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A mixed spectral-collocation and operator splitting method for the Wigner-Poisson equation
 

Summary: A mixed spectral-collocation and operator
splitting method for the Wigner-Poisson equation
Anton Arnold
ABSTRACT. The Wigner-Poisson equation is a kinetic pseudo-di erential equation to model
quantum transport. A combined spectral-collocation and operator splitting method is presented
and analyzed.
1: Introduction
In this paper we present and analyze an operator splitting method for the
Wigner-Poisson (WP) equation. The Wigner formalism( 10,6]), which represents a
phase-space description of quantum mechanics, has in recent years received a lot of
attention as a tool to simulate transport phenomena in ultra-integrated quantum
e ect semiconductor devices.
The real-valued Wigner distribution function w(x v t) describes the motion of
an electron ensemble in position-velocity (x v)-phase space under the action of the
electrostatic potential V (x t). The time evolution of w is governed by the Wigner
equation, which reads in scaled form
@tw + v@xw + V]w = 0 x 2 (; ) v 2 IR(1.1)
with the pseudo-di erential operator (PDO)
V]w = i
2

  

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

 

Collections: Mathematics