ABSTRACT The asymptotic analysis of a linear high-field Wigner-BGK equation is developped 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, it is obtained a quantum drift-diffusion equation for the position density, which is corrected by field-dependent terms of order epsilon. 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. Key words: Asymptotic analysis, quantum drift-diffusion model, Wigner equation, open quantum systems, singularly perturbed parabolic equations.
Diffusive corrections to asymptotics of a strong-field quantum transport equation / C. MANZINI; G. FROSALI. - In: PHYSICA D-NONLINEAR PHENOMENA. - ISSN 0167-2789. - STAMPA. - 239:(2010), pp. 1402-1415. [10.1016/j.physd.2009.10.016]
Diffusive corrections to asymptotics of a strong-field quantum transport equation
MANZINI, CHIARA;FROSALI, GIOVANNI
2010
Abstract
ABSTRACT The asymptotic analysis of a linear high-field Wigner-BGK equation is developped 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, it is obtained a quantum drift-diffusion equation for the position density, which is corrected by field-dependent terms of order epsilon. 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. Key words: Asymptotic analysis, quantum drift-diffusion model, Wigner equation, open quantum systems, singularly perturbed parabolic equations.File | Dimensione | Formato | |
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