Iteration scheme for the solution of the two-dimensional Schrödinger-Poisson equations in quantum structures

1997 ◽  
Vol 81 (12) ◽  
pp. 7880-7884 ◽  
Author(s):  
A. Trellakis ◽  
A. T. Galick ◽  
A. Pacelli ◽  
U. Ravaioli
Keyword(s):  
Iteration Scheme ◽  
Quantum Structures ◽  
Two Dimensional ◽  
Poisson Equations

scholarly journals Comparison of Iteration Schemes for the Solution of the Multidimensional Schrödinger-Poisson Equations

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 105-109 ◽  
Author(s):  
A. Trellakis ◽  
A. T. Galick ◽  
A. Pacelli ◽  
U. Ravaioli
Keyword(s):  
Coupled System ◽  
Iteration Scheme ◽  
Simple Expression ◽  
Software Implementation ◽  
Quantum Structures ◽  
System Of Differential Equations ◽  
Poisson Equations ◽  
Quantum Electron ◽  
Predictor Corrector ◽  
Bound Electron

We present a fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schrödinger's and Poisson's equations in quantum structures. A simple expression describing the dependence of the quantum electron density on the electrostatic potential is used to implement a predictor – corrector type iteration scheme for the solution of the coupled system of differential equations. This approach simplifies the software implementation of the nonlinear problem, and provides excellent convergence speed and stability. We demonstrate the algorithm by presenting an example for the calculation ofthe two-dimensional bound electron states within the cross-section of a GaAs-AlGaAs based quantum wire. For this example, six times fewer iterations are needed when our predictor – corrector approach is applied, compared to a corresponding underrelaxation algorithm.

Hot-phonon-assisted additional correlation in Al0.23Ga0.77N/GaN

2016 ◽  
Vol 55 (4) ◽  
Author(s):  
Arvydas Matulionis ◽  
Vytautas Aninkevičius ◽  
Mindaugas Ramonas
Keyword(s):  
Electron Gas ◽  
Tensor Component ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Two Dimensional Electron Gas ◽  
Poisson Equations ◽  
Well Model ◽  
Consistent Solution ◽  
Phonon Lifetime ◽  
Dimensional Electron Gas

The hot-phonon effect is considered for an Al0.23Ga0.77N/GaN structure with a two-dimensional electron gas subjected to an electric field applied in the plane of electron confinement. The hot-phonon accumulation is taken into account in the hot-phonon lifetime approximation for the quantum well model designed through a self-consistent solution of Schrödinger and Poisson equations. The field-dependent electron temperature and non-ohmic transport are obtained from the Monte Carlo simulation for a 3-subband model. The longitudinal tensor component of an additional correlation of electron velocities is estimated in the hotelectron temperature approximation and an essential dependence on the hot-phonon lifetime is demonstrated. The results are in a reasonable agreement with the experimental data for a similar structure with a two-dimensional electron gas.

Elementary derivation of the kinetic equation for the two-dimensional guiding centre plasma

1978 ◽  
Vol 19 (1) ◽  
pp. 121-133 ◽  
Author(s):  
Michael Mond ◽  
Georg Knorr
Keyword(s):  
Kinetic Equation ◽  
Langevin Equation ◽  
Time Scale ◽  
Equations Of Motion ◽  
Planck Equation ◽  
Stochastic Equations ◽  
Iteration Scheme ◽  
Two Dimensional ◽  
Hopf Equation ◽  
Rigorous Solution

A kinetic equation for a two-dimensional inviscid hydrodynamic fluid is derived in two ways. First, the equations of motion for the modes of the fluid are interpreted as stochastic equations resembling the Langevin equation. To lowest order a Fokker–Planck equation can be derived which is the kinetic equation for one mode. Secondly, a suitable iteration scheme is applied to the Hopf equation which results in the same kinetic equation. A parameter describing the time scale is arbitrary and cannot be determined by the applied methods alone. It is shown that the kinetic equation satisfies the conservation requirements and relaxes to an equilibrium which is a rigorous solution of the Hopf equation.

