Large Fourier transforms never exactly realized by braiding conformal blocks

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set \{\U(2), \textrm{CNOT}\}, the discrete Fourier transforms $F_N=(\omega^{ij})_{N\times N},i,j=0,1,..., N-1, \omega=e^{\frac{2\pi i}{N}}$, can be realized exactly by quantum circuits of size $O(n^2), n=\textrm{log}N$, and so can the discrete sine/cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms $F_N$ and the discrete sine/cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that approximation is unavoidable to implement the Fourier transforms by braiding conformal blocks

Seeing a c-theorem with holography

There is no known model in holography exhibiting a $c$-theorem where the central charges of the dual CFT are distinct. We examine a holographic model of RG flows in a framework where the bulk gravity theory contains higher curvature terms. The latter allows us to distinguish the flow of the central charges $a$ and $c$ in the dual field theories in four dimensions. One finds that the flow of $a$ is naturally monotonic but that of $c$ is not. Extending the analysis of holographic RG flows to higher dimensions, we are led to formulate a novel c-theorem in arbitrary dimensions for a universal coefficient appearing in the entanglement entropy of the fixed point CFT's.Comment: 5 pages, 1 figure, v2: minor change

Entanglement, fidelity and topological entropy in a quantum phase transition to topological order

We present a numerical study of a quantum phase transition from a spin-polarized to a topologically ordered phase in a system of spin-1/2 particles on a torus. We demonstrate that this non-symmetry-breaking topological quantum phase transition (TOQPT) is of second order. The transition is analyzed via the ground state energy and fidelity, block entanglement, Wilson loops, and the recently proposed topological entropy. Only the topological entropy distinguishes the TOQPT from a standard QPT, and remarkably, does so already for small system sizes. Thus the topological entropy serves as a proper order parameter. We demonstrate that our conclusions are robust under the addition of random perturbations, not only in the topological phase, but also in the spin polarized phase and even at the critical point.Comment: replaced with published versio

Three flavour Quark matter in chiral colour dielectric model

We investigate the properties of quark matter at finite density and temperature using the nonlinear chiral extension of Colour Dielectric Model (CCM). Assuming that the square of the meson fields devlop non- zero vacuum expectation value, the thermodynamic potential for interacting three flavour matter has been calculated. It is found that $$and$$ remain zero in the medium whereas $$ changes in the medium. As a result, $u$ and $d$ quark masses decrease monotonically as the temperature and density of the quark matter is increased.In the present model, the deconfinement density and temperature is found to be lower compared to lattice results. We also study the behaviour of pressure and energy density above critical temperature.Comment: Latex file. 5 figures available on request. To appear in Phys. Rev.

Regular and Irregular Boundary Conditions in the AdS/CFT Correspondence

We expand on Klebanov and Witten's recent proposal for formulating the AdS/CFT correspondence using irregular boundary conditions. The proposal is shown to be correct to any order in perturbation theory.Comment: 7 pages, typos correcte

Half-Life of 14^{14}O

We have measured the half-life of $^{14}$O, a superallowed $(0^{+} \to 0^{+})$ $\beta$ decay isotope. The $^{14}$O was produced by the $^{12}$C($^{3}$He,n)$^{14}$O reaction using a carbon aerogel target. A low-energy ion beam of $^{14}$O was mass separated and implanted in a thin beryllium foil. The beta particles were counted with plastic scintillator detectors. We find $t_{1/2} = 70.696\pm 0.052$ s. This result is $1.5\sigma$ higher than an average value from six earlier experiments, but agrees more closely with the most recent previous measurement.Comment: 10 pages, 5 figure

HST-NICMOS Observations of M31's Metal Rich Globular Clusters and Their Surrounding Fields: I. Techniques

We have obtained HST-NICMOS observations of five of M31's most metal rich globular clusters. These data allow photometry of individual stars in the clusters and their surrounding fields. However, to achieve our goals -- obtain accurate luminosity functions to compare with their Galactic counterparts, determine metallicities from the slope of the giant branch, identify long period variables, and estimate ages from the AGB tip luminosity, we must be able to disentangle the true properties of the population from the observational effects associated with measurements made in very crowded fields. In this paper we present a careful analysis of photometry in crowded regions, and show how image blending affects the results and interpretation of such data. Although this analysis is specifically for our NICMOS observations in M31, the techniques we develop can be applied to any imaging data taken in crowded fields; we show how the effects of image blending will even limit NGST. We use three different techniques to analyze the effects of crowding on our data, including the insertion of artificial stars (traditional completeness tests) and the creation of completely artificial clusters. They are used to derive threshold- and critical-blending radii for each cluster, which determine how close to the cluster center reliable photometry can be achieved. The simulations also allow us to quantify and correct for the effects of blending on the slope and width of the RGB at different surface brightness levels.Comment: AAS LaTeX v5.0, 18 pages. Submitted to the A

Atmospheric, Evolutionary, and Spectral Models of the Brown Dwarf Gliese 229 B

Theoretical spectra and evolutionary models that span the giant planet--brown dwarf continuum have been computed based on the recent discovery of the brown dwarf, Gliese 229 B. A flux enhancement in the 4--5 micron window is a universal feature from Jovian planets to brown dwarfs. We confirm the existence of methane and water in Gl 229 B's spectrum and find its mass to be 30 to 55 Jovian masses. Although these calculations focus on Gliese 229 B, they are also meant to guide future searches for extra-solar giant planets and brown dwarfs.Comment: 8 pages, plain TeX, plus four postscript figures, gzipped and uuencoded, accepted for Scienc