  Liouville's theorem on the conservation of phase space volume is violated by
Berry phase in the semiclassical dynamics of Bloch electrons. This leads to a
modification of the phase space density of states, whose significance is
discussed in a number of examples: field modification of the Fermi-sea volume,
connection to the anomalous Hall effect, and a general formula for orbital
magnetization. The effective quantum mechanics of Bloch electrons is also
sketched, where the modified density of states plays an essential role.
