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Rigorous drift-diffusion asymptotics of a high-field quantum transport equation

Chiara Manzini·Giovanni Frosali
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Abstract

The asymptotic analysis of a linear high-field Wigner-BGK equation is developped by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number $ε$, evolution equations are derived for the terms of zeroth and first order in $ε$. In particular, it is obtained a quantum drift-diffusion equation for the position density, which is corrected by field-dependent terms of order $ε$. Well-posedness and regularity of the approximate problems are established, and it is proved that the difference between exact and asymptotic solutions is of order $ε^2$, uniformly in time and for arbitrary initial data.

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Chiara Manzini, Giovanni Frosali. 2006-12-13. Rigorous drift-diffusion asymptotics of a high-field quantum transport equation. https://arxiv.org/abs/math-ph/0612040

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