Nonequilibrium approach to Bloch-Peierls-Berry dynamics

We examine Bloch-Peierls-Berry dynamics under a classical nonequilibrium dynamical formulation. In this formulation all coordinates in phase space formed by the position and crystal-momentum space are treated on an equal footing. Explicit demonstrations of no (naive) Liouville theorem and of the validity of the Darboux theorem are given. Regardless, the explicit equilibrium-distribution function is obtained. Similarities and differences to previous approaches are discussed, and in particular, an interesting singular situation becomes nonsingular in the presence of dissipation. Our results confirm the richness of Bloch-Peierls-Berry dynamics.