New Results in Sasaki-Einstein Geometry

This article is a summary of some of the author's work on Sasaki-Einstein geometry. A rather general conjecture in string theory known as the AdS/CFT correspondence relates Sasaki-Einstein geometry, in low dimensions, to superconformal field theory; properties of the latter are therefore reflected in the former, and vice versa. Despite this physical motivation, many recent results are of independent geometrical interest, and are described here in purely mathematical terms: explicit constructions of infinite families of both quasi-regular and irregular Sasaki-Einstein metrics; toric Sasakian geometry; an extremal problem that determines the Reeb vector field for, and hence also the volume of, a Sasaki-Einstein manifold; and finally, obstructions to the existence of Sasaki-Einstein metrics. Some of these results also provide new insights into Kahler geometry, and in particular new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.Comment: 31 pages, no figures. Invited contribution to the proceedings of the conference "Riemannian Topology: Geometric Structures on Manifolds"; minor typos corrected, reference added; published version; Riemannian Topology and Geometric Structures on Manifolds (Progress in Mathematics), Birkhauser (Nov 2008

Energy properness and Sasakian-Einstein metrics

In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition that admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type inequality. At the end of this paper, we also obtain a Miyaoka-Yau type inequality in Sasakian geometry.Comment: 27 page

Patterns on liquid surfaces: cnoidal waves, compactons and scaling

Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated . Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are discused. A finite-difference differential generalized Korteweg-de Vries equation is shown to describe the three-dimensional motion of the fluid surface and the limit of long and shallow channels one reobtains the well known KdV equation. A tentative expansion formula for the representation of the general solution of a nonlinear equation, for given initial condition is introduced on a graphical-algebraic basis. The model is useful in multilayer fluid dynamics, cluster formation, and nuclear physics since, up to an overall scale, these systems display liquid free surface behavior.Comment: 14 pages RevTex, 5 figures in p

Ultrafast Optical Spectroscopy of Micelle-Suspended Single-Walled Carbon Nanotubes

We present results of wavelength-dependent ultrafast pump-probe experiments on micelle-suspended single-walled carbon nanotubes. The linear absorption and photoluminescence spectra of the samples show a number of chirality-dependent peaks, and consequently, the pump-probe results sensitively depend on the wavelength. In the wavelength range corresponding to the second van Hove singularities (VHSs), we observe sub-picosecond decays, as has been seen in previous pump-probe studies. We ascribe these ultrafast decays to intraband carrier relaxation. On the other hand, in the wavelength range corresponding to the first VHSs, we observe two distinct regimes in ultrafast carrier relaxation: fast (0.3-1.2 ps) and slow (5-20 ps). The slow component, which has not been observed previously, is resonantly enhanced whenever the pump photon energy resonates with an interband absorption peak, and we attribute it to radiative carrier recombination. Finally, the slow component is dependent on the pH of the solution, which suggests an important role played by H$^+$ ions surrounding the nanotubes.Comment: 6 pages, 8 figures, changed title, revised, to be published in Applied Physics

New checks and subtleties for AdS/CFT and a-maximization

We provide a cross-check of AdS/CFT and a-charge maximization for a four dimensional $N$=1 SCFT with irrational R-charges. The gauge theory is the low energy effective theory of N D3-branes at the tip of the complex cone over the first del Pezzo surface. By carefully taking into account the subtle issue of flavor symmetry breaking at the fixed point, we show, using a-maximization, that this theory has in fact irrational central charge and R-charges. Our results perfectly match with those inherited from the recently discovered supergravity dual background. Along analogous lines, we make novel predictions for the still unknown AdS dual of the quiver theory for the second del Pezzo surface. This should flow to a SCFT with irrational charges, too. All of our results differ from previous findings in the literature and outline interesting subtleties in a-maximization and AdS/CFT techniques overlooked in the past.Comment: Latex, 16 pagex, 2 figures; v2, comments and a reference added; v3, typos correcte

Josephson-phase qubit without tunneling

We show that a complete set of one-bit gates can be realized by coupling the two logical states of a phase qubit to a third level (at higher energy) using microwave pulses. Thus, one can achieve coherent control without invoking any tunneling between the qubit levels. We propose two implementations, using rf-SQUIDs and d-wave Josephson junctions.Comment: REVTeX4, 4pp., 6 EPS figure files; N.B.: "Alec" is my first, and "Maassen van den Brink" my family name. v2: gate universality fleshed out, small fix in d-wave decoherence para, discussion expanded, two Refs. added. v3: some more Refs., a molecular example, and a few minor fixes; final, to appear in PRB Rapid

Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations

We study the distributions of traveling length l and minimal traveling time t through two-dimensional percolation porous media characterized by long-range spatial correlations. We model the dynamics of fluid displacement by the convective movement of tracer particles driven by a pressure difference between two fixed sites (''wells'') separated by Euclidean distance r. For strongly correlated pore networks at criticality, we find that the probability distribution functions P(l) and P(t) follow the same scaling Ansatz originally proposed for the uncorrelated case, but with quite different scaling exponents. We relate these changes in dynamical behavior to the main morphological difference between correlated and uncorrelated clusters, namely, the compactness of their backbones. Our simulations reveal that the dynamical scaling exponents for correlated geometries take values intermediate between the uncorrelated and homogeneous limiting cases

Modeling realistic Earth matter density for CP violation in neutrino oscillation

We examine the effect of a more realistic Earth matter density model which takes into account of the local density variations along the baseline of a possi ble 2100 km very long baseline neutrino oscillation experiment. Its influence to the measurement of CP violation is investigated and a comparison with the commonly used global density models made. Significant differences are found in the comparison of the results of the different density models.Comment: 16 pages, 8 figure