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The orbital moment (OM) of Bloch electrons has witnessed a surge in interestin out-of--equilibrium systems. Here, by developing a quantum kinetic theory,we show that the OM is in general not conserved in an electric field. The forcemoment produces a torque on the OM, which is determined by the quantumgeometric tensor and the group velocities of Bloch bands. The torque vanishesin two-band systems with particle-hole symmetry, but is nonzero otherwise. Fortilted massive Dirac fermions the torque is determined by the magnitude anddirection of the tilt.

Non-conservation of the orbital moment of Bloch electrons in an electric field