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This ghost state is a smooth extension of the solution at the exceptional point from the other side of the interface.
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The exceptional points in the energy spectrum are also analyzed.
The choice of recipes is determined by a classification scheme of the exceptional points.
This improved sensitivity is due to another exotic property of the exceptional points: Their response to perturbations is not linear to the perturbation strength.
Using a pair of coupled microdisk quantum cascade lasers, we demonstrate that in the vicinity of these exceptional points the coupled laser shows a characteristic reversal of its pump dependence, including a strongly decreasing intensity of the emitted laser light for increasing pump power.
The main idea is to have at least first order approximations for second order derivatives at those exceptional points.
In this paper, we classify these exceptional points and propose two recipes to maintain order of accuracy there, aiming at improving the previous coupling interface method [26].
Most elliptic interface solvers become complicated for complex interface problems at those "exceptional points" where there are not enough neighboring interior points for high order interpolation.
The coalescence point is found to be an exceptional point from the characteristic square-root scaling8 of the energy gap (see the inset figure in Fig. 2b).
On a continental scale, Knapp and Smith [ 47] indicated that ANPP has a strong linear relationship with annual precipitation, but there is an exceptional point of the lowest ANPP with the highest precipitation at the moist alpine meadow site.
We also noticed an exceptional point under the low LD level (Figure 6A), where the AR under the 0.25 MAF interval was lower than that under MAF intervals of 0.35 or higher.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com