Corrected Quantum Drift-Diffusion Equation via Compressed Chapman-Enskog Expansion

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  • Giovanni Frosali
  • Chiara Manzini

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https://doi.org/10.1685/

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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 S1_M1_FrosaliManzini0.png 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 S1_M1_FrosaliManzini1.png, uniformly in time for arbitrary initial data. [DOI: 10.1685 / CSC06085] About DOI

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2007-10-01

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##issue.vol## 1 (2006)

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Articles

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