Semiclassical and relaxation limits of bipolar quantum hydrodynamic model

TL;DR

This paper investigates the behavior of bipolar quantum hydrodynamic models for semiconductors, demonstrating convergence to classical models in semiclassical and relaxation limits through rigorous mathematical analysis.

Contribution

It provides the first rigorous proof of the global-in-time convergence of bipolar quantum hydrodynamic solutions to classical models in both semiclassical and relaxation limits.

Findings

Convergence of quantum to classical bipolar hydrodynamics in semiclassical limit.

Convergence to drift-diffusion system under combined limits.

Global-in-time strong solution convergence established.

Abstract

The global in-time semiclassical and relaxation limits of the bipolar quantum hydrodynamic model for semiconductors are investigated in $R^3$. We prove that the unique strong solution converges globally in time to the strong solution of classical bipolar hydrodynamical equation in the process of semiclassical limit and to that of the classical Drift-Diffusion system under the combined relaxation and semiclassical limits.