Coherent exciton transport in dendrimers and continuous-time quantum walks

We model coherent exciton transport in dendrimers by continuous-time quantum walks (CTQWs). For dendrimers up to the second generation the coherent transport shows perfect recurrences, when the initial excitation starts at the central node. For larger dendrimers, the recurrence ceases to be perfect, a fact which resembles results for discrete quantum carpets. Moreover, depending on the initial excitation site we find that the coherent transport to certain nodes of the dendrimer has a very low probability. When the initial excitation starts from the central node, the problem can be mapped onto a line which simplifies the computational effort. Furthermore, the long time average of the quantum mechanical transition probabilities between pairs of nodes show characteristic patterns and allow to classify the nodes into clusters with identical limiting probabilities. For the (space) average of the quantum mechanical probability to be still or again at the initial site, we obtain, based on the Cauchy-Schwarz inequality, a simple lower bound which depends only on the eigenvalue spectrum of the Hamiltonian.Comment: 8 pages, 8 figures, accepted for publication in J. Chem. Phy

SELLING SHARES TO RETAIL INVESTORS: AUCTION VS. FIXED PRICE

We analyze the problem of selling shares of a divisible good to a large number of buyers when demand is uncertain. We characterize equilibria of two popular mechanisms, a fixed price mechanism and a uniform price auction, and compare the revenues. While in the auction truthful bidding is a dominant strategy, we find that bidders have an incentive to overstate their demand in the fixed price mechanism. For some parameter values this yields the surprising result that the fixed price mechanism outperforms the auction.IPO, Uniform Price Auction, Open Offer, Proportional Rationing.

Coherent dynamics on hierarchical systems

We study the coherent transport modeled by continuous-time quantum walks, focussing on hierarchical structures. For these we use Husimi cacti, lattices dual to the dendrimers. We find that the transport depends strongly on the initial site of the excitation. For systems of sizes $N\le21$, we find that processes which start at central sites are nearly recurrent. Furthermore, we compare the classical limiting probability distribution to the long time average of the quantum mechanical transition probability which shows characteristic patterns. We succeed in finding a good lower bound for the (space) average of the quantum mechanical probability to be still or again at the initial site.Comment: 7 pages, 5 figure

Opportunity-Rich Schools and Sustainable Communities: Seven Steps to Align High-Quality Education With Innovations in City and Metropolitan Planning and Development

Details challenges and steps for linking quality education and community and economic vitality, including establishing a shared vision and metrics, aligning investments for prosperity, and expanding access via transportation. Lists promising practices

Localization of coherent exciton transport in phase space

We study numerically the dynamics of excitons on discrete rings in the presence of static disorder. Based on continuous-time quantum walks we compute the time evolution of the Wigner function (WF) both for pure diagonal (site) disorder, as well as for diagonal and off-diagonal (site and transfer) disorder. In both cases, large disorder leads to localization and destroys the characteristic phase space patterns of the WF found in the absence of disorder.Comment: 8 pages, 9 figures. slight revision of the text and addition of a new figure. to be published in Phys. Rev.

Measuring nonlinear stresses generated by defects in 3D colloidal crystals

The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect density rises to levels routinely found in real-world materials, transport is governed by local stresses that are predominantly nonlinear. Such stress fields however, cannot be measured using conventional bulk and local measurement techniques. Here, we report direct and spatially resolved experimental measurements of the nonlinear stresses surrounding colloidal crystalline defect cores, and show that the stresses at vacancy cores generate attractive interactions between them. We also directly visualize the softening of crystalline regions surrounding dislocation cores, and find that stress fluctuations in quiescent polycrystals are uniformly distributed rather than localized at grain boundaries, as is the case in strained atomic polycrystals. Nonlinear stress measurements have important implications for strain hardening, yield, and fatigue.Comment: in Nature Materials (2016