THE ONE-DIMENSIONAL PERIODIC BLOCH-POISSON EQUATION-Reference-Cited by-同舟云学术

THE ONE-DIMENSIONAL PERIODIC BLOCH-POISSON EQUATION

Published:1991-03 Issue:01 Volume:01 Page:83-112
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

ARNOLD ANTON¹,MARKOWICH PETER A.¹,MAUSER NORBERT²

Affiliation:

1. Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

2. Institut für Angewandte and Numerische Mathematik, TU-Wien, Wiedner Hauptstrasse 6–10, A-1040 Wien, Austria

Abstract

We analyze the Bloch-Poisson model describing quantum steady states of electrons in thermodynamical equilibrium. The problem is set in a one-dimensional periodic geometry. The existence of a unique smooth solution for every positive temperature is proved, a convergent iterative procedure useful for the numerical simulation is obtained, and the classical limit is analyzed.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021820259100006X

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1. On Asymmetric Quasiperiodic Solutions of Hartree–Fock Systems;Journal of Differential Equations;2002-01

2. The Thermal Equilibrium Solution of a Generic Bipolar Quantum Hydrodynamic Model;Communications in Mathematical Physics;1997-09-01

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4. Quantum hydrodynamics for semiconductors in the high-field case;Applied Mathematics Letters;1994-09

5. On absorbing boundary conditions for quantum transport equations;ESAIM: Mathematical Modelling and Numerical Analysis;1994