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On hybrid quantum–classical transport models
Author(s) -
Ben Abdallah Naoufel,
Tang Shaoqiang
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.494
Subject(s) - coupling (piping) , mathematics , boltzmann equation , boundary value problem , stationary state , quantum , scheme (mathematics) , statistical physics , mathematical analysis , physics , quantum mechanics , mechanical engineering , engineering
This paper contains a review on the coupling between classical models and quantum models for electron transport in semiconductors. Starting from the quantum analogue of the boundary value problem for the Vlasov equation, the coupling with the Boltzmann equation in the one‐dimensional stationary situation is reviewed for the stationary and time‐dependent problems. Then a numerical scheme based on the characteristics method is applied to the stationary hybrid model. Some mathematical properties of the scheme are proven and illustrated in some numerical experiments. Copyright © 2004 John Wiley & Sons, Ltd.