On the spectrum of a matrix model for the D=11 supermembrane compactified on a torus with non-trivial winding

The spectrum of the Hamiltonian of the double compactified D=11 supermembrane with non-trivial central charge or equivalently the non-commutative symplectic super Maxwell theory is analyzed. In distinction to what occurs for the D=11 supermembrane in Minkowski target space where the bosonic potential presents string-like spikes which render the spectrum of the supersymmetric model continuous, we prove that the potential of the bosonic compactified membrane with non-trivial central charge is strictly positive definite and becomes infinity in all directions when the norm of the configuration space goes to infinity. This ensures that the resolvent of the bosonic Hamiltonian is compact. We find an upper bound for the asymptotic distribution of the eigenvalues.Comment: 11 pages, LaTe

Critical Phenomena Inside Global Monopoles

The gravitational collapse of a triplet scalar field is examined assuming a hedgehog ansatz for the scalar field. Whereas the seminal work by Choptuik with a single, strictly spherically symmetric scalar field found a discretely self-similar (DSS) solution at criticality with echoing period $\Delta=3.44$, here a new DSS solution is found with period $\Delta=0.46$. This new critical solution is also observed in the presence of a symmetry breaking potential as well as within a global monopole. The triplet scalar field model contains Choptuik's original model in a certain region of parameter space, and hence his original DSS solution is also a solution. However, the choice of a hedgehog ansatz appears to exclude the original DSS.Comment: 5 pages, 5 figure

Complete RNA inverse folding: computational design of functional hammerhead ribozymes

Nanotechnology and synthetic biology currently constitute one of the most innovative, interdisciplinary fields of research, poised to radically transform society in the 21st century. This paper concerns the synthetic design of ribonucleic acid molecules, using our recent algorithm, RNAiFold, which can determine all RNA sequences whose minimum free energy secondary structure is a user-specified target structure. Using RNAiFold, we design ten cis-cleaving hammerhead ribozymes, all of which are shown to be functional by a cleavage assay. We additionally use RNAiFold to design a functional cis-cleaving hammerhead as a modular unit of a synthetic larger RNA. Analysis of kinetics on this small set of hammerheads suggests that cleavage rate of computationally designed ribozymes may be correlated with positional entropy, ensemble defect, structural flexibility/rigidity and related measures. Artificial ribozymes have been designed in the past either manually or by SELEX (Systematic Evolution of Ligands by Exponential Enrichment); however, this appears to be the first purely computational design and experimental validation of novel functional ribozymes. RNAiFold is available at http://bioinformatics.bc.edu/clotelab/RNAiFold/.Comment: 17 pages, 2 tables, 7 figures, final version to appear in Nucleic Acids Researc

Entanglement of two qubits mediated by one-dimensional plasmonic waveguides

We investigate qubit-qubit entanglement mediated by plasmons supported by one-dimensional waveguides. We explore both the situation of spontaneous formation of entanglement from an unentangled state and the emergence of driven steady-state entanglement under continuous pumping. In both cases, we show that large values for the concurrence are attainable for qubit-qubit distances larger than the operating wavelength by using plasmonic waveguides that are currently available.Comment: 4 pages, 4 figures. Minor Changes. Journal Reference added. Highlighted in Physic

Proof of a Momentum/Complexity Correspondence

We show that the holographic Complexity = Volume proposal satisfies a very general notion of Momentum/Complexity correspondence (PC), based on the Momentum Constraint of General Relativity. It relates the rate of complexity variation with an appropriate matter momentum flux through spacelike extremal surfaces. This formalizes the intuitive idea that `gravitational clumpling' of matter increases complexity, and the required notion of `infall momentum' is shown to have a Newtonian avatar which expresses this idea. The proposed form of the PC correspondence is found to be exact for any solution of Einstein's equations in 2+1 dimensions, and any spherically symmetric solution in arbitrary dimensions, generalizing all previous calculations using spherical thin shells. Gravitational radiation enters through a correction which does not have a straightforward interpretation as a PC correspondence. Other obstructions to an exact PC duality have a topological origin and arise in the presence of wormholes.Comment: 10 pages, 2 figures. Published versio