General dissipation coefficient in low-temperature warm inflation

In generic particle physics models, the inflaton field is coupled to other bosonic and fermionic fields that acquire large masses during inflation and may decay into light degrees of freedom. This leads to dissipative effects that modify the inflationary dynamics and may generate a nearly-thermal radiation bath, such that inflation occurs in a warm rather than supercooled environment. In this work, we perform a numerical computation and obtain expressions for the associated dissipation coefficient in supersymmetric models, focusing on the regime where the radiation temperature is below the heavy mass threshold. The dissipation coefficient receives contributions from the decay of both on-shell and off-shell degrees of freedom, which are dominant for small and large couplings, respectively, taking into account the light field multiplicities. In particular, we find that the contribution from on-shell decays, although Boltzmann-suppressed, can be much larger than that of virtual modes, which is bounded by the validity of a perturbative analysis. This result opens up new possibilities for realizations of warm inflation in supersymmetric field theories.Comment: 25 pages, 13 figures; revised version with new results added; published in JCA

Neutrino quasinormal modes of the Reissner-Nordstr\"om black hole

The neutrino quasinormal modes of the Reissner-Nordstr\"om (RN) black hole are investigated using continued fraction approach. We find, for large angular quantum number, that the quasinormal frequencies become evenly spaced and the spacing of the real part depends on the charge of the black hole and that of the imaginary part is zero. We then find that the quasinormal frequencies in the complex $\omega$ plane move counterclockwise as the charge increases. They get a spiral-like shape, moving out of their Schwarzschild value and ``looping in" towards some limiting frequency as the charge tends to the extremal value. The number of the spirals increases as the overtone number increases but it decreases as the angular quantum number increases. We also find that both the real and imaginary parts are oscillatory functions of the charge, and the oscillation becomes faster as the overtone number increases but it becomes slower as the angular quantum number increases.Comment: 11 pages, 3 figure

Multiscale analysis of re-entrant production lines: An equation-free approach

The computer-assisted modeling of re-entrant production lines, and, in particular, simulation scalability, is attracting a lot of attention due to the importance of such lines in semiconductor manufacturing. Re-entrant flows lead to competition for processing capacity among the items produced, which significantly impacts their throughput time (TPT). Such production models naturally exhibit two time scales: a short one, characteristic of single items processed through individual machines, and a longer one, characteristic of the response time of the entire factory. Coarse-grained partial differential equations for the spatio-temporal evolution of a "phase density" were obtained through a kinetic theory approach in Armbruster et al. [2]. We take advantage of the time scale separation to directly solve such coarse-grained equations, even when we cannot derive them explicitly, through an equation-free computational approach. Short bursts of appropriately initialized stochastic fine-scale simulation are used to perform coarse projective integration on the phase density. The key step in this process is lifting: the construction of fine-scale, discrete realizations consistent with a given coarse-grained phase density field. We achieve this through computational evaluation of conditional distributions of a "phase velocity" at the limit of large item influxes.Comment: 14 pages, 17 figure

On Horadam Sequences with Dense Orbits and Pseudo-Random Number Generators

Horadam sequence is a general recurrence of second order in the complex plane, depending on four complex parameters (two initial values and two recurrence coefficients). These sequences have been investigated over more than 60 years, but new properties and applications are still being discovered. Small parameter variations may dramatically impact the sequence orbits, generating numerous patterns: periodic, convergent, divergent, or dense within one dimensional curves. Here we explore Horadam sequences whose orbit is dense within a 2D region of the complex plane, while the complex argument is uniformly distributed in an interval. This enables the design of a pseudo-random number generator (PRNG) for the uniform distribution, for which we test periodicity, correlation, Monte Carlo estimation of π, and the NIST battery of tests. We then calculate the probability distribution of the radii of the sequence terms of Horadam sequences. Finally, we propose extensions of these results for generalized Horadam sequences of third order

