TY - JOUR
T1 - Quantum energy-transport and drift-diffusion models
AU - Degond, Pierre
AU - Méhats, Florian
AU - Ringhofer, Christian
N1 - Funding Information:
Supported by the European network HYKE, funded by the EC as contract HPRN-CT-2002-00282, and by NSF grant DECS-0218008.
PY - 2005/2
Y1 - 2005/2
N2 - We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through spatially non-local relations. Thanks to an h expansion of these models, h2 perturbations of the Classical Energy-Transport and Drift-Diffusion models are found. In the Drift-Diffusion case, the quantum correction is the Bohm potential and the model is still entropic. In the Energy-Transport case however, the quantum correction is a rather complex expression and the model cannot be proven entropic.
AB - We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through spatially non-local relations. Thanks to an h expansion of these models, h2 perturbations of the Classical Energy-Transport and Drift-Diffusion models are found. In the Drift-Diffusion case, the quantum correction is the Bohm potential and the model is still entropic. In the Energy-Transport case however, the quantum correction is a rather complex expression and the model cannot be proven entropic.
KW - Diffusion approximation
KW - Entropy minimization
KW - Quantum BGK operator
KW - Wigner equation
UR - http://www.scopus.com/inward/record.url?scp=15244345981&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=15244345981&partnerID=8YFLogxK
U2 - 10.1007/s10955-004-8823-3
DO - 10.1007/s10955-004-8823-3
M3 - Article
AN - SCOPUS:15244345981
SN - 0022-4715
VL - 118
SP - 625
EP - 667
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 3-4
ER -