We prove global-in-time existence and uniqueness of measure solutions of a nonlocal interaction system of two species in one spatial dimension. For initial data including atomic parts we provide a notion of gradient-flow solutions in terms of the pse
udo-inverses of the corresponding cumulative distribution functions, for which the system can be stated as a gradient flow on the Hilbert space $L^2(0,1)^2$ according to the classical theory by Brezis. For absolutely continuous initial data we construct solutions using a minimising movement scheme in the set of probability measures. In addition we show that the scheme preserves finiteness of the $L^m$-norms for all $min [1,+infty]$ and of the second moments. We then provide a characterisation of equilibria and prove that they are achieved (up to time subsequences) in the large time asymptotics. We conclude the paper constructing two examples of non-uniqueness of measure solutions emanating from the same (atomic) initial datum, showing that the notion of gradient flow solution is necessary to single out a unique measure solution.
We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications. Assuming a unif
orm coerciveness assumption on the diffusion part, which allows to consider a large class of systems with degenerate cross-diffusion (i.e. of porous medium type) and relaxes sets of assumptions previously considered in the literature, we prove global-in-time existence of weak solutions by means of a semi-implicit version of the Jordan-Kinderlehrer-Otto scheme. Our approach allows to consider nonlocal interaction terms not necessarily yielding a formal gradient flow structure.
We briefly comment on the paper by Albaladejo et al. [arXiv:1709.09101], rejecting its conclusions.
We argue that a $SO(d)$ magnetic monopole in an asymptotically AdS space-time is dual to a $d$-dimensional strongly coupled system in a solid state. In light of this, it would be remiss of us not to dub such a field configuration $solidon$. In the pr
esence of mixed boundary conditions, a solidon spontaneously breaks translations (among many other symmetries) and gives rise to Goldstone excitations on the boundary$-$the phonons of the solid. We derive the quadratic action for the boundary phonons in the probe limit and show that, when the mixed boundary conditions preserve conformal symmetry, the longitudinal and transverse sound speeds are related to each other as expected from effective field theory arguments. We then include backreaction and calculate the free energy of the solidon for a particular choice of mixed boundary conditions, corresponding to a relevant multi-trace deformation of the boundary theory. We find such free energy to be lower than that of thermal AdS. This suggests that our solidon undergoes a solid-to-liquid first order phase transition by melting into a Schwarzschild-AdS black hole as the temperature is raised.
Multiquark resonances are undoubtedly experimentally observed. The number of states and the amount of details on their properties has been growing over the years. It is very recent the discovery of two pentaquarks and the confirmation of four tetraqu
arks, two of which had not been observed before. We mainly review the theoretical understanding of this sector of particle physics phenomenology and present some considerations attempting a coherent description of the so called X and Z resonances. The prominent problems plaguing theoretical models, like the absence of selection rules limiting the number of states predicted, motivate new directions in model building. Data are reviewed going through all of the observed resonances with particular attention to their common features and the purpose of providing a starting point to further research.
We propose a new interpretation of the neutral and charged X, Z exotic hadron resonances. Hybridized-tetraquarks are neither purely compact tetraquark states nor bound or loosely bound molecules. The latter would require a negative or zero binding en
ergy whose counterpart in h-tetraquarks is a positive quantity. The formation mechanism of this new class of hadrons is inspired by that of Feshbach metastable states in atomic physics. The recent claim of an exotic resonance in the Bs pi+- channel by the D0 collaboration and the negative result presented subsequently by the LHCb collaboration are understood in this scheme, together with a considerable portion of available data on X, Z particles. Considerations on a state with the same quantum numbers as the X(5568) are also made.
The new data reported by ALICE on the production of light nuclei with pT < 10 GeV in Pb-Pb collisions at sqrt(s_NN) = 2.76 TeV are used to compute an order-of-magnitude estimate of the expected production cross sections of light nuclei in proton-prot
on collisions at high transverse momenta. We compare the hypertriton, helium-3 and deuteron production cross sections to that of X(3872), measured in prompt pp collisions by CMS. The results we find suggest a different production mechanism for the X(3872), making questionable any loosely bound molecule interpretation.
The nature of the so-called XYZ states is a long-standing problem. It has been suggested that such particles may be described as compact four-quark states or loosely bound meson molecules. In the present work we analyze the Z_c() -> eta_c rho decay u
sing both approaches. Such channel might provide useful insights on the nature of the Z_c(), helping discriminating between the two different models.
The phenomenology of the so-called X, Y and Z hadronic resonances is hard to reconcile with standard charmonium or bottomonium interpretations. It has been suggested that some of these new hadrons can possibly be described as tightly bound tetraquark
states and/or as loosely bound two-meson molecules. In the present paper we focus on the hypothetical existence of flavored, doubly charmed, tetraquarks. Such states might also carry double electric charge, and in this case, if discovered, they could univocally be interpreted in terms of compact tetraquarks. Flavored tetraquarks are also amenable to lattice studies as their interpolating operators do not overlap with ordinary meson ones. We show that doubly charmed tetraquarks could significantly be produced at LHC from B_c or Xi_bc heavy baryons.
