2,710 research outputs found

    The infrared structure of perturbative gauge theories

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    Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are explored, and high-precision phenomenological applications demand an ever more refined understanding. This review aims to provide a pedagogical overview of the subject. We briefly cover some of the early historical results, we provide some simple examples of low-order applications in the context of perturbative QCD, and discuss the necessary tools to extend these results to all perturbative orders. Finally, we describe recent developments concerning the calculation of soft anomalous dimensions in multi-particle scattering amplitudes at high orders, and we provide a brief introduction to the very active field of infrared subtraction for the calculation of differential distributions at colliders. © 2022 Elsevier B.V

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Constraining the anisotropic expansion of the universe with type ia supernovae and improving the treatment of selection effects within bayesian hierarchical models

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    In thesis, I aim to apply advanced methods in Bayesian statistical modelling on Type Ia Supernovae (SNIa) data to determine tighter constraints on the fiducial Lambda-Cold-Dark-Matter (LCDM) cosmology and improve the modelling of systematic uncertainties in the data. The body of work covered herein can be broadly classified into two main topics: I re-examine the contentious question of constraints on anisotropic expansion from SNIa in the light of a novel determination of peculiar velocities, which are crucial to test isotropy with SNe, out to distances < 200/h Mpc.The Bayesian hierarchical model BAHAMAS is adopted to constrain a dipole in the distance modulus in the context of the LCDM model and the deceleration parameter in a phenomenological Cosmographic expansion. I find no evidence for anisotropic expansion, and place a tight upper bound on the amplitude of a dipole, in a LCDM setting, and the Cosmographic expansion approach. Using Bayesian model comparison, I obtain posterior odds in excess of 900:1 (640:1) against a constant-in-redshift dipole for LCDM (Cosmographic expansion). One of the modern problems of Supernovae cosmology is accounting for selection effects caused by Malmquist bias in a principled way. Here, I present a complete formalism for handling selection effects in Type Ia supernova (SNIa) cosmology in the context of Bayesian Hierarchical Modeling. I demonstrate the method on simulated data sets where selection cuts are made on the apparent magnitude and show that previous results by Rubin et al, (2015) are incorrect and can lead to biased cosmological parameters reconstruction. I how this formalism is easily extended to include the Phillips corrections that are used to standardize SNe. The formalism presented exhibits better statistical properties in terms of bias and mean squared error relative to a traditional ad hoc style correction and the model of Rubin et al, (2015)Open Acces

    Locality and Exceptional Points in Pseudo-Hermitian Physics

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    Pseudo-Hermitian operators generalize the concept of Hermiticity. Included in this class of operators are the quasi-Hermitian operators, which define a generalization of quantum theory with real-valued measurement outcomes and unitary time evolution. This thesis is devoted to the study of locality in quasi-Hermitian theory, the symmetries and conserved quantities associated with non-Hermitian operators, and the perturbative features of pseudo-Hermitian matrices. An implicit assumption of the tensor product model of locality is that the inner product factorizes with the tensor product. Quasi-Hermitian quantum theory generalizes the tensor product model by modifying the Born rule via a metric operator with nontrivial Schmidt rank. Local observable algebras and expectation values are examined in chapter 5. Observable algebras of two one-dimensional fermionic quasi-Hermitian chains are explicitly constructed. Notably, there can be spatial subsystems with no nontrivial observables. Despite devising a new framework for local quantum theory, I show that expectation values of local quasi-Hermitian observables can be equivalently computed as expectation values of Hermitian observables. Thus, quasi-Hermitian theories do not increase the values of nonlocal games set by Hermitian theories. Furthermore, Bell's inequality violations in quasi-Hermitian theories never exceed the Tsirelson bound of Hermitian quantum theory. A perturbative feature present in pseudo-Hermitian curves which has no Hermitian counterpart is the exceptional point, a branch point in the set of eigenvalues. An original finding presented in section 2.6.3 is a correspondence between cusp singularities of algebraic curves and higher-order exceptional points. Eigensystems of one-dimensional lattice models admit closed-form expressions that can be used to explore the new features of non-Hermitian physics. One-dimensional lattice models with a pair of non Hermitian defect potentials with balanced gain and loss, Δ±iγ, are investigated in chapter 3. Conserved quantities and positive-definite metric operators are examined. When the defects are nearest neighbour, the entire spectrum simultaneously becomes complex when γ increases beyond a second-order exceptional point. When the defects are at the edges of the chain and the hopping amplitudes are 2-periodic, as in the Su-Schrieffer-Heeger chain, the PT-phase transition is dictated by the topological phase of the system. In the thermodynamic limit, PT-symmetry spontaneously breaks in the topologically non-trivial phase due to the presence of edge states. Chiral symmetry and representation theory are utilized in chapter 4 to derive large classes of pseudo-Hermitian operators with closed-form intertwining operators. These intertwining operators include positive-definite metric operators in the quasi-Hermitian case. The PT-phase transition is explicitly determined in a special case

