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The Semiclassical Limit in the quantum drift-diffusion Equations with Isentropic Pressure

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Chinese Annals of Mathematics,Series B 2008年第4期29卷 369-384页

作者： Li CHEN Qiangchang JU Department of Mathematical Sciences Tsinghua University Beijing 100084 China. Institute of Applied Physics and Computational Mathematics P. O. Box 8009-28 Beijing 100088 China.

The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditions. It is shown that the semiclassical limit of this solution solves the classical drift-diffusion model. In the meanwhile, the global existence of weak solutions is proved.

关键词： quantum drift-diffusion Weak solution Semiclassical limit Isentropic

SEMICLASSICAL LIMIT FOR BIPOLAR quantum drift-diffusion MODEL

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Acta Mathematica Scientia 2009年第2期29卷 285-293页

作者：琚强昌陈丽 Institute of Applied Physics and Computational Mathematics Department of Mathematical Sciences Tsinghua University

Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipol... 详细信息

关键词： quantum drift-diffusion weak solution semiclassical limit bipolar

The Existence and Long-Time Behavior of Weak Solution to Bipolar quantum drift-diffusion Model

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Chinese Annals of Mathematics,Series B 2007年第6期28卷 651-664页

作者： Xiuqing CHEN Li CHEN Huaiyu JIAN School of Sciences Beijing University of Posts and Telecommunications Beijing 100876 China Department of Mathematical Sciences Tsinghua University Beijing 100084 China

The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic *** semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary ***,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.

关键词： quantum drift-diffusion Weak solution Long-time behavior

The Semiclassical Limit in the quantum drift-diffusion Model

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Acta Mathematica Sinica,English Series 2009年第2期25卷 253-264页

作者： Qiang Chang JU Institute of Applied Physics and Computational Mathematics P. O. Box 8009-28 Beijing 100088 P. R. China

Semiclassical limit to the solution of isentropic quantum drift-diffusion model in semicon- ductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical drift-diff... 详细信息

关键词： quantum drift-diffusion weak solution semiclassical limit isentropic

Dirichlet-Neumann Problem for Unipolar Isentropic quantum drift-diffusion Model

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Tsinghua Science and Technology 2008年第4期13卷 560-569页

作者：陈丽陈秀卿 Department of Mathematical Sciences Tsinghua University Beijing 100084 China School of Sciences Beijing University of Posts and Telecommunications Beijing 100876 China

This paper studies the existence, semiclassical limit, and long-time behavior of weak solutions to the unipolar isentropic quantum drift-diffusion model, a fourth order parabolic system. Semi-discretization in time and entropy estimates give the global existence and semiclassical limit of nonnegative weak solutions to the one-dimensional model with a nonnegative large initial value and a Dirichlet-Neumann boundary condition. Furthermore, the weak solutions are proven to exponentially approach constant steady state as time increases to infinity.

关键词： quantum drift-diffusion fourth order parabolic system weak solution semiclassical limit exponential decay