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

COBE ground segment gyro calibration

Discussed here is the calibration of the scale factors and rate biases for the Cosmic Background Explorer (COBE) spacecraft gyroscopes, with the emphasis on the adaptation for COBE of an algorithm previously developed for the Solar Maximum Mission. Detailed choice of parameters, convergence, verification, and use of the algorithm in an environment where the reference attitudes are determined form the Sun, Earth, and star observations (via the Diffuse Infrared Background Experiment (DIRBE) are considered. Results of some recent experiments are given. These include tests where the gyro rate data are corrected for the effect of the gyro baseplate temperature on the spacecraft electronics

Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State

The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at Landau level filling fraction $\nu=5/2$. This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to determine the nature of the $\nu=5/2$ state, one must measure the quasiparticle braiding statistics. Here, we propose an experiment which can simultaneously determine the braiding statistics of quasiparticle excitations and, if they prove to be non-Abelian, produce a topologically-protected qubit on which a logical NOT operation is performed by quasiparticle braiding. Using the measured excitation gap at $\nu=5/2$, we estimate the error rate to be $10^{-30}$ or lower

The Three Loop Equation of State of QED at High Temperature

We present the three loop contribution (order $e^4$) to the pressure of massless quantum electrodynamics at nonzero temperature. The calculation is performed within the imaginary time formalism. Dimensional regularization is used to handle the usual, intermediate stage, ultraviolet and infrared singularities, and also to prevent overcounting of diagrams during resummation.Comment: ANL-HEP-PR-94-02, SPhT/94-054 (revised final version

Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams

It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.Comment: 6 pages, late

Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates

We construct an exactly solvable Hamiltonian acting on a 3-dimensional lattice of spin-$\frac 1 2$ systems that exhibits topological quantum order. The ground state is a string-net and a membrane-net condensate. Excitations appear in the form of quasiparticles and fluxes, as the boundaries of strings and membranes, respectively. The degeneracy of the ground state depends upon the homology of the 3-manifold. We generalize the system to $D\geq 4$, were different topological phases may occur. The whole construction is based on certain special complexes that we call colexes.Comment: Revtex4 file, color figures, minor correction

Model of ionic currents through microtubule nanopores and the lumen

It has been suggested that microtubules and other cytoskeletal filaments may act as electrical transmission lines. An electrical circuit model of the microtubule is constructed incorporating features of its cylindrical structure with nanopores in its walls. This model is used to study how ionic conductance along the lumen is affected by flux through the nanopores when an external potential is applied across its two ends. Based on the results of Brownian dynamics simulations, the nanopores were found to have asymmetric inner and outer conductances, manifested as nonlinear IV curves. Our simulations indicate that a combination of this asymmetry and an internal voltage source arising from the motion of the C-terminal tails causes a net current to be pumped across the microtubule wall and propagate down the microtubule through the lumen. This effect is demonstrated to enhance and add directly to the longitudinal current through the lumen resulting from an external voltage source, and could be significant in amplifying low-intensity endogenous currents within the cellular environment or as a nano-bioelectronic device.Comment: 43 pages, 6 figures, revised versio

Strange quark matter: mapping QCD lattice results to finite baryon density by a quasi-particle model

A quasi-particle model is presented which describes QCD lattice results for the 0, 2 and 4 quark-flavor equation of state. The results are mapped to finite baryo-chemical potentials. As an application of the model we make a prediction of deconfined matter with appropriate inclusion of strange quarks and consider pure quark stars.Comment: invited talk at Strangeness 2000, Berkeley; prepared version for the proceedings, 5 page

Explicit Character Formulae for Positive Energy UIRs of D=4 Conformal Supersymmetry

This paper continues the project of constructing the character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). In the first paper we gave the bare characters which represent the defining odd entries of the characters. Now we give the full explicit character formulae for N=1 and for several important examples for N=2 and N=4.Comment: 48 pages, TeX with Harvmac, overlap in preliminaries with arXiv:hep-th/0406154; some comments and references adde

Low-Energy Theorems for QCD at Finite Temperature and Chemical Potential

The low-energy theorems for QCD are generalized to finite temperature. and chemical potential, including non-zero quark masses.Comment: 6 pages late