Primordial non-Gaussianity in noncanonical warm inflation

We study the bispectrum of the primordial curvature perturbation on uniform-density hypersurfaces generated by a kind of the noncanonical warm inflation, wherein the inflation is provided by a noncanonical scalar inflaton field that is coupled to radiation through a thermal dissipation effect. We obtain an analytic form for the nonlinear parameter $f_{NL}$ that describes the non-Gaussianity in first-order cosmological perturbation theory and analyse the magnitude of this nonlinear parameter. We make a comparison between our result and those of the standard inflation and the canonical warm inflation. We also discuss when the contribution to the non-Gaussianity due to the second-order perturbation theory becomes more important and what effect can be observed. We take the Dirac-Born-Infeld (DBI) inflation as a concrete example to find how the sound speed and the thermal dissipation strength to decide the non-Gaussianity and to get a lower bound of the sound speed constrained by PLANCK.Comment: 7 pages, 2 figure

Consistency of the tachyon warm inflationary universe models

This study concerns the consistency of the tachyon warm inflationary models. A linear stability analysis is performed to find the slow-roll conditions, characterized by the potential slow-roll (PSR) parameters, for the existence of a tachyon warm inflationary attractor in the system. The PSR parameters in the tachyon warm inflationary models are redefined. Two cases, an exponential potential and an inverse power-law potential, are studied, when the dissipative coefficient $\Gamma=\Gamma_0$ and $\Gamma=\Gamma(\phi)$, respectively. A crucial condition is obtained for a tachyon warm inflationary model characterized by the Hubble slow-roll (HSR) parameter $\epsilon_{_H}$, and the condition is extendable to some other inflationary models as well. A proper number of e-folds is obtained in both cases of the tachyon warm inflation, in contrast to existing works. It is also found that a constant dissipative coefficient $(\Gamma=\Gamma_0)$ is usually not a suitable assumption for a warm inflationary model.Comment: 10 pages, 0 figures, accepted for publication in Journal of Cosmology and Astroparticle Physics (JCAP

Warm inflation in loop quantum cosmology: a model with a general dissipative coefficient

A general form of warm inflation with the dissipative coefficient $\Gamma=\Gamma_0(\phi /\phi_0) ^n(T/\tau_0) ^m$ in loop quantum cosmology is studied. In this case, we obtain conditions for the existence of a warm inflationary attractor in the context of loop quantum cosmology by using the method of stability analysis. The two cases when the dissipative coefficient is independent $(m=0)$ and dependent $(m\neq0)$ on temperature are analyzed specifically. In the latter case, we use the new power spectrum which should be used when considering temperature dependence in the dissipative coefficient. We find that the thermal effect is enhanced in the case $m>0$. As in the standard inflation in loop quantum cosmology, we also reach the conclusion that quantum effect leaves a tiny imprint on the cosmic microwave background (CMB) sky.Comment: 12 pages, accepted for publication in Rhys. Rev.

Triply-resonant Optical Parametric Oscillator by Four-wave Mixing with Rubidium Vapor inside an Optical Cavity

We present an experimental demonstration of simultaneous above-threshold oscillations of the Stokes and anti-Stokes fields together with the single pumping beam with rubidium atoms inside an optical standing-wave cavity. The triple resonant conditions can be achieved easily by making use of the large dispersions due to two-photon transitions in the three-level atomic system. This work provides a way to achieve high efficient nonlinear frequency conversion and the generated bright Stokes and anti-Stokes cavity output beams are potential resource for applications in quantum information science.Comment: Appear in Appl. Phys. Let

