Absorbing boundary conditions for relativistic quantum mechanics equations

Xavier Antoine (1) , Emmanuel Lorin (2) , Julien Sater (2) , François Fillion-Gourdeau (2) , André D. Bandrauk (3)

1 IECL - Institut Élie Cartan de Lorraine
2 School of Mathematics and Statistics [Ottawa]
3 UdeS - Université de Sherbrooke

This paper is devoted to the derivation of absorbing boundary conditions for the Klein-Gordon and Dirac equations modeling quantum and relativistic particles subject to classical electromagnetic fields. Microlocal analysis is the main ingredient in the derivation of these boundary conditions, which are obtained in the form of pseudo-differential equations. Basic numerical schemes are derived and analyzed to illustrate the accuracy of the derived boundary conditions.

Mots clés: Klein-Gordon equation; numerical approximation; wave equation; absorbing boundary conditions; pseudo-differential operators; Microlocal analysis; Dirac equation

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]

Xavier Antoine, Emmanuel Lorin, Julien Sater, François Fillion-Gourdeau, André D. Bandrauk. Absorbing boundary conditions for relativistic quantum mechanics equations. Journal of Computational Physics, 2014, 277 (15), pp.268-304. ⟨10.1016/j.jcp.2014.07.037⟩. ⟨hal-01094333⟩