Comment on “ Berry phase correction to electron density in solids ”

Comment on " Berry phase correction to electron density in solids " by Xiao et al. Abstract The main result of Xiao et al. In a recent paper on the semiclassical dynamics of a Bloch electron, Xiao, Shi and Niu [1] claim that, due to a Berry curvature term, Liouville's theorem on the conservation of the phase-space volume element would be violated, a fact which would have been overlooked so far. Their main results would then be to restore invariance by including a pre-factor. We show that all the mystery disappears if we use Hamiltonian mechanics. Giving a Hamil-tonian structure amounts indeed to giving a Hamiltonian and a Poisson-bracket which satisfies the Jacobi identity; the equations of motion read ˙