Diffusive corrections to asymptotics of a strong-field quantum transport equation

作者：Manzini Chiara; Frosali Giovanni^*

来源：Physica D: Nonlinear Phenomena , 2010, 239(15): 1402-1415.

DOI：10.1016/j.physd.2009.10.016

• Asymptotic analysis
• Quantum drift-diffusion model
• Wigner equation
• Open quantum systems
• Singularly perturbed parabolic equations

The asymptotic analysis of a linear high-field Wigner-BGK equation is developed by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number epsilon, evolution equations are derived for the terms of zeroth and first order in epsilon. In particular, a quantum drift-diffusion equation for the position density of electrons, with an epsilon-order correction on the field terms, is obtained. Well-posedness and regularity of the approximate problems are established, and a rigorous proof that the difference between exact and asymptotic solutions is of order epsilon(2), uniformly in time and for arbitrary initial data is given.

• 出版日期2010-8-1