The Global Existence and Semiclassical Limit of Weak Solutions to Multidimensional Quantum Drift-diffusion Model

2007 ◽  
Vol 7 (4) ◽  
Author(s):  
Xiuqing Chen
Keyword(s):  
Diffusion Model ◽  
Weak Solutions ◽  
Semiclassical Limit ◽  
Periodic Boundary Conditions ◽  
Drift Diffusion Model ◽  
Global Weak Solutions ◽  
Drift Diffusion ◽  
Initial Value ◽  
Fourth Order Parabolic System ◽  
Entropy Estimate

AbstractWe establish the global weak solutions to quantum drift-diffusion model, a fourth order parabolic system, in two or there space dimensions with large initial value and periodic boundary conditions and furthermore obtain the semiclassical limit by entropy estimate and compactness argument.

On the Multidimensional Bipolar Isothermal Quantum Drift-Diffusion Model

2012 ◽  
Vol 466-467 ◽  
pp. 186-190
Author(s):  
Jian Wei Dong
Keyword(s):  
Diffusion Model ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Mean Value ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Initial Value ◽  
Inequality Technique ◽  
Entropy Estimate ◽  
Three Space

The bipolar isothermal quantum drift-diffusion model in two or three space dimensions with initial value and periodic boundary conditions is investigated. The global existence of weak solution to the problem is obtained by using semi-discretizing in time and entropy estimate. Furthermore, it is shown that the solution to the problem exponentially approaches its mean value as time increases to infinity by using a series of inequality technique.

The Multidimensional Bipolar Quantum Drift-diffusion Model

2008 ◽  
Vol 8 (4) ◽  
Author(s):  
Xiuqing Chen ◽  
Yingchun Guo
Keyword(s):  
Weak Solution ◽  
Diffusion Model ◽  
Semiclassical Limit ◽  
Global Weak Solution ◽  
Mean Value ◽  
Doping Profile ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
New Methods ◽  
Fourth Order Parabolic System

AbstractWe investigate the bipolar quantum drift-diffusion model, a fourth order parabolic system, in two or there space dimensions. First, we establish the global weak solution with large initial value and periodic boundary conditions. Then we show the semiclassical limit by using new methods based on delicate interpolation estimates and compactness argument. Furthermore, when the doping profile is a constant, we find that the weak solution approaches its mean value exponentially as time increases to infinity.

scholarly journals Bounded weak solutions to a matrix drift–diffusion model for spin-coherent electron transport in semiconductors

2015 ◽  
Vol 25 (05) ◽  
pp. 929-958 ◽  
Author(s):  
Ansgar Jüngel ◽  
Claudia Negulescu ◽  
Polina Shpartko
Keyword(s):  
Diffusion Model ◽  
Weak Solutions ◽  
Spin Vector ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Vector Density ◽  
Cross Diffusion ◽  
Electron Density Matrix ◽  
Finite Volume Discretization ◽  
Bounded Weak Solutions

The global-in-time existence and uniqueness of bounded weak solutions to a spinorial matrix drift–diffusion model for semiconductors is proved. Developing the electron density matrix in the Pauli basis, the coefficients (charge density and spin-vector density) satisfy a parabolic 4 × 4 cross-diffusion system. The key idea of the existence proof is to work with different variables: the spin-up and spin-down densities as well as the parallel and perpendicular components of the spin-vector density with respect to the precession vector. In these variables, the diffusion matrix becomes diagonal. The proofs of the L∞ estimates are based on Stampacchia truncation as well as Moser- and Alikakos-type iteration arguments. The monotonicity of the entropy (or free energy) is also proved. Numerical experiments in one-space dimension using a finite-volume discretization indicate that the entropy decays exponentially fast to the equilibrium state.

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