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  • Writer's pictureG.G. Marion, van

Eric Pap Successfully Defends PhD

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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