Statistical Mechanics of an Ideal Gas of Non-Abelian Anyons

We study the thermodynamical properties of an ideal gas of non-Abelian Chern-Simons particles and we compute the second virial coefficient, considering the effect of general soft-core boundary conditions for the two-body wavefunction at zero distance. The behaviour of the second virial coefficient is studied as a function of the Chern-Simons coupling, the isospin quantum number and the hard-coreness parameters. Expressions for the main thermodynamical quantities at the lower order of the virial expansion are also obtained: we find that at this order the relation between the internal energy and the pressure is the same found (exactly) for 2D Bose and Fermi ideal gases. A discussion of the comparison of obtained findings with available results in literature for systems of hard-core non-Abelian Chern-Simons particles is also supplied.Comment: Submitted versio

Inferring, not just detecting: metrics for high-redshift sources observed with third-generation gravitational-wave detectors

The detection of black-hole binaries at high redshifts is a cornerstone of the science case of third-generation gravitational-wave interferometers. The star-formation rate peaks at z~2 and decreases by orders of magnitude by z~10. Any confident detection of gravitational waves from such high redshifts would imply either the presence of stars formed from pristine material originating from cosmological nucleosynthesis (the so-called population III stars), or black holes that are the direct relics of quantum fluctuations in the early Universe (the so-called primordial black holes). Crucially, detecting sources at cosmological distances does not imply inferring that sources are located there, with the latter posing more stringent requirements. To this end, we present two figures of merit, which we refer to as "z-z plot" and "inference horizon", that quantify the largest redshift one can possibly claim a source to be beyond. We argue that such inference requirements, in addition to detection requirements, should be investigated when quantifying the scientific payoff of future gravitational-wave facilities.Comment: 6 pages, 4 figure

Forecasting the detection capabilities of third-generation gravitational-wave detectors using GWFAST\texttt{GWFAST}

We introduce $\texttt{GWFAST}$, a novel Fisher-matrix code for gravitational-wave studies, tuned toward third-generation gravitational-wave detectors such as Einstein Telescope (ET) and Cosmic Explorer (CE). We use it to perform a comprehensive study of the capabilities of ET alone, and of a network made by ET and two CE detectors, as well as to provide forecasts for the forthcoming O4 run of the LVK collaboration. We consider binary neutron stars, binary black holes and neutron star-black hole binaries, and compute basic metrics such as the distribution of signal-to-noise ratio (SNR), the accuracy in the reconstruction of various parameters (including distance, sky localization, masses, spins and, for neutron stars, tidal deformabilities), and the redshift distribution of the detections for different thresholds in SNR and different levels of accuracy in localization and distance measurement. We examine the expected distribution and properties of `golden events', with especially large values of the SNR. We also pay special attention to the dependence of the results on astrophysical uncertainties and on various technical details (such as choice of waveforms, or the threshold in SNR), and we compare with other Fisher codes in the literature. In a companion paper we discuss the technical aspects of the code. Together with this paper, we publicly release the code $\texttt{GWFAST}$ at https://github.com/CosmoStatGW/gwfast, and the library $\texttt{WF4Py}$ implementing state-of-the-art gravitational-wave waveforms in pure $\texttt{Python}$ at https://github.com/CosmoStatGW/WF4Py.Comment: 43 + 9 pages, 24 + 3 Figures, $\texttt{GWFAST}$ available at https://github.com/CosmoStatGW/gwfast, $\texttt{WF4Py}$ available at https://github.com/CosmoStatGW/WF4P

Adding Gamma-ray Polarimetry to the Multi-Messenger Era

The last decade has seen the emergence of two new fields within astrophysics: gamma ray polarimetry and GW astronomy. The former, which aims to measure the polarization of gamma rays in the energy range of 10s to 100s of keV, from astrophysical sources, saw the launch of the first dedicated polarimeters such as GAP and POLAR. On the other hand, GW astronomy started with the detection of the first black hole mergers by LIGO in 2015, followed by the first multi messenger detection in 2017. While the potential of the two individual fields has been discussed in detail in the literature, the potential for joint observations has thus far been ignored. In this article, we aim to define how GW observations can best contribute to gamma ray polarimetry and study the scientific potential of joint analyses. In addition we aim to provide predictions on feasibility of such joint measurements in the near future. We study which GW observables can be combined with measurements from gamma ray polarimetry to improve the discriminating power regarding GRB emission models. We then provide forecasts for the joint detection capabilities of current and future GW detectors and polarimeters. Our results show that by adding GW data to polarimetry, a single precise joint detection would allow to rule out the majority of emission models. We show that in the coming years joint detections between GW and gamma ray polarimeters might already be possible. Although these would allow to constrain part of the model space, the probability of highly constraining joint detections will remain small in the near future. However, the scientific merit held by even a single such measurement makes it important to pursue such an endeavour. Furthermore, we show that using the next generation of GW detectors, such as the Einstein Telescope, joint detections for which GW data can better complement the polarization data become possible.Comment: 19 pages, 10 figures, Accepted for publication in A&

Abelian link invariants and homology

We consider the link invariants defined by the quantum Chern-Simons field theory with compact gauge group U(1) in a closed oriented 3-manifold M. The relation of the abelian link invariants with the homology group of the complement of the links is discussed. We prove that, when M is a homology sphere or when a link -in a generic manifold M- is homologically trivial, the associated observables coincide with the observables of the sphere S^3. Finally we show that the U(1) Reshetikhin-Turaev surgery invariant of the manifold M is not a function of the homology group only, nor a function of the homotopy type of M alone.Comment: 18 pages, 3 figures; to be published in Journal of Mathematical Physic

Chapter Post-stratification as a tool for enhancing the predictive power of classification methods

It is well known that, in classification problems, the predictive capacity of any decision-making model decreases rapidly with increasing asymmetry of the target variable (Sonquist et al., 1973; Fielding 1977). In particular, in segmentation analysis with a categorical target variable, very poor improvements of purity are obtained when the least represented modality counts less than 1/4 of the cases of the most represented modality. The same problem arises with other (theoretically more exhaustive) techniques such as Artificial Neural Networks. Actually, the optimal situation for classification analyses is the maximum uncertainty, that is, equidistribution of the target variable. Some classification techniques are more robust, by using, for example, the less sensitive logit transformation of the target variable (Fabbris & Martini 2002); however, also the logit transformation is strongly affected by the distributive asymmetry of the target variable. In this paper, starting from the results of a direct survey in which the target (binary) variable was extremely asymmetrical (10% vs. 90%, or greater asymmetry), we noted that also the logit model with the most significant parameters had very reduced fitting measures and almost zero predictive power. To solve this predictive issue, we tested post-stratification techniques, artificially symmetrizing a training sample. In this way, a substantially increase of fitting and predictive capacity was achieved, both in the symmetrized sample and, above all, in the original sample. In conclusion of the paper, an application of the same technique to a dataset of very different nature and size is described, demonstrating that the method is stable even in the case of analysis executed with all data of a population