6533b86efe1ef96bd12cc7fe
RESEARCH PRODUCT
The relaxation-time limit in the quantum hydrodynamic equations for semiconductors
Akitaka MatsumuraAnsgar JüngelHai-liang LiHai-liang Lisubject
PhysicsIndependent equationApplied MathematicsGlobal relaxation-time limitQuantum hydrodynamic equationsEuler equationsMomentumNonlinear systemsymbols.namesakeClassical mechanicsThird-order derivativesMaster equationQuantum drift–diffusion equationssymbolsMethod of quantum characteristicsPoisson's equationQuantum dissipationAnalysisdescription
Abstract The relaxation-time limit from the quantum hydrodynamic model to the quantum drift–diffusion equations in R 3 is shown for solutions which are small perturbations of the steady state. The quantum hydrodynamic equations consist of the isentropic Euler equations for the particle density and current density including the quantum Bohm potential and a momentum relaxation term. The momentum equation is highly nonlinear and contains a dispersive term with third-order derivatives. The equations are self-consistently coupled to the Poisson equation for the electrostatic potential. The relaxation-time limit is performed both in the stationary and the transient model. The main assumptions are that the steady-state velocity is irrotational, that the variations of the doping profile and the velocity at infinity are sufficiently small and, in the transient case, that the initial data are sufficiently close to the steady state. As a by-product, the existence of global-in-time solutions to the quantum drift–diffusion model in R 3 close to the steady-state is obtained.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-06-01 | Journal of Differential Equations |