Noise robustness in the detection of non separable random unitary maps

We briefly review a recently proposed method to detect properties of quantum noise processes and quantum channels. We illustrate in detail the method for detecting non separable random unitary channels and consider in particular the explicit examples of the CNOT and CZ gates. We analyse their robustness in the presence of noise for several quantum noise models.Comment: 10 pages, 1 figur

Detection methods to rule out completely co-positive and bi-entangling operations

In this work we extend the quantum channel detection method developed in [Phys. Rev. A 88, 042335 (2013)] and [Phys. Script. T153, 014044 (2013)] in order to detect other interesting convex sets of quantum channels. First we work out a procedure to detect non completely co-positive maps. Then we focus on the set of so-called bi-entangling operations and show how a map outside this set can be revealed. In both cases we provide explicit examples showing the theoretical technique and the corresponding experimental procedure.Comment: 6 pages, 2 figure

IBVPs for Scalar Conservation Laws with Time Discontinuous Fluxes

The initial boundary value problem for a class of scalar non autonomous conservation laws in one space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity assumptions on the flow are extended to a merely $\mathbf{L}^{\infty}$ dependence on time. These results ensure, for instance, the well posedness of a class of vehicular traffic models with time dependent speed limits. A traffic management problem is then shown to admit an optimal solution

Radio-X-ray Synergy to discover and Study Jetted Tidal Disruption Events

Observational consequences of tidal disruption of stars (TDEs) by supermassive black holes (SMBHs) can enable us to discover quiescent SMBHs, constrain their mass function, study formation and evolution of transient accretion disks and jet formation. A couple of jetted TDEs have been recently claimed in hard X-rays, challenging jet models, previously applied to $\gamma$-ray bursts and active galactic nuclei. It is therefore of paramount importance to increase the current sample. In this paper, we find that the best strategy is not to use up-coming X-ray instruments alone, which will yield between several (e-Rosita) and a couple of hundreds (Einstein Probe) events per year below redshift one. We rather claim that a more efficient TDE hunter will be the Square Kilometer Array (SKA) operating {\it in survey mode} at 1.4 GHz. It may detect up to several hundreds of events per year below $z \sim 2.5$ with a peak rate of a few tens per year at $z\approx 0.5$. Therefore, even if the jet production efficiency is {\it not } $100\%$ as assumed here, the predicted rates should be large enough to allow for statistical studies. The characteristic TDE decay of $t^{-5/3}$, however, is not seen in radio, whose flux is quite featureless. {\it Identification} therefore requires localization and prompt repointing by higher energy instruments. If radio candidates would be repointed within a day by future X-ray observatories (e.g. Athena and LOFT-like missions), it will be possible to detect up to $\approx 400$ X-ray counterparts, almost up to redshift $2$. The shortcome is that only for redshift below $\approx 0.4$ the trigger times will be less than 10 days from the explosion. In this regard the X-ray surveys are better suited to probe the beginning of the flare, and are therefore complementary to SKA.Comment: Astrophysical Journal (revised version

Note on lattice regularization and equal-time correlators for parton distribution functions

We show that a recent interesting idea to circumvent the difficulties with the continuation of parton distribution functions to the Euclidean region, that consists in looking at equal time correlators between proton states of infinite momentum, encounters some problems related to the power divergent mixing pattern of DIS operators, when implemented within the lattice regularization.Comment: 15 pages, no figures, Physical Review D (2017

Circular polarization signals of cloudy (exo)planets

The circular polarization of light that planets reflect is often neglected because it is very small compared to the linear polarization. It could, however, provide information on a planet's atmosphere and surface, and on the presence of life, because homochiral molecules that are the building blocks of life on Earth are known to reflect circularly polarized light. We compute $P_c$, the degree of circular polarization, for light that is reflected by rocky (exo)planets with liquid water or sulfuric acid solution clouds, both spatially resolved across the planetary disk and, for planets with patchy clouds, integrated across the planetary disk, for various planetary phase angles $\alpha$. The optical thickness and vertical distribution of the atmospheric gas and clouds, the size parameter and refractive index of the cloud particles, and $\alpha$ all influence $P_c$. Spatially resolved, $P_c$ varies between $\pm 0.20\%$ (the sign indicates the polarization direction). Only for small gas optical thicknesses above the clouds do significant sign changes (related to cloud particle properties) across the planets' hemispheres occur. For patchy clouds, the disk--integrated $P_c$ is typically smaller than $\pm 0.025\%$, with maximums for $\alpha$ between $40^\circ$ and $70^\circ$, and $120^\circ$ to $140^\circ$. As expected, the disk--integrated $P_c$ is virtually zero at $\alpha=0^\circ$ and 180$^\circ$. The disk--integrated $P_c$ is also very small at $\alpha \approx 100^\circ$. Measuring circular polarization signals appears to be challenging with current technology. The small atmospheric circular polarization signal could, however, allow the detection of circular polarization due to homochiral molecules. Confirmation of the detectability of such signals requires better knowledge of the strength of circular polarization signals of biological sources.Comment: 15 pages, 11 figures, Accepted for publication in Astronomy and Astrophysic

Hyperbolic predators vs parabolic preys

We present a nonlinear predator-prey system consisting of a nonlocal conservation law for predators coupled with a parabolic equation for preys. The drift term in the predators' equation is a nonlocal function of the prey density, so that the movement of predators can be directed towards region with high prey density. Moreover, Lotka-Volterra type right hand sides describe the feeding. A theorem ensuring existence, uniqueness, continuous dependence of weak solutions and various stability estimates is proved, in any space dimension. Numerical integrations show a few qualitative features of the solutions.Comment: 35 pages, 7 figure

Hilbert Functions of Filtered Modules

In this presentation we shall deal with some aspects of the theory of Hilbert functions of modules over local rings, and we intend to guide the reader along one of the possible routes through the last three decades of progress in this area of dynamic mathematical activity. Motivated by the ever increasing interest in this field, our goal is to gather together many new developments of this theory into one place, and to present them using a unifying approach which gives self-contained and easier proofs. In this text we shall discuss many results by different authors, following essentially the direction typified by the pioneering work of J. Sally. Our personal view of the subject is most visibly expressed by the presentation of Chapters 1 and 2 in which we discuss the use of the superficial elements and related devices. Basic techniques will be stressed with the aim of reproving recent results by using a more elementary approach. Over the past few years several papers have appeared which extend classical results on the theory of Hilbert functions to the case of filtered modules. The extension of the theory to the case of general filtrations on a module has one more important motivation. Namely, we have interesting applications to the study of graded algebras which are not associated to a filtration, in particular the Fiber cone and the Sally-module. We show here that each of these algebras fits into certain short exact sequences, together with algebras associated to filtrations. Hence one can study the Hilbert function and the depth of these algebras with the aid of the know-how we got in the case of a filtration.Comment: 127 pages, revised version. Comments and remarks are welcom