Abstract: We characterize preserved extreme points of the unit ball of Lipschitz-free spaces F (X) in terms of simple geometric conditions on the underlying metric space (X, d). Namely, the preserved extreme points are the elementary molecules corresponding to pairs of points p, q in X such that the triangle inequality d (p, q) <= d (p, r) + d (q, r) is uniformly strict for r away from p, q. For compact X, this condition reduces to the triangle inequality being strict. As a consequence, we give an affirmative answer to a conjecture of N. Weaver that compact spaces are concave if and only if they have no triple of metrically aligned points, and we show that all extreme points are preserved for several classes of compact metric spaces X, including Holder and countable compacta.

Abstract: We study in detail the method proposed recently to study the vector-vector interaction using the N/D method and dispersion relations, which concludes that, while, for J = 0, one finds bound states, in the case of J = 2, where the interaction is also attractive and much stronger, no bound state is found. In that work, approximations are done for N and D and a subtracted dispersion relation for D is used, with subtractions made up to a polynomial of second degree in s – s(th), matching the expression to 1 – VG at threshold. We study this in detail for the rho rho interaction and to see the convergence of the method we make an extra subtraction matching 1 – VG at threshold up to (s – s(th))(3). We show that the method cannot be used to extrapolate the results down to 1270 MeV where the f(2)(1270) resonance appears, due to the artificial singularity stemming from the “on-shell” factorization of the rho exchange potential. In addition, we explore the same method but folding this interaction with the mass distribution of the rho, and we show that the singularity disappears and the method allows one to extrapolate to low energies, where both the (s – s(th))(2) and (s – s(th))(3) expansions lead to a zero of Re D(s), at about the same energy where a realistic approach produces a bound state. Even then, the method generates a large Im D(s) that we discuss is unphysical.

Abstract: In the past decade, a new class of bright transient radio sources with millisecond duration has been discovered. The origin of these so-called fast radio bursts (FRBs) is still a mystery, despite the growing observational efforts made by various multiwavelength and multimessenger facilities. To date, many models have been proposed to explain FRBs, but neither the progenitors nor the radiative and the particle acceleration processes at work have been clearly identified. In this paper, we assess whether hadronic processes may occur in the vicinity of the FRB source. If they do, FRBs may contribute to the high-energy cosmic-ray and neutrino fluxes. A search for these hadronic signatures was carried out using the ANTARES neutrino telescope. The analysis consists in looking for high-energy neutrinos, in the TeV-PeV regime, that are spatially and temporally coincident with the detected FRBs. Most of the FRBs discovered in the period 2013-2017 were in the field of view of the ANTARES detector, which is sensitive mostly to events originating from the Southern hemisphere. From this period, 12 FRBs were selected and no coincident neutrino candidate was observed. Upper limits on the per-burst neutrino fluence were derived using a power-law spectrum, dN/DE nu proportional to E-nu(-gamma), for the incoming neutrino flux, assuming spectral indexes gamma = 1.0, 2.0, 2.5. Finally, the neutrino energy was constrained by computing the total energy radiated in neutrinos, assuming different distances for the FRBs. Constraints on the neutrino fluence and on the energy released were derived from the associated null results.

Abstract: The proposed Deep Underground Neutrino Experiment (DUNE) utilizes a wide-band on-axis tunable muon-(anti) neutrino beam with a baseline of 1300 km to search for CP violation with high precision. Given the long baseline, DUNE is also sensitive to effects due to matter induced non-standard neutrino interactions (NSI) which can interfere with the standard three-flavor oscillation paradigm. Hence it is desirable to design strategies to disentangle effects due to NSI from standard oscillations. In this article, we exploit the tunability of the DUNE neutrino beam over a wide-range of energies to devise an experimental strategy for separating oscillation effects due to NSI from the standard three-flavor oscillation scenario. Using chi(2) analysis, we obtain an optimal combination of beam tunes and distribution of run times in neutrino and anti-neutrino modes that would enable DUNE to isolate new physics scenarios from the standard. We can distinguish scenarios at 3 sigma (5 sigma) level for almost all (similar to 50%) values of delta. To the best of our knowledge, our strategy is entirely new and has not been reported elsewhere.

Abstract: A discrete-time Quantum Walk (QW) is an operator driving the evolution of a single particle on the lattice, through local unitaries. In a previous paper, we showed that QWs over the honeycomb and triangular lattices can be used to simulate the Dirac equation. We apply a spacetime coordinate transformation upon the lattice of this QW, and show that it is equivalent to introducing spacetime-dependent local unitaries-whilst keeping the lattice fixed. By exploiting this duality between changes in geometry, and changes in local unitaries, we show that the spacetime-dependent QW simulates the Dirac equation in (2 + 1)-dimensional curved spacetime. Interestingly, the duality crucially relies on the non linear-independence of the three preferred directions of the honeycomb and triangular lattices: The same construction would fail for the square lattice. At the practical level, this result opens the possibility to simulate field theories on curved manifolds, via the quantum walk on different kinds of lattices.