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Solution of the time-dependent Schrödinger equation using uniform complex scaling
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
2008 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 78, no 3, 032502- p.Article in journal (Refereed) Published
Abstract [en]

The formalism of complex rotation of the radial coordinate is studied in the context of time-dependent systems. The applicability of this method is discussed and illustrated with numerical examples involving atoms exposed to electromagnetic field pulses. Complex rotation proves to be an efficient tool to obtain ionization probabilities and rates. Although, in principle, any information about the system may be obtained from the rotated wave function by transforming it back to its unrotated form, a good description of the ionized part of the wave function is generally subject to numerical challenges. It is, however, found that the combination of complex rotation and Floquet formalism offers an alternative and promising possibility to retrieve the physical information.

Place, publisher, year, edition, pages
2008. Vol. 78, no 3, 032502- p.
National Category
Atom and Molecular Physics and Optics
Research subject
Chemical Physics
Identifiers
URN: urn:nbn:se:su:diva-15066DOI: 10.1103/PhysRevA.78.032502ISI: 000259689400069OAI: oai:DiVA.org:su-15066DiVA: diva2:181586
Available from: 2008-12-03 Created: 2008-12-03 Last updated: 2017-12-13Bibliographically approved
In thesis
1. On the use of the uniform complex scaling-method for studying time-dependent systems
Open this publication in new window or tab >>On the use of the uniform complex scaling-method for studying time-dependent systems
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

During the last few decades, laser technology has gone through a series of revolutionary improvements. With light pulses in the sub-femtosecond regime now experimentally available, an explicit time-dependent Hamilton operator is indispensable for a proper theoretical description of the interactions of atoms with such pulses. However, these theoretical studies are computationally very demanding, which motivates the search for new numerical methods and algorithms to approach time-dependent problems. This thesis contributes to this research field, with the main focus on the use of complex-scaled Hamilton operators. Thus, the formalism of complex scaling is studied in the context of its application to explicitly time-dependent atomic systems.

Both non-relativistic and relativistic dynamics are investigated. The numerical advantages and the possibilities to extract physical quantities from complex-scaled wave functions are discussed. Of special interest is the ability to treat resonance states. These are multiply excited electronic states with sufficient energy to decay through Auger transitions to the surrounding continuum. With complex scaling, the Hamilton operator is non-Hermitian and such resonance states can be obtained as eigenstates.

To analyze the non-bound part of the wave function requires essentially the construction of a second wave function; the left state vector. This additional wave function is, however, not easily constructed numerically in the complex scaling-method. To circumvent some of the numerical problems, we have proposed three different methods. These methods are based on Floquet theory, a propagation on a complex time-grid and time-dependent perturbation theory. By carefully investigating the numerical properties of the left state vector, we have thus studied the non-bound part of the system.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2012. 58 p.
National Category
Atom and Molecular Physics and Optics
Research subject
Chemical Physics
Identifiers
urn:nbn:se:su:diva-74683 (URN)978-91-7447-487-9 (ISBN)
Public defence
2012-04-20, lecture room FB42, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:15 (English)
Opponent
Supervisors
Note
At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Submitted.Available from: 2012-03-29 Created: 2012-03-20 Last updated: 2012-03-28Bibliographically approved

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