Corrected Quantum Drift-Diffusion Equation via Compressed Chapman-Enskog Expansion
Abstract
In this paper we perform the asymptotic analysis for the Wigner equation with a relaxation-time
collisional operator.
The asymptotic analysis is based on the compressed Chapman--Enskog expansion procedure.
Such procedure permits to investigate the initial layer and bulk problems, in order to obtain the
drift-diffusion approximation to the solution with an accuracy.
With such results we can find a corrector of the initial value for the drift-diffusion problem and
we are able to show that the difference between the exact and asymptotic solutions is of order ,
uniformly in time for arbitrary initial data.
[DOI: 10.1685 / CSC06085] About DOI
collisional operator.
The asymptotic analysis is based on the compressed Chapman--Enskog expansion procedure.
Such procedure permits to investigate the initial layer and bulk problems, in order to obtain the
drift-diffusion approximation to the solution with an accuracy.
With such results we can find a corrector of the initial value for the drift-diffusion problem and
we are able to show that the difference between the exact and asymptotic solutions is of order ,
uniformly in time for arbitrary initial data.
[DOI: 10.1685 / CSC06085] About DOI
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PDFDOI: https://doi.org/10.1685/
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