Leo Mangeolle
I will present a systematic derivation of the semi-classical kinetic equation for neutral bosons from their quantum kinetic equation. It incorporates the semi-classical topological dynamics of wavepackets in the form of geometric properties of the energy eigenstates, such as the Berry phases and curvatures, generalized to phase space. This makes it possible to treat inhomogeneous systems, including boundaries, textures, etc., in a compact and natural manner, and to compute the associated observable quantities, such as energy and current densities, away from equilibrium. In particular, the thermal conductivity tensor is exactly obtained. This provides a self-contained rigorous derivation of the intrinsic thermal Hall effect of neutral bosons such as phonons and magnons, avoiding subtleties associated with magnetization currents. It also allows to include extrinsic effects, such as the side-jump contribution in the presence of disorder.