Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

Jacobi Identity for Vertex Algebras in Higher Dimensions

Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.Comment: 35 pages, references adde

Two regularizations - two different models of Nambu-Jona-Lasinio

Two variants of the Nambu--Jona-Lasinio model -- the model with 4-dimensional cutoff and the model with dimensionally-analytical regularization -- are systematically compared. It is shown that they are, in essence, two different models of light-quark interaction. In the mean-field approximation the distinction becomes apparent in a behavior of scalar amplitude near the threshold. For 4-dimensional cutoff the pole term can be extracted, which corresponds to sigma-meson. For dimensionally-analytical regularization the singularity of the scalar amplitude is not pole, and this singularity is quite disappeared at some value of the regularization parameter. Still more essential distinction of these models exists in the next-to-leading order of mean-field expansion. The calculations of meson contributions in the quark chiral condensate and in the dynamical quark mass demonstrate, that these contributions though their relatively smallness can destabilize the Nambu--Jona-Lasinio model with 4-dimensional cutoff. On the contrary, the Nambu--Jona-Lasinio model with dimensionally-analytical regularization is stabilized with the next-to-leading order, i.e. the value of the regularization parameter shifts to the stability region, where these contributions decrease.Comment: 14 pages; Journal version; parameter fixing procedure is modifie

Randomized Benchmarking using Non-Destructive Readout in a 2D Atom Array

Neutral atoms are a promising platform for scalable quantum computing, however prior demonstration of high fidelity gates or low-loss readout methods have employed restricted numbers of qubits. Using randomized benchmarking of microwave-driven single-qubit gates, we demonstrate single qubit gate errors of $8(2)\times10^{-5}$ on 225 atoms using conventional, destructive readout. This exceeds the threshold for fault-tolerance. We further demonstrate suppression of measurement errors via low-loss, non-destructive and state-selective readout on 49 atoms. This enables post-selection for atom loss, which is a primary source of errors in present setups.Comment: 6 pages, 4 figures plus Supplementary Materia

Fibromyalgia: dental aspects

Fibromyalgia is a disease accompanied by diffuse chronic pain for >3 months and tenderness on palpation in at least 11 of 18 anatomic points (American College of Rheumatology criteria). Gnathalgia was also included in the revised fibromyalgia criteria in 2010. Some patients have facial pain spots, symptoms and signs of temporomandibular dysfunction in combination with chronic fatigue and sleep disorder. The paper presents the results of an anonymous questionnaire survey in patients with a valid diagnosis of fibromyalgia. The patients with this disease require a follow-up by a family physician, a rheumatologist, and a dentist

HST hot-Jupiter transmission spectral survey: Haze in the atmosphere of WASP-6b

We report Hubble Space Telescope (HST) optical to near-infrared transmission spectroscopy of the hot Jupiter WASP-6b, measured with the Space Telescope Imaging Spectrograph (STIS) and Spitzer's InfraRed Array Camera (IRAC). The resulting spectrum covers the range $0.29-4.5\,\mu$m. We find evidence for modest stellar activity of WASP-6b and take it into account in the transmission spectrum. The overall main characteristic of the spectrum is an increasing radius as a function of decreasing wavelength corresponding to a change of $\Delta (R_p/R_{\ast})=0.0071$ from 0.33 to $4.5\,\mu$m. The spectrum suggests an effective extinction cross-section with a power law of index consistent with Rayleigh scattering, with temperatures of $973\pm144$ K at the planetary terminator. We compare the transmission spectrum with hot-Jupiter atmospheric models including condensate-free and aerosol-dominated models incorporating Mie theory. While none of the clear-atmosphere models is found to be in good agreement with the data, we find that the complete spectrum can be described by models that include significant opacity from aerosols including Fe-poor Mg$_2$SiO$_4$, MgSiO$_3$, KCl and Na$_2$S dust condensates. WASP-6b is the second planet after HD189733b which has equilibrium temperatures near $\sim1200$ K and shows prominent atmospheric scattering in the optical.Comment: 18 pages, 15 figures, 7 table

Bose-Einstein condensation in trapped dipolar gases

We discuss Bose-Einstein condensation in a trapped gas of bosonic particles interacting dominantly via dipole-dipole forces. We find that in this case the mean-field interparticle interaction and, hence, the stability diagram are governed by the trapping geometry. Possible physical realisations include ultracold heteronuclear molecules, or atoms with laser induced electric dipole moments.Comment: 4 pages, 4 figure