Absorbing boundary conditions for relativistic quantum mechanics equations

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...

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Published inJournal of computational physics Vol. 277; no. 15; pp. 268 - 304
Main Authors Antoine, X., Lorin, E., Sater, J., Fillion-Gourdeau, F., Bandrauk, A.D.
Format Journal Article
LanguageEnglish
Published United States Elsevier Inc 15.11.2014
Elsevier
Subjects
Absorbing boundary conditions
ACCURACY
Analysis of PDEs
APPROXIMATIONS
BOUNDARY CONDITIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DIRAC EQUATION
KLEIN-GORDON EQUATION
Mathematical Physics
Mathematics
Microlocal analysis
Numerical Analysis
Numerical approximation
Physics
Pseudo-differential operators
QUANTUM MECHANICS
Quantum Physics
RELATIVISTIC RANGE
Wave equation
Wave equation
Numerical approximation
Microlocal analysis
Pseudo-differential operators
Absorbing boundary conditions
Dirac equation
Klein–Gordon equation
absorbing boundary conditions
pseudo-differential operators
Klein-Gordon equation
wave equation
numerical approximation
Online AccessGet full text
ISSN0021-9991
1090-2716
DOI10.1016/j.jcp.2014.07.037

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Abstract 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.
AbstractList 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.
Author Lorin, E.
Antoine, X.
Sater, J.
Fillion-Gourdeau, F.
Bandrauk, A.D.
Author_xml – sequence: 1
  givenname: X.
  surname: Antoine
  fullname: Antoine, X.
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– sequence: 2
  givenname: E.
  surname: Lorin
  fullname: Lorin, E.
  email: elorin@math.carleton.ca
  organization: Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4, Canada
– sequence: 3
  givenname: J.
  surname: Sater
  fullname: Sater, J.
  email: julien.sater@hotmail.com
  organization: School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5B6, Canada
– sequence: 4
  givenname: F.
  surname: Fillion-Gourdeau
  fullname: Fillion-Gourdeau, F.
  email: filliong@CRM.UMontreal.ca
  organization: Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4, Canada
– sequence: 5
  givenname: A.D.
  surname: Bandrauk
  fullname: Bandrauk, A.D.
  email: andre.bandrauk@usherbrooke.ca
  organization: Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4, Canada
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Issue 15
Keywords Wave equation
Numerical approximation
Microlocal analysis
Pseudo-differential operators
Absorbing boundary conditions
Dirac equation
Klein–Gordon equation
absorbing boundary conditions
pseudo-differential operators
Klein-Gordon equation
wave equation
numerical approximation
Language English
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Snippet This paper is devoted to the derivation of absorbing boundary conditions for the Klein–Gordon and Dirac equations modeling quantum and relativistic particles...
This paper is devoted to the derivation of absorbing boundary conditions for the Klein-Gordon and Dirac equations modeling quantum and relativistic particles...
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SubjectTerms Absorbing boundary conditions
ACCURACY
Analysis of PDEs
APPROXIMATIONS
BOUNDARY CONDITIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DIRAC EQUATION
KLEIN-GORDON EQUATION
Mathematical Physics
Mathematics
Microlocal analysis
Numerical Analysis
Numerical approximation
Physics
Pseudo-differential operators
QUANTUM MECHANICS
Quantum Physics
RELATIVISTIC RANGE
Wave equation
Title Absorbing boundary conditions for relativistic quantum mechanics equations
URI https://dx.doi.org/10.1016/j.jcp.2014.07.037
https://hal.science/hal-01094333
https://www.osti.gov/biblio/22382145
Volume 277
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