In quantum mechanics it is often required to describe in a semiclassical approximation the motion of particles moving within a given energy band. Such a representation leads to the appearance of an analogues of fictitious forces, associated with the Berry curvature, in the semiclassical equations of motion. The purpose of this paper is to derive systematically the kinetic Boltzmann equations displaying these effects in the case that the band is degenerate, and as such the Berry curvature is generically non-Abelian. We use the formalism of phase-space quantum mechanics to derive the results.
|Original language||American English|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|State||Published - 15 Sep 2017|
Bibliographical noteFunding Information:
I wish to thank B Spivak, A Andreev, M Khodas and P Wiegmann for extensive discussions. I acknowledge the Israeli Science Foundation, which supported this research through grant 1466/15.
© 2017 IOP Publishing Ltd.
- Anomalous velocity
- Berry curvature
- Berry phase
- Boltzmann equation
- Wigner transform
- kinetic equation