A quantum dot has been etched in bilayer graphene connected by two small constrictions to the leads. We show that this structure does not behave like a single quantum dot but consists of at least three sites of localized charge in series. The high symmetry and electrical stability of the device allowed us to triangulate the positions of the different sites of localized charge and find that one ...

In this paper, we continue the study of domino-tilings of Aztec diamonds (introduced in [1] and [2]). In particular, we look at certain ways of placing “barriers” in the Aztec diamond, with the constraint that no domino may cross a barrier. Remarkably, the number of constrained tilings is independent of the placement of the barriers. We do not know of a simple combinatorial explanation of this ...

We introduce an algorithm that is able to find the facets of Coulomb diamonds in quantum dot arrays. simulate these arrays using constant-interaction model, and rely only on one-dimensional raster scans (rays) learn a model device regularized maximum likelihood estimation. This allows us determine, for given charge state device, which transitions exist what compensated gate voltages are. For sm...

The geometry of causal diamonds or Alexandrov open sets whose initial and final events p and q respectively have a proper-time separation τ small compared with the curvature scale is a universal. The corrections from flat space are given as a power series in τ whose coefficients involve the curvature at the centre of the diamond. We give formulae for the total 4-volume V of the diamond, the are...

This note derives the characteristic polynomial of a graph that represents nonjump moves in a generalized game of checkers. The number of spanning trees is also determined.