Heat-kernel Coefficients and Spectra of the Vector Laplacians on Spherical Domains with Conical Singularities

The spherical domains $S^d_\beta$ with conical singularities are a convenient arena for studying the properties of tensor Laplacians on arbitrary manifolds with such a kind of singular points. In this paper the vector Laplacian on $S^d_\beta$ is considered and its spectrum is calculated exactly for any dimension $d$. This enables one to find the Schwinger-DeWitt coefficients of this operator by using the residues of the $\zeta$-function. In particular, the second coefficient, defining the conformal anomaly, is explicitly calculated on $S^d_\beta$ and its generalization to arbitrary manifolds is found. As an application of this result, the standard renormalization of the one-loop effective action of gauge fields is demonstrated to be sufficient to remove the ultraviolet divergences up to the first order in the conical deficit angle.Comment: plain LaTeX, 23 pp., revised version, a misprint in expressions (1.8) and (4.38) of the second heat coefficient for the vector Laplacian is corrected. No other change

Simulation of static and random errors on Grover's search algorithm implemented in a Ising nuclear spin chain quantum computer with few qubits

We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first and second neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations of the external fields. By averaging over many repetitions of the algorithm, the output state becomes effectively a mixed state. We study its overlap with the nominal output state of the algorithm, which is called fidelity. We find either an exponential or a Gaussian decay for the fidelity as a function of the strength of the noise, depending on the type of noise (static or random) and whether error supression is applied (the 2pi k-method) or not.Comment: 18 pages, 8 figures, extensive revision with new figure

Heterotic Compactification, An Algorithmic Approach

We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in heterotic compactifications. This is done in the context of complete intersection Calabi-Yau manifolds in a single projective space where we classify positive monad bundles. Using a combination of analytic methods and computer algebra we prove stability for all such bundles and compute the complete particle spectrum, including gauge singlets. In particular, we find that the number of anti-generations vanishes for all our bundles and that the spectrum is manifestly moduli-dependent.Comment: 36 pages, Late

Finite Temperature Effective Potential for Gauge Models in de Sitter Space

The one-loop effective potential for gauge models in static de Sitter space at finite temperatures is computed by means of the $\zeta$--function method. We found a simple relation which links the effective potentials of gauge and scalar fields at all temperatures. In the de Sitter invariant and zero-temperature states the potential for the scalar electrodynamics is explicitly obtained, and its properties in these two vacua are compared. In this theory the two states are shown to behave similarly in the regimes of very large and very small radii a of the background space. For the gauge symmetry broken in the flat limit ($a \to \infty$) there is a critical value of a for which the symmetry is restored in both quantum states. Moreover, the phase transitions which occur at large or at small a are of the first or of the second order, respectively, regardless the vacuum considered. The analytical and numerical analysis of the critical parameters of the above theory is performed. We also established a class of models for which the kind of phase transition occurring depends on the choice of the vacuum.Comment: 23 pages, LaTeX, 5 figure.ep

Radio Spectra of Giant Radio Galaxies from RATAN-600 Data

Measurements of the flux densities of the extended components of seven giant radio galaxies obtained using the RATAN-600 radio telescope at wavelengths of 6.25 and 13 cm ar e presented. The spectra of components of these radio galaxies are constructed using these new RA TAN-600 data together with data from the WENSS, NVSS, and GB6 surveys. The spectral indices in the stu died frequency range are calculated, and the need for detailed estimates of the integrated contributi on of such objects to the background emission is demonstrated.Comment: 7 pages, 2 figures, 5 table

The Magellanic Edges Survey III. Kinematics of the disturbed LMC outskirts

We explore the structural and kinematic properties of the outskirts of the Large Magellanic Cloud (LMC) using data from the Magellanic Edges Survey (MagES) and Gaia EDR3. Even at large galactocentric radii ($8^\circ<R<11^\circ$), we find the north-eastern LMC disk is relatively unperturbed: its kinematics are consistent with a disk of inclination ~$36.5^\circ$ and line-of-nodes position angle ~$145^\circ$ east of north. In contrast, fields at similar radii in the southern and western disk are significantly perturbed from equilibrium, with non-zero radial and vertical velocities, and distances significantly in front of the disk plane implied by our north-eastern fields. We compare our observations to simple dynamical models of the Magellanic/Milky Way system which describe the LMC as a collection of tracer particles within a rigid potential, and the Small Magellanic Cloud (SMC) as a rigid Hernquist potential. A possible SMC crossing of the LMC disk plane ~400 Myr ago, in combination with the LMC's infall to the Milky Way potential, can qualitatively explain many of the perturbations in the outer disk. Additionally, we find the claw-like and arm-like structures south of the LMC have similar metallicities to the outer LMC disk ([Fe/H]~-1), and are likely comprised of perturbed LMC disk material. The claw-like substructure is particularly disturbed, with out-of-plane velocities >60 km s$^{-1}$ and apparent counter-rotation relative to the LMC's disk motion. More detailed N-body models are necessary to elucidate the origin of these southern features, potentially requiring repeated interactions with the SMC prior to ~1 Gyr ago.Comment: Accepted by MNRA

Numerical simulation of a Controlled-Controlled-Not (CCN) quantum gate in a chain of three interacting nuclear spins system

We present the study of a quantum Controlled-Controlled-Not gate, implemented in a chain of three nuclear spins weakly Ising interacting between all of them, that is, taking into account first and second neighbor spin interactions. This implementation is done using a single resonant $\pi$-pulse on the initial state of the system (digital and superposition). The fidelity parameter is used to determine the behavior of the CCN quantum gate as a function of the ratio of the second neighbor interaction coupling constant to the first neighbor interaction coupling constant ($J'/J$). We found that for $J'/J\ge 0.02$ we can have a well defined CCN quantum gate.Comment: 9 pages, 5 fugure