Magnus–lanczos methods with simplified commutators for the schrödinger equation with a time-dependent potential

Arieh Iserles, Karolina Kropielnicka, Pranav Singh

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The computation of the Schrödinger equation featuring time-dependent potentials is of great importance in quantum control of atomic and molecular processes. These applications often involve highly oscillatory potentials and require inexpensive but accurate solutions over large spatio-temporal windows. In this work we develop Magnus expansions where commutators have been simplified. Consequently, the exponentiation of these Magnus expansions via Lanczos iterations is significantly cheaper than that for traditional Magnus expansions. At the same time, and unlike most competing methods, we simplify integrals instead of discretizing them via quadrature at the outset—this gives us the flexibility to handle a variety of potentials, being particularly effective in the case of highly oscillatory potentials, where this strategy allows us to consider significantly larger time steps.

Original languageEnglish
Pages (from-to)1547-1569
Number of pages23
JournalSIAM Journal on Numerical Analysis
Volume56
Issue number3
Early online date5 Jun 2018
DOIs
Publication statusPublished - 2018

Keywords

  • Anticommutators
  • Integral-preserving
  • Lanczos iterations
  • Large time steps
  • Lie algebra
  • Magnus expansion
  • Oscillatory potentials
  • Schrödinger equation
  • Simplified commutators
  • Time-dependent potential

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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