Hybrid coupling of a one-dimensional energy-transport Schrodinger system

被引：0

作者：

Jourdana, Clement ^{[1
]}

Pietra, Paola ^{[2
]}

Vauchelet, Nicolas ^{[3
,4
]}

机构：

[1] Univ Grenoble Alpes, Lab Jean Kuntzmann, F-38000 Grenoble, France

[2] CNR, Ist Matemat Applicata & Tecnol Informat E Magenes, Via Ferrata 1, I-27100 Pavia, Italy

[3] UPMC Univ Paris 06, Lab Jacques Louis Lions, CNRS, UMR 7598, F-75005 Paris, France

[4] INRIA Paris Rocquencourt, EPI MAMBA, F-75005 Paris, France

来源：

MONATSHEFTE FUR MATHEMATIK | 2017年 / 184卷 / 04期

关键词：

Schrodinger equation; Boltzmann equation; Energy-transport system; Spherical harmonic expansion system; Semiconductors; Interface conditions; Mixed finite elements; DRIFT-DIFFUSION MODEL; PARTIALLY QUANTIZED PARTICLES; MAXIMUM-ENTROPY PRINCIPLE; MACROSCOPIC MODELS; SUBBAND MODEL; SEMICONDUCTORS; APPROXIMATION; SIMULATIONS; EQUATIONS; COMPUTATION;

D O I：

10.1007/s00605-016-1008-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider one dimensional coupled classical-quantum models for quantum semiconductor device simulations. The coupling occurs in the space variable: the domain of the device is divided into a region with strong quantum effects (quantum zone) and a region where quantum effects are negligible (classical zone). In the classical zone, transport in diffusive approximation is modeled through diffusive limits of the Boltzmann transport equation. It can lead to an energy-transport model, obtained using a Spherical Harmonic Expansion model as intermediate step. The quantum transport is described by the Schrodinger equation. The aim of this work is to focus on the derivation of boundary conditions at the interface between the classical and quantum regions. Numerical simulations are provided for a resonant tunneling diode with the energy-transport model.

引用

页码：563 / 596

页数：34

共 50 条

[31] A NEW METHOD FOR APPROXIMATE SOLUTION OF ONE-DIMENSIONAL SCHRODINGER-EQUATIONS [J].

TRAVLOS, SD ;

BOEYENS, JCA .

THEORETICA CHIMICA ACTA, 1994, 87 (06) :453-464

[32] Modified Scattering for the One-Dimensional Schrodinger Equation with a Subcritical Dissipative Nonlinearity [J].

Liu, Xuan ;

Zhang, Ting .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2025, 37 (01) :577-601

[33] Highly precise solutions of the one-dimensional Schrodinger equation with an arbitrary potential [J].

Zakrzewski, A. J. .

COMPUTER PHYSICS COMMUNICATIONS, 2006, 175 (06) :397-403

[34] An example of embedded singular continuous spectrum for one-dimensional Schrodinger operators [J].

Tchebotareva, O .

LETTERS IN MATHEMATICAL PHYSICS, 2005, 72 (03) :225-231

[35] Inverse problem of scattering theory for a class one-dimensional Schrodinger equation [J].

Mamedov, Kh R. ;

Nabiev, A. A. .

QUAESTIONES MATHEMATICAE, 2019, 42 (07) :841-856

[36] Relaxation limit of the one-dimensional bipolar Euler-Poisson system in the bound domain [J].

Kong, Haiyue ;

Li, Yeping .

APPLIED MATHEMATICS AND COMPUTATION, 2016, 274 :1-13

[37] Transport and heating of electrons in semiconductors with a one-dimensional superlattice [J].

Yu. A. Romanov ;

E. V. Demidov .

Physics of the Solid State, 1999, 41 :1555-1563

[38] A New Multiscale Discontinuous Galerkin Method for the One-Dimensional Stationary Schrodinger Equation [J].

Dong, Bo ;

Shu, Chi-Wang ;

Wang, Wei .

JOURNAL OF SCIENTIFIC COMPUTING, 2016, 66 (01) :321-345

[39] Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrodinger Model [J].

Bica, Ion ;

Mucalica, Ana .

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2022, 30 (02) :45-62

[40] Regularity of the Rotation Number for the One-Dimensional Time-Continuous Schrodinger Equation [J].

Amor, Sana Hadj .

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2012, 15 (04) :331-342

← 1 2 3 4 5 →