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On the use of the uniform complex scaling-method for studying time-dependent systems
Stockholm University, Faculty of Science, Department of Physics. (Computational atomic physics)
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: urn:nbn:se:su:diva-74683ISBN: 978-91-7447-487-9 (print)OAI: oai:DiVA.org:su-74683DiVA: diva2:511188
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
List of papers
1. Solution of the time-dependent Schrödinger equation using uniform complex scaling
Open this publication in new window or tab >>Solution of the time-dependent Schrödinger equation using uniform complex scaling
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.

National Category
Atom and Molecular Physics and Optics
Research subject
Chemical Physics
Identifiers
urn:nbn:se:su:diva-15066 (URN)10.1103/PhysRevA.78.032502 (DOI)000259689400069 ()
Available from: 2008-12-03 Created: 2008-12-03 Last updated: 2017-12-13Bibliographically approved
2. Solution of the Dirac equation for hydrogenlike systems exposed to intense electromagnetic pulses
Open this publication in new window or tab >>Solution of the Dirac equation for hydrogenlike systems exposed to intense electromagnetic pulses
2009 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 79, no 4, 043418- p.Article in journal (Refereed) Published
Abstract [en]

The time-dependent Dirac equation is solved numerically and compared to the corresponding prediction of the nonrelativistic Schrödinger equation for hydrogenlike systems exposed to intense laser pulses. It is found that for a correct description of effects beyond the dipole approximation, virtual electron-positron pairs can be very important. Relativistic effects in the ionization dynamics of highly charged systems are studied.

National Category
Atom and Molecular Physics and Optics
Research subject
Nuclear Physics; Chemical Physics
Identifiers
urn:nbn:se:su:diva-32134 (URN)10.1103/PhysRevA.79.043418 (DOI)000265947500018 ()
Available from: 2009-12-04 Created: 2009-12-04 Last updated: 2017-12-12Bibliographically approved
3. Wave functions associated with time-dependent, complex-scaled Hamiltoniansevaluated on a complex time grid
Open this publication in new window or tab >>Wave functions associated with time-dependent, complex-scaled Hamiltoniansevaluated on a complex time grid
2012 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 85, no 1, 013419- p.Article in journal (Refereed) Published
Abstract [en]

We solve the time-dependent Schr ̈ dinger equation with the method of uniform complex scaling and investigateothe possibility to evaluate the solution on a complex time grid. With this approach it is possible to calculateproperties that relate directly to the continuum part of the complex scaled wave function, such as the photoelectronspectrum after photoabsorption.

National Category
Atom and Molecular Physics and Optics
Research subject
Physics; Chemical Physics
Identifiers
urn:nbn:se:su:diva-72162 (URN)10.1103/PhysRevA.85.013419 (DOI)000299842200008 ()
Note

3

Available from: 2012-02-03 Created: 2012-02-03 Last updated: 2017-12-08Bibliographically approved
4. Modifying H− resonance asymmetries with short light pulses
Open this publication in new window or tab >>Modifying H− resonance asymmetries with short light pulses
2012 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 85, no 5, 053413- p.Article in journal (Refereed) Published
Abstract [en]

We present a method, based on time-dependent perturbation theory and complex rotation, to treat the interaction of a short light pulse with a correlated atomic system. The pulse is built from two short and weak pulses with Gaussian envelopes that are centred at two different frequencies.The method is applied to the negative hydrogen ion in the vicinity of a doubly excited resonanceand it is shown that the two light pulses can be used to alter the Fano profile of a resonance.

National Category
Atom and Molecular Physics and Optics
Research subject
Chemical Physics
Identifiers
urn:nbn:se:su:diva-74642 (URN)10.1103/PhysRevA.85.053413 (DOI)000303909900007 ()
Available from: 2012-03-19 Created: 2012-03-19 Last updated: 2017-12-07Bibliographically approved

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