We develop a theory of the Berry-phase effect in anomalous transport in ferromagnets driven by statistical forces such as the gradient of temperature or chemical potential. Here a charge Hall current arises from the Berry-phase correction to the orbital magnetization rather than from the anomalous velocity, which does not exist in the absence of a mechanical force. A finite-temperature formula ...

On the space L, of loops in the group of Hamiltonian symplecto-morphisms of a symplectic quantizable manifold, we define a closed Z-valued 1-form Ω. If Ω vanishes, the prequantization map can be extended to a group representation. On L one can define an action integral as an R/Z-valued function, and the cohomology class [Ω] is the obstruction to the lifting of that action integral to an R-value...

We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light into the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay’s angle with averaging over the classical torus and Berry’s phase with averaging over the entire classical phase...