AdS/CFT Correspondence and Quotient Space Geometry

We consider a version of the $AdS_{d+1}/CFT_{d}$ correspondence, in which the bulk space is taken to be the quotient manifold $AdS_{d+1} /\Gamma$ with a fairly generic discrete group $\Gamma$ acting isometrically on $AdS_{d+1}$. We address some geometrical issues concerning the holographic principle and the UV/IR relations. It is shown that certain singular structures on the quotient boundary ${\bf S}^{d}/\Gamma$ can affect the underlying physical spectrum. In particular, the conformal dimension of the most relevant operators in the boundary CFT can increase as $\Gamma$ becomes ``large''. This phenomenon also has a natural explanation in terms of the bulk supergravity theory. The scalar two-point function is computed using this quotient version of the AdS/CFT correspondence, which agrees with the expected result derived from conformal invariance of the boundary theory.Comment: 28 pages, Latex, no figures. Minor changes, version to appear in JHE

Optical spectroscopy of molecular junctions: Nonequilibrium Green's functions perspective

We consider optical spectroscopy of molecular junctions from the quantum transport perspective when radiation field is quantized and optical response of the system is simulated as photon flux. Using exact expressions for photon and electronic fluxes derived within the nonequilibrium Green function (NEGF) methodology and utilizing fourth order diagrammatic perturbation theory in molecular coupling to radiation field we perform simulations employing realistic parameters. Results of the simulations are compared to the bare perturbation theory (PT) usually employed in studies on nonlinear optical spectroscopy to classify optical processes. We show that the bare PT violates conservation laws, while flux conserving NEGF formulation mixes optical processes.Comment: 10 pages, 6 figure

Simulation of optical response functions in molecular junctions

We discuss theoretical approaches to nonlinear optical spectroscopy of molecular junctions. Optical response functions are derived in the form convenient for implementation of Green function techniques, and their expressions in terms of pseudoparticle nonequilibrium Green functions are proposed. The formulation allows to account for both intra-molecular interactions and hybridization of molecular states due to coupling to contacts. Two-dimensional optical spectroscopy in junctions is considered as an example.Comment: 11 pages, 7 figure

Global Solutions to Nonconvex Optimization of 4th-Order Polynomial and Log-Sum-Exp Functions

This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of fourth-order polynomial and a log-sum-exp function. Such a problem arises extensively in engineering and sciences. Based on the canonical duality-triality theory, this nonconvex problem is transformed to an equivalent dual problem, which can be solved easily under certain conditions. We proved that both global minimizer and the biggest local extrema of the primal problem can be obtained analytically from the canonical dual solutions. As two special cases, a quartic polynomial minimization and a minimax problem are discussed. Existence conditions are derived, which can be used to classify easy and relative hard instances. Applications are illustrated by several nonconvex and nonsmooth examples

Scope and Mechanistic Investigations on the Solvent-Controlled Regio- and Stereoselective Formation of Enol Esters from the Ruthenium-Catalyzed Coupling Reaction of Terminal Alkynes and Carboxylic Acids

The ruthenium-hydride complex (PCy3)2(CO)RuHCl was found to be a highly effective catalyst for the alkyne-to-carboxylic acid coupling reaction to give synthetically useful enol ester products. A strong solvent effect was observed for the ruthenium catalyst in modulating the activity and selectivity; the coupling reaction in CH2Cl2 led to the regioselective formation of gem-enol ester products, while the stereoselective formation of (Z)-enol esters was obtained in THF. The coupling reaction was found to be strongly inhibited by PCy3. The coupling reaction of both PhCO2H/PhC≡CD and PhCO2D/PhC≡CH led to extensive deuterium incorporation on the vinyl positions of the enol ester products. An opposite Hammett value was observed when the correlation of a series of para-substituted p-X-C6H4CO2H (X = OMe, CH3, H, CF3, CN) with phenylacetylene was examined in CDCl3 (ρ = +0.30) and THF (ρ = −0.68). Catalytically relevant Ru-carboxylate and -vinylidene-carboxylate complexes, (PCy3)2(CO)(Cl)Ru(κ2-O2CC6H4-p-OMe) and (PCy3)2(CO)(Cl)RuC(═CHPh)O2CC6H4-p-OMe, were isolated, and the structure of both complexes was completely established by X-ray crystallography. A detailed mechanism of the coupling reaction involving a rate-limiting C−O bond formation step was proposed on the basis of these kinetic and structural studies. The regioselective formation of the gem-enol ester products in CH2Cl2 was rationalized by a direct migratory insertion of the terminal alkyne via a Ru-carboxylate species, whereas the stereoselective formation of (Z)-enol ester products in THF was explained by invoking a Ru-vinylidene species