Institute of Theoretical Physics

Quantum Dynamics of Many-Particle Systems




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:

  1. J. S. Briggs and J. M. Rost in Eur. Phys. J. D 10, 311 (2000).
  2. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984).
  3. T. Kirchner et al., Phys. Rev. A 65, 042727 (2002).
  4. H. J. Lüdde et al., J. Phys. B 29, 4423 (1996); O. J. Kroneisen et al., J. Phys. A 32, 2141 (1999).
  5. T. Kirchner et al., Phys. Rev. A 62, 042704 (2000); Phys. Rev. A 64, 012711 (2001); J. Phys. b 35, 925 (2002).
  6. M. Keim et al., Phys. Rev. A 67, 062711 (2003).
  7. T. Kirchner et al., Phys. Rev. A 58, 2063 (1998).
  8. T. Kirchner and M. Horbatsch, Phys. Rev. A 63, 062718 (2001); T. Kirchner et al., J. Phys. B 37, 2379 (2004).
  9. T. Kirchner, Phys. Rev. Lett. 89, 093202 (2002); Phys. Rev. A 69, 063412 (2004).

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