Markowich, P. A.; Mauser, N. J.; Poupaud, F. A Wigner-function approach to (semi)classical limits: Electrons in a periodic potential. (English) Zbl 0805.35106 J. Math. Phys. 35, No. 3, 1066-1094 (1994). 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. Cited in 1 ReviewCited in 43 Documents MSC: 35Q40 PDEs in connection with quantum mechanics 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory Keywords:derivation of the semiclassical Liouville equation; semiclassical macroscopic densities PDFBibTeX XMLCite \textit{P. A. Markowich} et al., J. Math. Phys. 35, No. 3, 1066--1094 (1994; Zbl 0805.35106) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.