Asymmetries in symmetric quantum walks on two-dimensional networks

We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast, directed transport through the network to the opposite corner. This transport is not ballistic in nature, but rather produced by quantum mechanical interference. In the long time limit, certain walks show an asymmetric limiting probability distribution; this feature depends on the starting site and, remarkably, on the precise size of the network. The limiting probability distributions show patterns which are correlated with the initial condition. This might have consequences for the application of continuous time quantum walk algorithms.Comment: 9 pages, 12 figures, revtex

Quantum transport on two-dimensional regular graphs

We study the quantum-mechanical transport on two-dimensional graphs by means of continuous-time quantum walks and analyse the effect of different boundary conditions (BCs). For periodic BCs in both directions, i.e., for tori, the problem can be treated in a large measure analytically. Some of these results carry over to graphs which obey open boundary conditions (OBCs), such as cylinders or rectangles. Under OBCs the long time transition probabilities (LPs) also display asymmetries for certain graphs, as a function of their particular sizes. Interestingly, these effects do not show up in the marginal distributions, obtained by summing the LPs along one direction.Comment: 22 pages, 11 figure, acceted for publication in J.Phys.

Synthesis of the originally proposed structures of elatenyne and an enyne from Laurencia majuscula

A bidirectional synthesis of the originally proposed structures for the natural products elatenyne and a chloroenyne from Laurencia majuscula is described along with a reassessment of the structures of the halogenated enynes based upon a C-13 NMR chemical shift/structure correlation

Remarks on singular Cayley graphs and vanishing elements of simple groups

Let Γ be a finite graph and let A(Γ) be its adjacency matrix. Then Γ is singular if A(Γ) is singular. The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. Here we investigate this problem for Cayley graphs Cay(G,H) when G is a finite group and when the connecting set H is a union of conjugacy classes of G. In this situation, the singularity problem reduces to finding an irreducible character χ of G for which ∑h∈Hχ(h)=0. At this stage, we focus on the case when H is a single conjugacy class hG of G; in this case, the above equality is equivalent to χ(h)=0 . Much is known in this situation, with essential information coming from the block theory of representations of finite groups. An element h∈G is called vanishing if χ(h)=0 for some irreducible character χ of G. We study vanishing elements mainly in finite simple groups and in alternating groups in particular. We suggest some approaches for constructing singular Cayley graphs

Internationalisation and development in East Asian higher education: an introduction

It is important to recognise that comparison is not a method or even an academic technique; rather, it is a discursive strategy… Good comparisons often come from the experience of strangeness and absences. (Benedict Anderson, 2016

Exploring the solid state and solution structural chemistry of the utility amide potassium hexamethyldisilazide (KHMDS)

The structural chemistry of eleven donor complexes of the important Brønsted base potassium 1,1,1,3,3,3-hexamethyldisilazide (KHMDS) has been studied. Depending on the donor, each complex adopted one of four general structural motifs. Specifically, in this study the donors employed were toluene (to give polymeric 1 and dimeric 2), THF (dimeric 3), N,N,N',N'-tetramethylethylenediamine (TMEDA) (dimeric 4), (R,R)-N,N,N',N'-tetramethyl-1,2-diaminocyclohexane [(R,R)-TMCDA] (dimeric 5), 12-crown-4 (dimeric 6), N,N,N',N'-tetramethyldiaminoethyl ether (TMDAE) (tetranuclear dimeric 8 and monomeric 10), N,N,N',N',N''-pentamethyldiethylentriamine (PMDETA) (tetranuclear dimeric 7), tris[2-dimethyl(amino)ethyl]amine (Me6TREN) (tetranuclear dimeric 9) and tris{2-(2-methoxyethoxy)ethyl}amine (TMEEA) (monomeric 11). The complexes were also studied in solution by 1H and 13C NMR spectroscopy as well as DOSY NMR spectroscopy

Calculations Predict That Carbon Tunneling Allows the Degenerate Cope Rearrangement of Semibullvalene to Occur Rapidly at Cryogenic Temperatures

Article on calculations predicting that carbon tunneling allows the degenerate cope rearrangement of semibullvalene to occur rapidly at cryogenic temperatures