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A Wigner-function approach to (semi)classical limits: Electrons in a periodic potential. (English) Zbl 0805.35106

Summary: A rigorous derivation of the semiclassical Liouville equation for electrons which move in a crystal lattice (without the influence of an external field) is presented. The approach is based on carrying out the semiclassical limit in the band-structure Wigner equation. The semiclassical macroscopic densities are also obtained as limits of the corresponding quantum quantities.

MSC:

35Q40 PDEs in connection with quantum mechanics
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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[1] DOI: 10.1142/S0218202593000072 · Zbl 0772.35061 · doi:10.1142/S0218202593000072
[2] DOI: 10.1016/0370-1573(84)90151-0 · doi:10.1016/0370-1573(84)90151-0
[3] DOI: 10.1143/PTPS.98.109 · doi:10.1143/PTPS.98.109
[4] DOI: 10.1070/PU1983v026n04ABEH004345 · doi:10.1070/PU1983v026n04ABEH004345
[5] DOI: 10.1007/BF01764126 · Zbl 0800.73029 · doi:10.1007/BF01764126
[6] DOI: 10.1103/RevModPhys.34.645 · doi:10.1103/RevModPhys.34.645
[7] DOI: 10.1103/PhysRev.115.809 · Zbl 0086.45101 · doi:10.1103/PhysRev.115.809
[8] DOI: 10.1007/BF02790171 · Zbl 0408.35067 · doi:10.1007/BF02790171
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