The diffusive thermal conductivity tensor of the A 1 -phase of superfluid 3 He at low temperatures and melting pressure are calculated beyond the s-p approximation, by using the Boltzmann equation approach. The interaction between normal-normal, normal-Bogoliubov and Bogoliubov-Bogoliubov quasiparticles in the collision integrals are considered for important scattering processes such as binary process. At low temperatures, we show that the scattering between Bogoliubov and normal quasiparticles in binary processes plays an important role in the A 1 -phase, and Bogoliubov-Bogoliubov interaction is ignorable.We show that the two normal and superfluid components take part in elements of the diffusive thermal conductivity tensor differently. We obtain the result that the elements of the diffusive thermal conductivities, K xx , K yy and K zz , are proportional to T −1 , and also that the superfluid components of the diffusive thermal conductivity tensor, K xx↑ and K zz↑ , are proportional to T 3 and T , respectively.

In this paper, we investigate quantum correlation of an interacting Fermi system, which is a nodal superconductor (d-wave superconductor) at zero temperature, via quantum entanglement of two electron spins forming Cooper pairs (Werner state), tripartite and quantum discord. The energy gap depends on the angle between the electron momentum and the nodal axis; and at zero temperature we use an approximation in which the energy gap is considered as the linear function of the angle. After calculating single-electron Green's functions, the two-electron space-spin density matrix, which has X-state form, is obtained. The dependence of quantum correlation to the relative distance of electrons spins of Cooper pair and energy gap is investigated. One of the results is, for d-wave case, concurrence (as a measure of entanglement), quantum discord and tripartite are sensitive to the change of magnitude of gap. Another result is both concurrence and discord oscillate. Then, we consider three-dimensional rectangular nanosuperconducting grain in the weak coupling frame. The nano-size effect is entered via gap fluctuation. The dependence of quantum correlation to length of superconductor and lower bound of robustness of tripartite entanglement are determined. Moreover, we show that quantum correlation of d-wave nano-size superconducting grain strongly depends on length of grain (in contrast to swave case). In general, it is found that the length of grain lower, the effect of nano-size on quantum correlation higher. Quantum tripartite for nano-scale d-wave superconductor is better than for bulk d-wave superconductor. However, we find out both bulk and nano-size s-wave superconductors have the same tripartite. Furthermore, entanglement length and quantum correlation length are investigated and it is shown that there is a length of superconductor in which discord becomes zero. Also, for a given fixed length of superconductor, both a peak in discord and a peak in concurrence occur simultaneously.

PACS 67.57.HiThe diffusive thermal conductivity tensor of the A 1 -phase of superfluid 3 He at low temperatures and melting pressure are calculated by s-p approximation, by using the Boltzmann equation approach. We obtain that the elements of the diffusive thermal conductivities, K xx , K yy , and K zz , are proportional to T -1 . Then we compare the results of this paper and our results of thermal conductivity based on Pfitzner procedure. Temperature dependence of both results is equal but numerical coefficients of them are little different. Also we show that Boguliubov-normal interaction is important in comparison to other interactions.

Using perturbed Bogoliubov equations, we study the linear response to a weak orbital magnetic field of the heat conductivity of the normal-superfluid interface of a polarized Fermi gas at sufficiently low temperature. We consider the various scattering regions of the BCS regime and analytically obtain the transmission coefficients and the heat conductivity across the interface in an arbitrary weak orbital field. For a definite choice of the field, we consider various values of the scattering length in the BCS range and numerically obtain the allowed values of the average and species-imbalance chemical potentials. Thus, taking Andreev reflection into account, we describe how the heat conductivity is affected by the field and the species imbalance. In particular, we show that the additional heat conductivity due to the orbital field increases with the species imbalance, which is more noticeable at higher temperatures. Our results indicate how the heat conductivity may be controlled, which is relevant to sensitive magnetic field sensors/regulators at the interface.

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