Ulm 2004 – scientific programme

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PV: Plenarvorträge

PV V

PV V: Plenary Talk

Tuesday, March 16, 2004, 09:00–10:00, H22

Mathematical Theory of the Interaction of Matter and Light — •Volker Bach — Universität Mainz

In 1905, Einstein published his famous paper on the photoelectric effect, for which he was later awarded the Nobel prize in physics. For the first time, the energy differences of atomic or molecular states were linked to the wave length of the emitted or absorbed light by the formula

Δ E = h   ν (1)

appearing in this paper. Today, one hundred years after Einstein’s discovery, we are used to the notion of unstable excited atomic states that relax to the ground state under emission of a photon which obeys Eq. (1) or, conversely, the excitation of the ground state by absorption of a photon.

While everything about these processes seem to be understood, the purpose of the talk is to critically review the status of the theory of such processes from the mathematical point of view. The models to be discussed result from the study of the dynamics of nonrelativistic matter coupled to the quantized radiation field. The mathematical rigorous description of such systems has had some progress during the past decade which will be reported on. Especially the following aspects will be discussed:

Stability of Ground States; Why doesn’t an Atom or Molecule dissolve after switching on the coupling to the radiation field?

Instability of Excited States; What is the mathematically adequate description of excited states, and in which sense are these unstable?

Photoelectric Effect; Do we understand the photoelectric effect from a mathematical viewpoint?

Scattering Theory; Ist Scattering asymptotically complete?

Dissipation; What happens when matter is coupled to one or several heat baths?