Convergency of the Monte Carlo algorithm for the solution of the Wigner quantum-transport equation

Authors:
M. Nedjalkov;I. Dimov;F. Rossi;C. Jacoboni
Affiliations:
Center for Informatics and Computer Technology Acad. G. Bountchev Str. B125A, Sofia, Bulgaria;Center for Informatics and Computer Technology Acad. G. Bountchev Str. B125A, Sofia, Bulgaria;Dipartimento di Fisica and Istituto Nazionale di Fisica della Materia Università di Modena, Via Campi 213/A, I-41100 Modena, Italy;Dipartimento di Fisica and Istituto Nazionale di Fisica della Materia Università di Modena, Via Campi 213/A, I-41100 Modena, Italy
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1996

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Abstract

The Wigner function provides a convenient description for single-particle quantum transport in space dependent systems, such as modern nanoelectronic devices. A Monte Carlo algorithm has been recently introduced for the solution of this integro-differential equation. However, when the potential applied to the system has different limits at + and -~, a convergence problem arises for the kernel of the integral part of the equation. In this paper, we discuss the rigorous mathematical aspects of the convergency of the solution of the Wigner equation and of the Neumann expansion on which the Monte Carlo algorithm is based.