Comment on τ\tau decay puzzle

We analize the current data on $\tau$-lepton decays and show that they are consistent with the Standard ModelComment: 5 pages, 1 figure (available from de authors), Latex, preprint IFT-P.022/9

Neutrix Calculus and Finite Quantum Field Theory

In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT,obtaining finite renormalizations. While none of the physically measurable results in renormalizable QFT is changed, quantum gravity is rendered more manageable in the neutrix framework.Comment: 10 pages; LaTeX; version to appear in J. Phys. A: Math. Gen. as a Letter to the Edito

Faster Base64 Encoding and Decoding Using AVX2 Instructions

Web developers use base64 formats to include images, fonts, sounds and other resources directly inside HTML, JavaScript, JSON and XML files. We estimate that billions of base64 messages are decoded every day. We are motivated to improve the efficiency of base64 encoding and decoding. Compared to state-of-the-art implementations, we multiply the speeds of both the encoding (~10x) and the decoding (~7x). We achieve these good results by using the single-instruction-multiple-data (SIMD) instructions available on recent Intel processors (AVX2). Our accelerated software abides by the specification and reports errors when encountering characters outside of the base64 set. It is available online as free software under a liberal license.Comment: software at https://github.com/lemire/fastbase6

Spatial search by quantum walk

Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log N) for d=2. We consider an alternative search algorithm based on a continuous time quantum walk on a graph. The case of the complete graph gives the continuous time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup.Comment: v2: 12 pages, 4 figures; published version, with improved arguments for the cases where the algorithm fail

A novel heteroditopic terpyridine-pincer ligand as building block for mono- and heterometallic Pd(II) and Ru(II) complexes

A palladium-catalyzed Stille coupling reaction was employed as a versatile method for the synthesis of a novel terpyridine-pincer (3, TPBr) bridging ligand, 4'-{4-BrC6H2(CH2NMe2)(2)-3,5}-2,2':6',2 ''-terpyridine. Mononuclear species [PdX(TP)] (X = Br, Cl), [Ru(TPBr)(tpy)](PF6)(2), and [Ru(TPBr)(2)](PF6)(2), synthesized by selective metalation of the NCNBr-pincer moiety or complexation of the terpyridine of the bifunctional ligand TPBr, were used as building blocks for the preparation of heterodi- and trimetallic complexes [Ru(TPPdCl)(tpy)](PF6)(2) (7) and [Ru(TPPdCl)(2)]-(PF6)(2) (8). The molecular structures in the solid state of [PdBr(TP)] (4a) and [Ru(TPBr)(2)](PF6)(2) (6) have been determined by single-crystal X-ray analysis. Electrochemical behavior and photophysical properties of the mono-and heterometallic complexes are described. All the above di- and trimetallic Ru complexes exhibit absorption bands attributable to (MLCT)-M-1 (Ru -> tpy) transitions. For the heteroleptic complexes, the transitions involving the unsubstituted tpy ligand are at a lower energy than the tpy moiety of the TPBr ligand. The absorption bands observed in the electronic spectra for TPBr and [PdCl(TP)] have been assigned with the aid of TD-DFT calculations. All complexes display weak emission both at room temperature and in a butyronitrile glass at 77 K. The considerable red shift of the emission maxima relative to the signal of the reference compound [Ru(tpy)(2)](2+) indicates stabilization of the luminescent (MLCT)-M-3 state. For the mono- and heterometallic complexes, electrochemical and spectroscopic studies (electronic absorption and emission spectra and luminescence lifetimes recorded at room temperature and 77 K in nitrile solvents), together with the information gained from IR spectroelectrochemical studies of the dimetallic complex [Ru(TPPdSCN)(tpy)](PF6)(2), are indicative of charge redistribution through the bridging ligand TPBr. The results are in line with a weak coupling between the {Ru(tpy)(2)} chromophoric unit and the (non)metalated NCN-pincer moiety

Universal four-component Fermi gas in one dimension

A four-component Fermi gas in one dimension with a short-range four-body interaction is shown to exhibit a one-dimensional analog of the BCS-BEC crossover. Its low-energy physics is governed by a Tomonaga-Luttinger liquid with three spin gaps. The spin gaps are exponentially small in the weak coupling (BCS) limit where they arise from the charge-density-wave instability, and become large in the strong coupling (BEC) limit because of the formation of tightly-bound tetramers. We investigate the ground-state energy, the sound velocity, and the gap spectrum in the BCS-BEC crossover and discuss exact relationships valid in our system. We also show that a one-dimensional analog of the Efimov effect occurs for five bosons while it is absent for fermions. Our work opens up a very rich new field of universal few-body and many-body physics in one dimension.Comment: 9 pages, 3 figures; (v2) Efimov effect for 5 bosons in 1D is discussed; (v3) expanded versio

On SIC-POVMs in Prime Dimensions

The generalized Pauli group and its normalizer, the Clifford group, have a rich mathematical structure which is relevant to the problem of constructing symmetric informationally complete POVMs (SIC-POVMs). To date, almost every known SIC-POVM fiducial vector is an eigenstate of a "canonical" unitary in the Clifford group. I show that every canonical unitary in prime dimensions p > 3 lies in the same conjugacy class of the Clifford group and give a class representative for all such dimensions. It follows that if even one such SIC-POVM fiducial vector is an eigenvector of such a unitary, then all of them are (for a given such dimension). I also conjecture that in all dimensions d, the number of conjugacy classes is bounded above by 3 and depends only on d mod 9, and I support this claim with computer computations in all dimensions < 48.Comment: 6 pages, no figures. v3 Refs added, improved discussion of previous work. Ref to a proof of the main conjecture also adde

Optimal parametrizations of adiabatic paths

The parametrization of adiabatic paths is optimal when tunneling is minimized. Hamiltonian evolutions do not have unique optimizers. However, dephasing Lindblad evolutions do. The optimizers are simply characterized by an Euler-Lagrange equation and have a constant tunneling rate along the path irrespective of the gap. Application to quantum search algorithms recovers the Grover result for appropriate scaling of the dephasing. Dephasing rates that beat Grover imply hidden resources in Lindblad operators.Comment: 4 pages, 2 figures; To prevent from misunderstanding, we clarified the discussion of an apparent speedup in the Grover algorithm; figures improved + minor change

The Puzzling Mutual Orbit of the Binary Trojan Asteroid (624) Hektor

Asteroids with satellites are natural laboratories to constrain the formation and evolution of our solar system. The binary Trojan asteroid (624) Hektor is the only known Trojan asteroid to possess a small satellite. Based on W.M. Keck adaptive optics observations, we found a unique and stable orbital solution, which is uncommon in comparison to the orbits of other large multiple asteroid systems studied so far. From lightcurve observations recorded since 1957, we showed that because the large Req=125-km primary may be made of two joint lobes, the moon could be ejecta of the low-velocity encounter, which formed the system. The inferred density of Hektor's system is comparable to the L5 Trojan doublet (617) Patroclus but due to their difference in physical properties and in reflectance spectra, both captured Trojan asteroids could have a different composition and origin.Comment: 13 pages, 3 figures, 2 table