The CMB Bispectrum

We use a separable mode expansion estimator with WMAP data to estimate the bispectrum for all the primary families of non-Gaussian models. We review the late-time mode expansion estimator methodology which can be applied to any non-separable primordial and CMB bispectrum model, and we demonstrate how the method can be used to reconstruct the CMB bispectrum from an observational map. We extend the previous validation of the general estimator using local map simulations. We apply the estimator to the coadded WMAP 5-year data, reconstructing the WMAP bispectrum using $l<500$ multipoles and $n=31$ orthonormal 3D eigenmodes. We constrain all popular nearly scale-invariant models, ensuring that the theoretical bispectrum is well-described by a convergent mode expansion. Constraints from the local model \fnl=54.4\pm 29.4 and the equilateral model \fnl=143.5\pm 151.2 (\Fnl = 25.1\pm 26.4) are consistent with previously published results. (Here, we use a nonlinearity parameter \Fnl normalised to the local case, to allow more direct comparison between different models.) Notable new constraints from our method include those for the constant model \Fnl = 35.1 \pm 27.4 , the flattened model \Fnl = 35.4\pm 29.2, and warm inflation \Fnl = 10.3\pm 27.2. We investigate feature models surveying a wide parameter range in both the scale and phase, and we find no significant evidence of non-Gaussianity in the models surveyed. We propose a measure \barFnl for the total integrated bispectrum and find that the measured value is consistent with the null hypothesis that CMB anisotropies obey Gaussian statistics. We argue that this general bispectrum survey with the WMAP data represents the best evidence for Gaussianity to date and we discuss future prospects, notably from the Planck satellite

Projective and Coarse Projective Integration for Problems with Continuous Symmetries

Temporal integration of equations possessing continuous symmetries (e.g. systems with translational invariance associated with traveling solutions and scale invariance associated with self-similar solutions) in a ``co-evolving'' frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with the evolving solution) leads to improved accuracy because of the smaller time derivative in the new spatial frame. The slower time behavior permits the use of {\it projective} and {\it coarse projective} integration with longer projective steps in the computation of the time evolution of partial differential equations and multiscale systems, respectively. These methods are also demonstrated to be effective for systems which only approximately or asymptotically possess continuous symmetries. The ideas of projective integration in a co-evolving frame are illustrated on the one-dimensional, translationally invariant Nagumo partial differential equation (PDE). A corresponding kinetic Monte Carlo model, motivated from the Nagumo kinetics, is used to illustrate the coarse-grained method. A simple, one-dimensional diffusion problem is used to illustrate the scale invariant case. The efficiency of projective integration in the co-evolving frame for both the macroscopic diffusion PDE and for a random-walker particle based model is again demonstrated

Compound basis arising from the basic A1(1)A^{(1)}_{1}-module

A new basis for the polynomial ring of infinitely many variables is constructed which consists of products of Schur functions and Q-functions. The transition matrix from the natural Schur function basis is investigated.Comment: 12 page

Magnetic Field Trapping High-T_c Superconductors

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Warming up for Planck

The recent Planck results and future releases on the horizon present a key opportunity to address a fundamental question in inflationary cosmology of whether primordial density perturbations have a quantum or thermal origin, i.e. whether particle production may have significant effects during inflation. Warm inflation provides a natural arena to address this issue, with interactions between the scalar inflaton and other degrees of freedom leading to dissipative entropy production and associated thermal fluctuations. In this context, we present relations between CMB observables that can be directly tested against observational data. In particular, we show that the presence of a thermal bath warmer than the Hubble scale during inflation decreases the tensor-to-scalar ratio with respect to the conventional prediction in supercooled inflation, yielding $r< 8|n_t|$, where $n_t$ is the tensor spectral index. Focusing on supersymmetric models at low temperatures, we determine consistency relations between the observables characterizing the spectrum of adiabatic scalar and tensor modes, both for generic potentials and particular canonical examples, and which we compare with the WMAP and Planck results. Finally, we include the possibility of producing the observed baryon asymmetry during inflation through dissipative effects, thereby generating baryon isocurvature modes that can be easily accommodated by the Planck data.Comment: 14 pages, 10 figures. Published in JCA

Non-Gaussianity from false vacuum inflation: Old curvaton scenario

We calculate the three-point correlation function of the comoving curvature perturbation generated during an inflationary epoch driven by false vacuum energy. We get a novel false vacuum shape bispectrum, which peaks in the equilateral limit. Using this result, we propose a scenario which we call "old curvaton". The shape of the resulting bispectrum lies between the local and the false vacuum shapes. In addition we have a large running of the spectral index.Comment: 13 pages, 3 figures; v2 with minor revison; v3 final version to appear on JCA