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Liouville's theorem on the conservation of phase space volume is violated byBerry phase in the semiclassical dynamics of Bloch electrons. This leads to amodification of the phase space density of states, whose significance isdiscussed in a number of examples: field modification of the Fermi-sea volume,connection to the anomalous Hall effect, and a general formula for orbitalmagnetization. The effective quantum mechanics of Bloch electrons is alsosketched, where the modified density of states plays an essential role.Comment: Minor revision. Journal info updat

Berry Phase Correction to Electron Density of States in Solids