scholarly journals Green's functions for the wave, Helmholtz and Poisson equations in a two-dimensional boundless domain

2013 ◽  
Vol 35 (1) ◽  
Author(s):  
Roberto Toscano Couto
Keyword(s):  
Green's Functions ◽  
Fourier Transforms ◽  
Green’S Functions ◽  
Plane Domain ◽  
Integral Representations ◽  
Two Dimensional ◽  
Entire Plane ◽  
Poisson Equations ◽  
New Procedures ◽  
Real Poles

In this work, Green's functions for the two-dimensional wave, Helmholtz and Poisson equations are calculated in the entire plane domain by means of the two-dimensional Fourier transform. New procedures are provided for the evaluation of the improper double integrals related to the inverse Fourier transforms that furnish these Green's functions. The integrals are calculated by using contour integration in the complex plane. The method consists basically in applying the correct prescription for circumventing the real poles of the integrand as well as in using well-known integral representations of some Bessel functions.

scholarly journals Two-Dimensional Incompressible Viscous Flow Simulation Using Velocity-Vorticity Dual Reciprocity Boundary Element Method

2004 ◽  
Vol 20 (3) ◽  
pp. 177-185 ◽  
Author(s):  
T. I. Eldho ◽  
D. L. Young
Keyword(s):  
Boundary Element Method ◽  
Viscous Flow ◽  
Boundary Element ◽  
Computational Domain ◽  
Two Dimensional ◽  
Flow Problems ◽  
Poisson Equations ◽  
Incompressible Viscous Flow ◽  
Vorticity Transport ◽  
Element Method

AbstractThis paper describes a computational model based on the dual reciprocity boundary element method (DRBEM) for the solution of two-dimensional incompressible viscous flow problems. The model is based on the Navier-Stokes equations in velocity-vorticity variables. The model includes the solution of vorticity transport equation for vorticity whose solenoidal vorticity components are obtained by solving Poisson equations involving the velocity and vorticity components. Both the Poisson equations and the vorticity transport equations are solved iteratively using DRBEM and combined to determine the velocity and vorticity vectors. In DRBEM, all source terms, advective terms and time dependent terms are converted into boundary integrals and hence the computational domain of the problem reduces by one. Internal points are considered wherever solution is required. The model has been applied to simulate two-dimensional incompressible viscous flow problems with low Reynolds (Re) number in a typical square cavity. Results are obtained and compared with other models. The DRBEM model has been found to be reasonable and satisfactory.

scholarly journals Oblique and Asymmetric Klein Tunneling across Smooth NP Junctions or NPN Junctions in 8-Pmmn Borophene

Nanomaterials ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1462
Author(s):  
Zhan Kong ◽  
Jian Li ◽  
Yi Zhang ◽  
Shu-Hui Zhang ◽  
Jia-Ji Zhu
Keyword(s):  
Phase Diagram ◽  
Electrical Resistance ◽  
Normal Incidence ◽  
Quantum Structures ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac Cone ◽  
Klein Tunneling ◽  
Properties Of Materials ◽  
Massless Fermions

The tunneling of electrons and holes in quantum structures plays a crucial role in studying the transport properties of materials and the related devices. 8-Pmmn borophene is a new two-dimensional Dirac material that hosts tilted Dirac cone and chiral, anisotropic massless Dirac fermions. We adopt the transfer matrix method to investigate the Klein tunneling of massless fermions across the smooth NP junctions and NPN junctions of 8-Pmmn borophene. Like the sharp NP junctions of 8-Pmmn borophene, the tilted Dirac cones induce the oblique Klein tunneling. The angle of perfect transmission to the normal incidence is 20.4∘, a constant determined by the Hamiltonian of 8-Pmmn borophene. For the NPN junction, there are branches of the Klein tunneling in the phase diagram. We find that the asymmetric Klein tunneling is induced by the chirality and anisotropy of the carriers. Furthermore, we show the oscillation of electrical resistance related to the Klein tunneling in the NPN junctions. One may analyze the pattern of electrical resistance and verify the existence of asymmetric Klein tunneling experimentally.

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