Anomalous Transport Phenomena in $p_x+ip_y$ Superconductors

Spontaneous breaking of time-reversal symmetry in superconductors with the $p_x+ip_y$ symmetry of the order parameter allows for a class of effects which are analogous to the anomalous Hall effect in ferromagnets. These effects exist below the critical temperature, $T<T_{c}$. We develop a kinetic theory of such effects. In particular, we consider anomalous Hall thermal conductivity, the polar Kerr effect, the anomalous Hall effect, and the anomalous photo- and acousto-galvanic effects.