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THE MODIFIED QUANTUM WIGNER SYSTEM IN WEIGHTED $L^{2}$ -SPACE

Published online by Cambridge University Press:  13 October 2016

BIN LI*
Affiliation:
Department of Mathematics, Jincheng College of Sichuan University, Chengdu 611731, PR China email [email protected]
HAN YANG
Affiliation:
College of Mathematics, Southwest Jiaotong University, Chengdu 611756, PR China email [email protected]
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Abstract

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This paper is concerned with the modified Wigner (respectively, Wigner–Fokker–Planck) Poisson equation. The quantum mechanical model describes the transport of charged particles under the influence of the modified Poisson potential field without (respectively, with) the collision operator. Existence and uniqueness of a global mild solution to the initial boundary value problem in one dimension are established on a weighted $L^{2}$ -space. The main difficulties are to derive a priori estimates on the modified Poisson equation and prove the Lipschitz properties of the appropriate potential term.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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