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AN OPERATOR SPLITTING METHOD FOR THE WIGNER-POISSON PROBLEM
 

Summary: AN OPERATOR SPLITTING METHOD
FOR THE WIGNER-POISSON PROBLEM
Anton Arnold*
and
Christian Ringhofer**
Abstract. The Wigner{Poisson equation describes the quantum{mechanical motion of elec-
trons in a selfconsistent electrostatic eld. The equation consists of a transport term and a
non{linear pseudo{di erential operator. In this paper we analyze an operator splitting method
for the linear Wigner equation and the coupled Wigner{Poisson problem. For this semidis-
cretization in time, consistency, and non{linear stability are established in an L2{framework.
We present a numerical example to illustrate the method.
The rst author was partially supported by the grants ERBCHRXCT930413 from the
EC, `Acciones Integradas, 1994' from the DAAD, and the DFG (project `Analysis und
Numerik von kinetischen Quantentransportmodellen').
x1. Introduction.
In this paper we shall study an operator splitting method to discretize the linear Wigner
equation and the coupled Wigner{Poisson system. The Wigner formalism, which repres-
ents a phase{space description of quantum mechanics, has in recent years attracted consi-
derable attention of solid state physicists for simulating quantum e ects in ultra{integrated
semiconductor devices, like resonant tunneling diodes, e.g. ( 11]).

  

Source: Arnold, Anton - Institut für Analysis und Scientific Computing, Technische Universität Wien

 

Collections: Mathematics