Friday October 1, 2004, from 13-??
Department of Mathematical Sciences, University of Aarhus
Auditorium D4, Building 531

Programme

Coupled Harmonic Oscillators in the Thermodynamic Limit

Jacob Schach Møller (Aarhus)

Abstract
In this talk we study the low-lying excited states of coupled harmonic
oscillators. We verify that the wellknown perturbative and semiclassical
pictures persist in the thermodynamic limit.
The two key ingredients are: A detailed analysis of the logarithm of the
ground state eigenfunction. The fact that the Schrödinger operator is
(up to a constant) a zeroth order Hodge Laplacian, associated with a
twisted exterior derivative introduced by Witten.

Stark hamiltonians: dynamics of 1D Bloch electrons in
high momentum regime and growth of energy for driven quantum rings.

Gheorghe Nenciu (Bucharest)

Abstract
We consider the dynamics of a 1D Bloch electron
subjected to a constant electric field
, described in the temporal gauge
by the Hamiltonian

The periodic potential is supposed to be less singular
than the -like potential (Dirac comb). The main result is a rigor
ous proof
of Ao's claim that for a large class of initial conditions
(high momentum regime) there is no dynamical localization. The proof is ba
sed
on the mathematical substantiation of the two simplifying assumptions
made in physical literature: the transitions between far away bands
can be neglected and the transitions at the quasi-crossing can be describe
d
by Landau-Zener like formulae. By Avron and Nemirovski connection
our results implies also the increase of energy for
weakly singular driven quantum rings.

The multiconfiguration methods for atoms and molecules

Mathieu Lewin (Copenhagen)

Abstract
We present our recent results on the multiconfiguration
methods, which are used in Quantum Chemistry for the description of
non-relativistic electrons in atoms and molecules. They are the natural
generalization of the well-known Hartree-Fock theory. In particular, we
present a new definition of approximate excited states which are certain
critical points of the multiconfiguration functional. We also show how
this definition can be used in practice to compute the first excited
state and present numerical results.

On a Bogoliubov-Dirac-Fock theory

Christian Hainzl (Copenhagen)

Abstract
We study a generalized Dirac-Fock
theory where we take not only real electrons,
but also the electrons filling the Dirac sea.
Assuming that the uniformly filled sea has no physical consequence
we derive a functional which is bounded from below.
This functional we minimize and get as absolut
minimizer a deformed vacuum in the presence of external fields.
In the case of atoms, we minimize in fixed charge sector.
As a consequence we derive a selfconsistent equation
for the minimizer which consists of the
know Dirac-Fock mean field operator on the one hand
and plus polarization corrections on the other hand.
The crucial point is that we derive these
equations simply by minimizing.