Calculating the local-type fNL for slow-roll inflation with a non-vacuum initial state

Single-field slow-roll inflation with a non-vacuum initial state has an enhanced bispectrum in the local limit. We numerically calculate the local-type fNL signal in the CMB that would be measured for such models (including the full transfer function and 2D projection). The nature of the result depends on several parameters, including the occupation number N_k, the phase angle \theta_k between the Bogoliubov parameters, and the slow-roll parameter \epsilon. In the most conservative case, where one takes \theta_k \approx \eta_0 k (justified by physical reasons discussed within) and \epsilon\lesssim 0.01, we find that 0 < fNL < 1.52 (\epsilon/0.01), which is likely too small to be detected in the CMB. However, if one is willing to allow a constant value for the phase angle \theta_k and N_k=O(1), fNL can be much larger and/or negative (depending on the choice of \theta_k), e.g. fNL \approx 28 (\epsilon/0.01) or -6.4 (\epsilon/0.01); depending on \epsilon, these scenarios could be detected by Planck or a future satellite. While we show that these results are not actually a violation of the single-field consistency relation, they do produce a value for fNL that is considerably larger than that usually predicted from single-field inflation.Comment: 8 pages, 1 figure. v2: Version accepted for publication in PRD. Added greatly expanded discussion of the phase angle \theta_k; this allows the possibility of enhanced fNL, as mentioned in abstract. More explicit comparisons with earlier wor

Stochastic Inflation and the Lower Multipoles in the CMB Anisotropies

We generalize the treatment of inflationary perturbations to deal with the non-Markovian colored noise emerging from any realistic approach to stochastic inflation. We provide a calculation of the power-spectrum of the gauge-invariant comoving curvature perturbation to first order in the slow-roll parameters. Properly accounting for the constraint that our local patch of the Universe is homogeneous on scales just above the present Hubble radius, we find a blue tilt of the power-spectrum on the largest observable scales, in agreement with the WMAP data which show an unexpected suppression of the low multipoles of the CMB anisotropy. Our explanation of the anomalous behaviour of the lower multipoles of the CMB anisotropies does not invoke any ad-hoc introduction of new physical ingredients in the theory.Comment: 9 pages, 2 figure

Factorization in integrable systems with impurity

This article is based on recent works done in collaboration with M. Mintchev, E. Ragoucy and P. Sorba. It aims at presenting the latest developments in the subject of factorization for integrable field theories with a reflecting and transmitting impurity.Comment: 7 pages; contribution to the XIVth International Colloquium on Integrable systems, Prague, June 200

Gauge-Invariant Quasi-Free States on the Algebra of the Anyon Commutation Relations

Let $X=\mathbb R^2$ and let $q\in\mathbb C$, $|q|=1$. For $x=(x^1,x^2)$ and $y=(y^1,y^2)$ from $X^2$, we define a function $Q(x,y)$ to be equal to $q$ if $x^1y^1$, and to $\Re q$ if $x^1=y^1$. Let $\partial_x^+$, $\partial_x^-$ ($x\in X$) be operator-valued distributions such that $\partial_x^+$ is the adjoint of $\partial_x^-$. We say that $\partial_x^+$, $\partial_x^-$ satisfy the anyon commutation relations (ACR) if $\partial^+_x\partial_y^+=Q(y,x)\partial_y^+\partial_x^+$ for $x\ne y$ and $\partial^-_x\partial_y^+=\delta(x-y)+Q(x,y)\partial_y^+\partial^-_x$ for $(x,y)\in X^2$. In particular, for $q=1$, the ACR become the canonical commutation relations and for $q=-1$, the ACR become the canonical anticommutation relations. We define the ACR algebra as the algebra generated by operator-valued integrals of $\partial_x^+$, $\partial_x^-$. We construct a class of gauge-invariant quasi-free states on the ACR algebra. Each state from this class is completely determined by a positive self-adjoint operator $T$ on the real space $L^2(X,dx)$ which commutes with any operator of multiplication by a bounded function $\psi(x^1)$. In the case $\Re q0$), we discuss the corresponding particle density $\rho(x):=\partial_x^+\partial_x^-$. For $\Re q\in(0,1]$, using a renormalization, we rigorously define a vacuum state on the commutative algebra generated by operator-valued integrals of $\rho(x)$. This state is given by a negative binomial point process. A scaling limit of these states as $\kappa\to\infty$ gives the gamma random measure, depending on parameter $\Re q$

Non Gaussian extrema counts for CMB maps

In the context of the geometrical analysis of weakly non Gaussian CMB maps, the 2D differential extrema counts as functions of the excursion set threshold is derived from the full moments expansion of the joint probability distribution of an isotropic random field, its gradient and invariants of the Hessian. Analytic expressions for these counts are given to second order in the non Gaussian correction, while a Monte Carlo method to compute them to arbitrary order is presented. Matching count statistics to these estimators is illustrated on fiducial non-Gaussian "Planck" data.Comment: 4 pages, 1 figur

Anyonic Realization of the Quantum Affine Lie Superalgebra U_q(A(M,N)^{(1)})

We give a realization of the quantum affine Lie superalgebras U_q(A(M,N))^(1) in terms of anyons defined on a one or two-dimensional lattice, the deformation parameter q being related to the statistical parameter $\nu$ of the anyons by q = exp(i\pi\nu). The construction uses anyons contructed from usual fermionic oscillators and deformed bosonic oscillators. As a byproduct, realization deformed in any sector of the quantum superalgebras U_q(A(M,N)) is obtained.Comment: 14p LaTeX Document (should be run twice

The pulsed electron deposition technique for biomedical applications: A review

The "pulsed electron deposition" (PED) technique, in which a solid target material is ablated by a fast, high-energy electron beam, was initially developed two decades ago for the deposition of thin films of metal oxides for photovoltaics, spintronics, memories, and superconductivity, and dielectric polymer layers. Recently, PED has been proposed for use in the biomedical field for the fabrication of hard and soft coatings. The first biomedical application was the deposition of low wear zirconium oxide coatings on the bearing components in total joint replacement. Since then, several works have reported the manufacturing and characterization of coatings of hydroxyapatite, calcium phosphate substituted (CaP), biogenic CaP, bioglass, and antibacterial coatings on both hard (metallic or ceramic) and soft (plastic or elastomeric) substrates. Due to the growing interest in PED, the current maturity of the technology and the low cost compared to other commonly used physical vapor deposition techniques, the purpose of this work was to review the principles of operation, the main applications, and the future perspectives of PED technology in medicine