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Coherent reaction of Fermi superfluid on correlated disorder

Motivated by the disparity between the experimentally observed properties of superfluid 3He in aerogel and predictions of the Abrikosov and Gorkov theory of superconducting alloys we consider effect of correlated pair-breaking impurities on the temperature dependence of the square of magnitude of the average order parameter and related thermodynamic properties of a Fermi superfluid. We show that the correlations, increasing the spectral density of the fluctuations with small wave vectors increase the transition temperature and enhance a temperature region below Tc where fluctuations of the order parameter dominate. Outside of this region we treat effect of impurities as a perturbation and express corrections to thermodynamic properties in terms of the structure factor of impurities. Assuming a simple model expression for correlation function of aerogel we find corrections to the temperature dependence of the NMR frequency shifts for A-like and B-like phases of 3He and compare these with experimental data.