Eric Pap, mentor of the FotU students, had successfully defended his PhD Thesis On the Geometry of Adiabatic Quantum Mechanics. This was essentially the first FotU project: One on the border of Math and Physics. It was supervised by Daniël Boer (from the VSI) and Holger Waalkens (from the BI). You can hear Eric give a presentation about it here.
The project concerns adiabatic quantum systems, those where the (external) parameters of the model (present in the Hamiltonian) are changed slowly over time in a particular way. One is usually interested in the transport of the quantum state during this process which, in the case of Hermitian Hamiltonians, picks up a (Berry) phase along any closed loop in the parameter space.
In the case of non-Hermitian Hamiltonians, the parameters can loop around exceptional points (EPs), where the change to the state is not just a phase: There is an interchange of levels (generalized geometric phase). In his thesis, Eric introduces a mathematical framework that can cope with EPs and the generalized geometric phase simultaneously. This framework is in line with the parallel transport description that is used in the Hermitian case.
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