Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory

We study the S-matrix of planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics; in particular, the higher-point amplitudes we consider can be obtained from those with lowest-points by a collinear uplifting. Based on a compact formula for one-loop N${}^2$MHV amplitudes, we use an equation proposed previously to compute, for the first time, the complete two-loop NMHV and three-loop MHV octagons, which we conjecture to uplift to give the full $n$-point amplitudes up to simpler logarithmic terms or dilogarithmic terms.Comment: v2: important typos fixed. 38 pages, 4 figures. An ancillary file with two-loop NMHV "remainders" for n=10,12 can be found at http://www.nbi.dk/~schuot/nmhvremainders.zi

Photon-photon gates in Bose-Einstein condensates

It has recently been shown that light can be stored in Bose-Einstein condensates for over a second. Here we propose a method for realizing a controlled phase gate between two stored photons. The photons are both stored in the ground state of the effective trapping potential inside the condensate. The collision-induced interaction is enhanced by adiabatically increasing the trapping frequency and by using a Feshbach resonance. A controlled phase shift of $\pi$ can be achieved in one second.Comment: 4 pages, 3 figure

Bipartite graph partitioning and data clustering

Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, we propose a new data clustering method based on partitioning the underlying bipartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. We show that an approximate solution to the minimization problem can be obtained by computing a partial singular value decomposition (SVD) of the associated edge weight matrix of the bipartite graph. We point out the connection of our clustering algorithm to correspondence analysis used in multivariate analysis. We also briefly discuss the issue of assigning data objects to multiple clusters. In the experimental results, we apply our clustering algorithm to the problem of document clustering to illustrate its effectiveness and efficiency.Comment: Proceedings of ACM CIKM 2001, the Tenth International Conference on Information and Knowledge Management, 200

Electronic Tuning of Mixed Quinoidal‐Aromatic Conjugated Polyelectrolytes: Direct Ionic Substitution on Polymer Main‐Chains

The synthesis of conjugated polymers with ionic substituents directly bound to their main chain repeat units is a strategy for generating strongly electron-accepting conjugated polyelectrolytes, as demonstrated through the synthesis of a series of ionic azaquinodimethane (iAQM) compounds. The introduction of cationic substituents onto the quinoidal para-azaquinodimethane (AQM) core gives rise to a strongly electron-accepting building block, which can be employed in the synthesis of ionic small molecules and conjugated polyelectrolytes (CPEs). Electrochemical measurements alongside theoretical calculations indicate notably low-lying LUMO values for the iAQMs. The optical band gaps measured for these compounds are highly tunable based on structure, ranging from 2.30 eV in small molecules down to 1.22 eV in polymers. The iAQM small molecules and CPEs showcase the band gap reduction effects of combining the donor-acceptor strategy with the bond-length alternation reduction strategy. As a demonstration of their utility, the iAQM CPEs so generated were used as active agents in photothermal therapy

Fully Quantum Approach to Optomechanical Entanglement

The radiation pressure induced coupling between an optical cavity field and a mechanical oscillator can create entanglement between them. In previous works this entanglement was treated as that of the quantum fluctuations of the cavity and mechanical modes around their classical mean values. Here we provide a fully quantum approach to optomechanical entanglement, which goes beyond the approximation of classical mean motion plus quantum fluctuation, and applies to arbitrary cavity drive. We illustrate the real-time evolution of optomechanical entanglement under drive of arbitrary detuning to show the existence of high, robust and stable entanglement in blue detuned regime, and highlight the quantum noise effects that can cause entanglement sudden death and revival.Comment: 10 pages, 5 figure