Research Interests of Tom Kirchner's group
The time-dependent many-electron problem
This issue is central to many different physical problems, such as
heavy-particle collisions from and the interaction of intense laser
fields with the building blocks of matter (atoms, molecules, clusters,
...). In many situations the impinging ion or the radiation field can
be described as a classical environment that transfers energy
to the electrons and introduces an explicit time dependence into
the electronic quantum system via its classical evolution.
These ideas have been recently put forward in [1].
The task is then to solve a time-dependent
Schrödinger equation (TDSE), and this is a tough problem when many
electrons are active.
A very elegant way to formulate the problem is provided by time-dependent
density functional theory (TDDFT): Its basic theorem [2] says that the
interacting many-body problem can be mapped exactly onto a set of
single-particle equations (the so-called time-dependent Kohn-Sham (TDKS)
equations) that are driven by a local effective potential.
This looks like an enormous simplification of the problem but,
of course, some important difficulties remain.
One such problem is that the form of the effective single-particle
potential is not known exactly. At this point approximations
enter the game.
Another problem is that exact expressions for many important
observables are also lacking. This is a consequence of the
fact that no (practical) prescription of how to construct the
many-particle wave funtion is provided by TDDFT.
This seems to be a little ironic:
We know that the wave function and (almost) all
observables are unique functionals of the one-particle
density, but we do not know how these functionals look like.
A significant part of our research is concerned with the
question of how to construct a practical (i.e., an approximate
but meaningful) scheme based on TDDFT in order to
describe laser-matter interactions and
atomic collisions that involve many active electrons.
We have also participated in perturbative studies of atomic
collision processes, which have been rather successful for the
description of the fine details of electron ejection [3].
Current aspects of this endeavor are:
-
Development and application of optimized dynamical basis sets for
the description of time-dependent quantum systems: In this area,
we have contributed (and, hopefully, will be able to contribute
further on) to the developement of the
Basis Generator Method (BGM) [4].
-
Time-dependent response modelsin ion-atom collisions with many
active electrons: The models investigated so far [5]
are intended to serve as guidelines for the
construction of first-principles response schemes. For the two-electron
(spin-singlet) problem such a scheme (on the exchange-only level)
has recently been implemented [6].
-
Extraction of observables for many-particle transitions from
effective single-particle models:
this issue is, as mentioned above, one of the outstanding problems of TDDFT.
Only on the so-called exchange-only level do we know how to extract
observables which correspond to multiple-electron transitions [7].
A step beyond this level would be a major breakthrough...
-
Description of ion-ion and ion-atom collisions:
investigation of basic processes
(excitation, ionization, charge transfer) and many-electron transitions:
currently, we are mainly interested in collision systems with active electrons
on the projectile and on the target in the initial state.
Such systems give rise to interesting effects connected with the
antisymmetry of the total wave function of all electrons (so-called
Pauli blocking) [8].
-
Laser-assisted ion-atom collisions: The idea to influence
atomic collisions with laser light is not a new one, but it has gained
some momentum, recently. Questions of current interest are what kind
of laser-field
induced modifications of electronic processes will be observable in future experiments
and to which extent they can be manipulated or even controlled [9].
The motivation behind all these works is (at least) twofold: (i) to elucidate
(some aspects of) the quantum few-body problem; (ii) to help
explain and understand experimental studies in
the field. Naturally, these two aspects are interrelated, and the
exchange of ideas and
collaborations with other research groups (theoretical and experimental)
have been crucial in order to gain new insights. We have been and are
collaborating with:
-
Reiner Dreizler,
Matthias Keim,
Hans Jürgen
Lüdde, ..., Johann Wolfgang Goethe-Universität, Frankfurt, Germany
-
Marko Horbatsch,
York University, Toronto, Canada
-
Laszlo Gulyas,
ATOMKI, Debrecen, Hungary
-
Alejandro Amaya-Tapia,
Centro de Ciencias Fisicas, UNAM, Mexico
-
Michael Schulz, University of Missouri-Rolla, Rolla (MO), USA
-
Robert Moshammer, Joachim Ullrich and colleagues,
Max-Planck-Institut für Kernphysik , Heidelberg, Germany
-
John Tanis, Western Michigan University, Kalamazoo (MI), USA
-
Eduardo Montenegro and coworkers, PUC, Rio der Janeiro, Brazil
-
Steven Knoop, Ronnie Hoekstra, Reinhard Morgenstern,
KVI , Groningen, The Netherlands
Recent overviews:
-
A review article published in
Recent Res. Devel. Physics, 5, 433 (2004)
-
two articles
which are included in the Springer book
Many Particle Quantum Dynamics in Atomic and Molecular Fragmentation
(ed. by J. Ullrich and V. P. Shevelko) published in July 2003.
If you are interested in details you should consult our
published articles . Some older
stuff can be found on the page
Atomic Collision Theory of the group of
Prof. Dr. R. M. Dreizler and
Prof. Dr. H. J. Lüdde who supervised Tom Kirchner's PhD-thesis a couple of
years ago. Some relevant projects before the year 2000 are described there.
References:
- J. S. Briggs and J. M. Rost in Eur. Phys. J. D 10, 311 (2000).
- E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984).
- T. Kirchner et al., Phys. Rev. A 65, 042727 (2002).
-
H. J. Lüdde et al., J. Phys. B 29, 4423 (1996);
O. J. Kroneisen et al., J. Phys. A 32, 2141 (1999).
-
T. Kirchner et al., Phys. Rev. A 62, 042704
(2000); Phys. Rev. A 64, 012711 (2001);
J. Phys. b 35, 925 (2002).
- M. Keim et al., Phys. Rev. A 67, 062711 (2003).
- T. Kirchner et al., Phys. Rev. A 58, 2063 (1998).
-
T. Kirchner and M. Horbatsch, Phys. Rev. A 63, 062718 (2001);
T. Kirchner et al., J. Phys. B 37, 2379 (2004).
- T. Kirchner, Phys. Rev. Lett. 89, 093202 (2002); Phys. Rev. A 69, 063412 (2004).
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