base sequence: either there is no unzipping phase transition at all, or the transition is realized via a sequence of jumps with magnitude comparable to the size of the system. Both scenarios are different from the behavior of the average number of unzipped base pairs (non-self-averaging). The results can be relevant for explaining the biological purpose of correlated structures in DNA.

The Faraday rotation angle Θ is calculated in a diffusive regime in a three dimensional disordered slab. It is shown that tan Θ is (i) an oscillating function of the magnetic field or the medium's internal properties, and (ii) proportional to the ratio of the inelastic mean free path l in to the mean free path l, that is to the average number of photon scatterings. The maximum rotation is achieved at frequencies when the photon's elastic mean free path is minimal. We have obtained the rotation angle of polar backscattered light taking into account the maximally crossed diagrams. The latter leads to an ellipticity in the backscattered wave that can serve as precursor of weak localization.The critical strength of magnetic field B c ∼ g c ∼ λ/l beyond which rotation in backscattered wave disappears. The traversal time of an electromagnetic wave through the slab is estimated in a diffusive regime. The disorder enhanced the traversal time by an additional factor l in /l, in comparison with a free light propagation time. Comparison with the experimental data is carried out.