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

Authors

  • Giovanni Frosali
  • Chiara Manzini

DOI:

https://doi.org/10.1685/

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 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

Downloads

Published

2007-10-01

Issue

Vol. 1 (2006)

Section

Articles

License

Authors who submit to this journal agree to the following terms: a) Authors retain copyright over their work, while allowing the SIMAI to place this accepted work under a Creative Commons Attribution License (CC license), which allows others to freely access, use, and share the work, with an acknowledgement of the work's authorship. b) Authors are able to waive the terms of the CC license and enter into separate, additional contractual arrangements for the non-exclusive distribution and subsequent publication of this work (e.g., publish a revised version in a journal, post it to an institutional repository or publish it in a book). with an acknowledgement of its initial publication on “Communications to SIMAI Congress”. c) In addition, authors are encouraged to post and share their work online (e.g., in institutional repositories or on their website).