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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

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

A Sixth-Order Parabolic System in Semiconductors

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Chinese Annals of Mathematics,Series B 2011年第2期32卷 265-278页

作者： Xiuqing CHEN Li CHEN Caiyun SUN School of Sciences Beijing University of Posts and Telecommunications Beijing 100876 China Department of Mathematical Sciences Tsinghua University Beijing 100084 China Department of Basic Sciences North China Institute of Science and Technology Beijing 101601 China

The authors investigate the global existence and semiclassical limit of weak solutions to a sixth-order parabolic system,which is a quantum-corrected macroscopic model derived recently to simulate the quantum effects ... 详细信息

关键词： Weak solution semiclassical limit Sixth-order parabolic system

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

Asymptotic Analysis of Quantum Dynamics in Crystals: the Bloch-Wigner Transform, Bloch Dynamics and Berry Phase

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Acta Mathematicae Applicatae Sinica 2013年第3期29卷 465-476页

作者： Weinan E Jian-feng LU Xu YANG Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University School of Mathematical Sciences Peking University

We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.

关键词： semiclassical limit Bloch-Wigner transform Bloch dynamics Berry phase asymptotic analysis

Weak solutions to one-dimensional quantum drift-diffusion equations for semiconductors

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Journal of Southeast University(English Edition) 2006年第4期22卷 577-581页

作者：蒋卫祥管平东南大学理学院南京210096

The weak solutions to the stationary quantum drift-diffusion equations （QDD） for semiconductor devices are investigated in one space dimension. The proofs are based on a reformulation of the system as a fourth-order elliptic boundary value problem by using an exponential variable transformation. The techniques of a priori estimates and Leray-Schauder＇s fixed-point theorem are employed to prove the existence. Furthermore, the uniqueness of solutions and the semiclassical limit δ→0 from QDD to the classical drift-diffusion （DD） model are studied.

关键词： semiconductor device quantum drift-diffusion equations existence and uniqueness exponential variable transformation semiclassical limit