On thermal ionization for open quantum systems

This thesis addresses the phenomenon of ionization of an idealized atom by a surrounding infinitely extended quantized electromagnetic field at positive temperature. According to Planck's law one expects photons with arbitrary high energy, which eventually exceed the ionization threshold of the atom. Mathematically, this can be interpreted as the absence of time-invariant normal states in a suitable dynamical system. Such problems can be converted into a spectral-theoretical question by means of the self-adjoint generator of the time evolution - the Liouvillian L. In this setting it suffices to show that zero is not an eigenvalue of L. The goal of this thesis is the proof of thermal ionization for more concrete models with less restrictions than in previous works, including a QED-like coupling term with a spatial decay and an idealized atom, given as Schrödinger operator. With respect to the atom it will be differentiated between two cases: first, potentials with infinitely many bound states, but only finitely many coupled to the field, and second, compactly supported smooth potentials. For the latter there are, apart from the spatial decay, no further artificial restrictions required in the coupling. The proof is based on positive commutators. On the field it uses the generator of translations, and for the atom the generator of dilations (first case) or the generator of dilations in the space of scattering functions (second case). By means of an approximated version of Fermi's Golden Rule one obtains a uniform result in every bounded temperature range.