Cyclic permutation-time symmetric structure with coupled gain-loss microcavities

We study the coupled even number of microcavities with the balanced gain and loss between any pair of their neighboring components. The effective non-Hermitian Hamiltonian for such structure has the cyclic permutation-time symmetry with respect to the cavity modes, and this symmetry determines the patterns of the dynamical evolutions of the cavity modes. The systems also have multiple exceptional points for the degeneracy of the existing supermodes, exhibiting the "phase transition" of system dynamics across these exceptional points. We illustrate the quantum dynamical properties of the systems with the evolutions of cavity photon numbers and correlation functions. Moreover, we demonstrate the effects of the quantum noises accompanying the amplification and dissipation of the cavity modes. The reciprocal light transportation predicted with the effective non-Hermitian models for the similar couplers is violated by the unavoidable quantum noises.Comment: The version to be published, 8 pages, 6 figure

The Maximum Wiener Index of Trees with Given Degree Sequences

The Wiener index of a connected graph is the sum of topological distances between all pairs of vertices. Since Wang gave a mistake result on the maximum Wiener index for given tree degree sequence, in this paper, we investigate the maximum Wiener index of trees with given degree sequences and extremal trees which attain the maximum value.Comment: 19 pages, 2 figure

Observational Constraints on Two-field Warm Inflation

We study the two-field warm inflation models with a double quadratic potential and a linear temperature dependent dissipative coefficient. We derived the evolution equation of all kinds of perturbations without assuming slow-roll approximation, and obtained the curvature power spectrum at the end of inflation with a fully numerical method. Then we compute the scalar spectral index $n_s$, tensor-to-scalar ratio $r$ for several representative potentials, and compare our results with observational data. At last, we use Planck data to constrain the parameters in our models. This work is a natural extension of single-field warm inflation, and the aim of this work is to present some features of multi-field warm inflation using a simple two-field model.Comment: 13 pages, 6 figures. Accepted for publication in Physical Review

New face-centered photonic square lattices with flat bands

We report two new classes of face-centered photonic square lattices with flat bands which we call the Lieb-I and the Lieb-II lattices. There are 5 and 7 sites in the corresponding unit cells of the simplest Lieb-I and Lieb-II lattices, respectively. The number of flat bands $m$ in the new Lieb lattices is related to the number of sites $N$ in the unit cell by $m=(N-1)/2$. Physical properties of the lattices with even and odd number of flat bands are different. We also consider localization of light in such Lieb lattices. If the input beam excites the flat-band mode, it will not diffract during propagation, owing to the strong localization in the flat-band mode. For the Lieb-II lattice, we also find that the beam will oscillate and still not diffract during propagation, because of the intrinsic oscillating properties of certain flat-band modes. The period of oscillation is determined by the energy difference between the two flat bands. This study provides a new platform for the investigation of flat-band modes.Comment: 9 pages, 4 figures, comments and criticisms are welcom

Two-field Warm Inflation and Its Scalar Perturbations on Large Scales

We explore the homogeneous background dynamics and the evolution of generated perturbations of cosmological inflation that is driven by multiple scalar fields interacting with a perfect fluid.Then we apply the method to warm inflation driven by two scalar fields and a radiation fluid, and present general results about the evolution of the inflaton and radiation. After decomposing the perturbations into adiabatic and entropy modes, we give the equation of motion of adiabatic and entropy perturbations on large scales. Then, we give numerical results of background and perturbation equations in a concrete model (the dissipative coefficient $\Gamma \propto H$). At last, we use the most recent observational data to constrain our models and give the observationally allowed regions of parameters. This work is a natural extension of warm inflation to multi-field cases.Comment: 10 pages, 4 figure

Are observables necessarily Hermitian?

Observables are believed that they must be Hermitian in quantum theory. Based on the obviously physical fact that only eigenstates of observable and its corresponding probabilities, i.e., spectrum distribution of observable are actually observed, we argue that observables need not necessarily to be Hermitian. More generally, observables should be reformulated as normal operators including Hermitian operators as a subclass. This reformulation is consistent with the quantum theory currently used and does not change any physical results. The Clauser-Horne-Shimony-Holt (CHSH) inequality is taken as an example to show that our opinion does not conflict with conventional quantum theory and gives the same physical results. Reformulation of observables as normal operators not only coincides with the physical facts but also will deepen our understanding of measurement in quantum theory.Comment: 5 pages, 1 figur