Summary
By solving the Bloch equation the expression of the equilibrium Wigner function is obtained up to first order in the scaled Planck constant for arbitrary energy bands.
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References
Romano, V.: J. Math. Phys. 48, 123504-1–123504-24 (2007)
Gardner, C., Ringhofer, C.: SIAM J. Appl. Math. 54, 409–427 (1994)
Wigner, E.: Phys. Rev. 40, 749–759 (1932)
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Romano, V. (2010). The Equilibrium Wigner Function in the Case of Nonparabolic Energy Bands. In: Fitt, A., Norbury, J., Ockendon, H., Wilson, E. (eds) Progress in Industrial Mathematics at ECMI 2008. Mathematics in Industry(), vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12110-4_15
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DOI: https://doi.org/10.1007/978-3-642-12110-4_15
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