uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Global error control of the time-propagation for the Schrödinger equation with a time-dependent Hamiltonian
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.
Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
2009 (English)Report (Other academic)
Place, publisher, year, edition, pages
2009.
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2009-021
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-108364OAI: oai:DiVA.org:uu-108364DiVA: diva2:235577
Available from: 2009-09-16 Created: 2009-09-16 Last updated: 2011-11-18Bibliographically approved
In thesis
1. Numerical methods for quantum molecular dynamics
Open this publication in new window or tab >>Numerical methods for quantum molecular dynamics
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The time-dependent Schrödinger equation models the quantum nature of molecular processes. Numerical simulations of these models help in understanding and predicting the outcome of chemical reactions.

In this thesis, several numerical algorithms for evolving the Schrödinger equation with an explicitly time-dependent Hamiltonian are studied and their performance is compared for the example of a pump-probe and an interference experiment for the rubidium diatom. For the important application of interaction dynamics between a molecule and a time-dependent field, an efficient fourth order Magnus-Lanczos propagator is derived. Error growth in the equation is analyzed by means of a posteriori error estimation theory and the self-adjointness of the Hamiltonian is exploited to yield a low-cost global error estimate for numerical time evolution. Based on this theory, an h,p-adaptive Magnus-Lanczos propagator is developed that is capable to control the global error. Numerical experiments for various model systems (including a three dimensional model and a dissociative configuration) show that the error estimate is effective and the number of time steps needed to meet a certain accuracy is reduced due to adaptivity.

Moreover, the thesis proposes an efficient numerical optimization framework for the design of femtosecond laser pulses with the aim of manipulating chemical reactions. This task can be formulated as an optimal control problem with the electric field of the laser being the control variable. In the algorithm described here, the electric field is Fourier transformed and it is optimized over the Fourier coefficients. Then, the frequency band is narrowed which facilitates the application of a quasi-Newton method. Furthermore, the restrictions on the frequency band make sure that the optimized pulse can be realized by the experimental equipment. A numerical comparison shows that the new method can outperform the Krotov method, which is a standard scheme in this field.

Place, publisher, year, edition, pages
Uppsala University, 2009
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2009-004
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-108366 (URN)
Supervisors
Available from: 2009-10-09 Created: 2009-09-16 Last updated: 2017-08-31Bibliographically approved

Open Access in DiVA

No full text

Other links

http://www.it.uu.se/research/publications/reports/2009-021/

Authority records BETA

Kormann, KatharinaHolmgren, SverkerKarlsson, Hans O.

Search in DiVA

By author/editor
Kormann, KatharinaHolmgren, SverkerKarlsson, Hans O.
By organisation
Division of Scientific ComputingComputational ScienceQuantum Chemistry
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 908 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf