Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions

Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions

In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum el...

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Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 79; no. 2 Pt 2; p. 026707
Main Authors: Lötstedt, Erik, Jentschura, Ulrich D
Format: Journal Article
Language:English
Published: United States 01-02-2009
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Abstract In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.
AbstractList In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.
ArticleNumber 026707
Author Jentschura, Ulrich D
Lötstedt, Erik
Author_xml – sequence: 1
  givenname: Erik
  surname: Lötstedt
  fullname: Lötstedt, Erik
  email: erik.loetstedt@mpi-hd.mpg.de
  organization: Max-Planck-Institut für Kernphysik, Postfach 10 39 80, 69029 Heidelberg, Germany. erik.loetstedt@mpi-hd.mpg.de
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  givenname: Ulrich D
  surname: Jentschura
  fullname: Jentschura, Ulrich D
BackLink https://www.ncbi.nlm.nih.gov/pubmed/19391874$$D View this record in MEDLINE/PubMed
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