We consider Hamiltonians of models describing non-relativistic quantum mechanical matter coupled to a relativistic field of bosons. If the free Hamiltonian has an eigenvalue, we show that this eigenvalue persists also for nonzero coupling. The eigenvalue of the free Hamiltonian may be degenerate provided…
Cham (ZG): Springer International Publishing, 2024-05
We consider the spin boson model with external magnetic field. We prove a path integral formula for the heat kernel, known as Feynman–Kac–Nelson (FKN) formula. We use this path integral representation to express the ground state energy as a stochastic integral. Based on this connection, we determine…
Cham (ZG): Springer International Publishing, 2022-03-07
When considering models of nonrelativistic quantum mechanical particles interacting with a field of massless relativistic bosons, one encounters an infrared problem. Heuristically, this is due to the fact that small energy fluctuations can create an infinite number of low-energy bosons, which causes…
We show the existence of ground states in the massless spin boson model without any infrared regularization. Our proof is non-perturbative and relies on a compactness argument. It works for arbitrary values of the coupling constant under the hypothesis that the second derivative of the ground state energy…
We study a concrete model of a confined particle in form of a Schrödinger operator with a compactly supported smooth potential coupled to a bosonic field at positive temperature. We show, that the model exhibits thermal ionization for any positive temperature, provided the coupling is sufficiently small.…
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.…
In der vorliegenden Arbeit betrachten wir Modelle der nicht-relativistischen Quantenelektrodynamik in Dipol-Approximation und studieren Phänomene, die bei kleinen Energien in diesen quanten-mechanischen Systemen auftreten. Wir untersuchen die analytische Abhängigkeit des kleinsten Energie-Eigenwertes…