Spin diffusive modes and thermal transport in neutron star crusts

In this contribution we first review a method for obtaining the collective modes of pair-correlated neutron matter as found in a neutron star inner crust. We discuss two classes of modes corresponding to density and spin perturbations with energy spectra $\omega = \omega_0 + \alpha q^2$, where $\omega_0 = 2\Delta$ is the threshold frequency and $\Delta$ is the gap in the neutron fluid spectrum. For characteristic values of Landau parameters in neutron star crusts the exitonic density modes have $\alpha < 0$, therefore they live below the pair-breaking continuum $\omega_0$ and are undamped. For spin diffusive modes $\alpha > 0$ and they exist above $\omega_0$ which implies that these modes are damped. As an application of these findings we compute the thermal conductivity due to spin diffusive modes and show that it scales as $T^{1/2} \exp(-2\omega_0/T)$ in the case where their two-by-two scattering cross-section is weakly dependent on temperature.