    Peering into the Dark: Investigating dark matter and neutrinos with cosmology and astrophysics

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    The LCDM model of modern cosmology provides a highly accurate description of our universe. However, it relies on two mysterious components, dark matter and dark energy. The cold dark matter paradigm does not provide a satisfying description of its particle nature, nor any link to the Standard Model of particle physics. I investigate the consequences for cosmological structure formation in models with a coupling between dark matter and Standard Model neutrinos, as well as probes of primordial black holes as dark matter. I examine the impact that such an interaction would have through both linear perturbation theory and nonlinear N-body simulations. I present limits on the possible interaction strength from cosmic microwave background, large scale structure, and galaxy population data, as well as forecasts on the future sensitivity. I provide an analysis of what is necessary to distinguish the cosmological impact of interacting dark matter from similar effects. Intensity mapping of the 21 cm line of neutral hydrogen at high redshift using next generation observatories, such as the SKA, would provide the strongest constraints yet on such interactions, and may be able to distinguish between different scenarios causing suppressed small scale structure. I also present a novel type of probe of structure formation, using the cosmological gravitational wave signal of high redshift compact binary mergers to provide information about structure formation, and thus the behaviour of dark matter. Such observations would also provide competitive constraints. Finally, I investigate primordial black holes as an alternative dark matter candidate, presenting an analysis and framework for the evolution of extended mass populations over cosmological time and computing the present day gamma ray signal, as well as the allowed local evaporation rate. This is used to set constraints on the allowed population of low mass primordial black holes, and the likelihood of witnessing an evaporation

    Asymptotics of stochastic learning in structured networks

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    High-Purity Entanglement of Hot Propagating Modes Using Nonreciprocity

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    Distributed quantum information processing and communication protocols demand the ability to generate entanglement among propagating modes. However, thermal fluctuations can severely limit the fidelity and purity of propagating entangled states, especially for low-frequency modes relevant for radio-frequency (RF) signals. Here we propose nonreciprocity as a resource to render continuous-variable entanglement of propagating modes robust against thermal fluctuations. By utilising a cold-engineered reservoir we break the symmetry of reciprocity in a standard two-mode squeezing interaction between a low- and a high-frequency mode, and show that the rerouting of thermal fluctuations allows the generation of flying entangled states with high purity. Our approach requires only pairwise Gaussian interactions and is thus ideal for parametric circuit QED implementations

    Sobolev-Wigner spaces

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    In this paper, we provide new results about the free Malliavin calculus on the Wigner space first developed in the breakthrough work of Biane and Speicher. We define in this way the higher-order Malliavin derivatives, and we study their associated Sobolev-Wigner spaces. Using these definitions, we are able to obtain a free counterpart of the of the Stroock formula and various variances identities. As a consequence, we obtain a sophisticated proof a la Ustunel, Nourdin and Peccati of the product formula between two multiple Wigner integrals. We also study the commutation relations (of different significations) on the Wigner space, and we show for example the absence of non-trivial bounded central Malliavin differentiable functionals and the absence of non-trivial Malliavin differentiable projections

    Beam scanning by liquid-crystal biasing in a modified SIW structure

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    A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium
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