Physical systems with loss or gain feature resonant modes that are decaying or growing exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, a so-called "exceptional point" occurs, around which many fascinating phenomena have recently been reported to arise [1][2][3][4][5][6] . Particularly intriguing behavior is predicted to appear when encircling an exceptional point sufficiently slowly 7,8 , like a state-flip or the accumulation of a geometric phase 9,10 . Experiments dedicated to this issue could already successfully explore the topological structure of exceptional points [11][12][13] , but a full dynamical encircling and the breakdown of adiabaticity inevitably associated with it 14-21 remained out of reach of any measurement so far. Here we

The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process predicted for an adiabatic encircling of an exceptional point. In this work we analyse this and related processes for the generic system of two coupled oscillator modes with loss or gain. We identify a characteristic system evolution consisting of periods of quasi-stationarity interrupted by abrupt non-adiabatic transitions, and we present a qualitative and quantitative description of this switching behaviour by connecting the problem to the phenomenon of stability loss delay. This approach makes accurate predictions for the breakdown of the adiabatic theorem as well as the occurrence of chiral behavior observed previously in this context, and provides a general framework to model and understand quasi-adiabatic dynamical effects in non-Hermitian systems.

We report the structural and electronic properties of an artificial graphene/Ni (111) (111), and mildly corrugated graphene on Ir(111), allows to disentangle the two key properties which lead to the observed increased interaction, namely lattice matching and electronic interaction. Although the latter determines the strength of the hybridization, we find an important influence of the local carbon configuration resulting from the lattice mismatch.

We have investigated the electronic structure of graphene supported on Re(0001) before and after the intercalation of one monolayer of Ag by means of angle-resolved photoemission spectroscopy measurements and density functional theory calculations. The intercalation of Ag reduces the graphene-Re interaction and modifies the electronic band structure of graphene. Although the linear dispersion of the π state of graphene in proximity of the Fermi level highlights a rather weak graphene-noble metal layer interaction, we still observe a significant hybridization between the Ag bands and the π state in lower energy regions. These results demonstrate that covering a surface with a noble metal layer does decouple the electronic states, but still leads to a noticeable change in the electronic structure of graphene.

The boundaries of waveguides and nanowires have drastic influence on their coherent scattering properties. Designing the boundary profile is thus a promising approach for transmission and band-gap engineering with many applications. By performing an experimental study of microwave transmission through rough waveguides we demonstrate that a recently proposed surface scattering theory can be employed to predict the measured transmission properties from the boundary profiles and vice versa. A new key ingredient of this theory is a scattering mechanism which depends on the squared gradient of the surface profiles. We demonstrate the non-trivial effects of this scattering mechanism by detailed mode-resolved microwave measurements and numerical simulations.Comment: 5 pages 4 figure