In previous work we analyzed the linear stability of non-relativistic $\ell$-boson stars with respect to radial modes and showed that ground state configurations are stable with respect to these modes, whereas excited states are unstable. In this work we extend the analysis to non-spherical linear mode perturbations. To this purpose, we expand the wave function in terms of tensor spherical harmonics which allows us to decouple the perturbation equations into a family of radial problems. By using a combination of analytic and numerical methods, we show that ground state configurations with $\ell > 1$ possess exponentially in time growing non-radial modes, whereas only oscillating modes are found for $\ell=0$ and $\ell=1$. This leads us to conjecture that nonrelativistic $\ell$-boson stars in their ground state are stable for $\ell=1$ as well as $\ell=0$, while ground state and excited configurations with $\ell > 1$ are unstable.

Cosmic rays with energies up to a few PeV are known to be accelerated within the Milky Way. Traditionally, it has been presumed that supernova remnants were the main source of very-high-energy cosmic rays but theoretically it is difficult to get protons to PeV energies and observationally there simply is no evidence to support the remnants as sources of hadrons with energies above a few tens of TeV. One possible source of protons with those energies is the Galactic Center region. Here we report observations of 1-100 TeV gamma rays coming from the 'Cygnus Cocoon', which is a superbubble surrounding a region of OB2 massive star formation. These gamma rays are likely produced by 10-1000 TeV freshly accelerated CRs originating from the enclosed star forming region Cygnus OB2. Hitherto it was not known that such regions could accelerate particles to these energies. The measured flux is likely originated by hadronic interactions. The spectral shape and the emission profile of the Cocoon changes from GeV to TeV energies, which reveals the transport of cosmic particles and historical activity in the superbubble.

In previous work, we have found new static, spherically symmetric boson star solutions which generalize the standard boson stars by allowing a particular superposition of scalar fields in which each of the fields is characterized by a fixed value of its non-vanishing angular momentum number $\ell$. We call such solutions "$\ell$-boson stars". Here, we perform a series of fully non-linear dynamical simulations of perturbed $\ell$-boson stars in order to study their stability, and the final fate of unstable configurations. We show that for each value of $\ell$, the configuration of maximum mass separates the parameter space into stable and unstable regions. Stable configurations, when perturbed, oscillate around the unperturbed solution and very slowly return to a stationary configuration. Unstable configurations, in contrast, can have three different final states: collapse to a black hole, migration to the stable branch, or explosion (dissipation) to infinity. Just as it happens with $\ell=0$ boson stars, migration to the stable branch or dissipation to infinity depends on the sign of the total binding energy of the star: bound unstable stars collapse to black holes or migrate to the stable branch, whereas unbound unstable stars either collapse to a black hole or explode to infinity. Thus, the parameter $\ell$ allows us to construct a new set of stable configurations. All our simulations are performed in spherical symmetry, leaving a more detailed stability analysis including non-spherical perturbations for future work.

We study the linear stability of nonrelativistic $\ell$-boson stars, describing static, spherically symmetric configurations of the Schrödinger-Poisson system with multiple wave functions having the same value of the angular momentum $\ell$. In this work we restrict our analysis to time-dependent perturbations of the radial profiles of the $2\ell+1$ wave functions, keeping their angular dependency fixed. Based on a combination of analytic and numerical methods, we find that for each $\ell$, the ground state is linearly stable, whereas the $n$'th excited states possess $2n$ unstable (exponentially in time growing) modes. Our results also indicate that all excited states correspond to saddle points of the conserved energy functional of the theory.

We summarize recent progress in applying the worldline formalism to the analytic calculation of one-loop N-point amplitudes. This string-inspired approach is well-adapted to avoiding some of the calculational inefficiencies of the standard Feynman diagram approach, most notably by providing master formulas that sum over diagrams differing only by the position of external legs and/or internal propagators. We illustrate the mathematical challenge involved with the low-energy limit of the N-photon amplitudes in scalar and spinor QED, and then present an algorithm that, in principle, solves this problem for the much more difficult case of the N-point amplitudes at full momentum in phi^3 theory. The method is based on the algebra of inverse derivatives in the Hilbert space of periodic functions orthogonal to the constant ones, in which the Bernoulli numbers and polynomials play a central role.

The evolution of the muon content of very high energy air showers (EAS) in the atmosphere is investigated with data of the KASCADE-Grande observatory. For this purpose, the muon attenuation length in the atmosphere is obtained to $\Lambda_\mu = 1256 \, \pm 85 \, ^{+229}_{-232}(\mbox{syst})\, \mbox{g/cm}^2$ from the experimental data for shower energies between $10^{16.3}$ and $10^{17.0} \, \mbox{eV}$. Comparison of this quantity with predictions of the high-energy hadronic interaction models QGSJET-II-02, SIBYLL 2.1, QGSJET-II-04 and EPOS-LHC reveals that the attenuation of the muon content of measured EAS in the atmosphere is lower than predicted. Deviations are, however, less significant with the post-LHC models. The presence of such deviations seems to be related to a difference between the simulated and the measured zenith angle evolutions of the lateral muon density distributions of EAS, which also causes a discrepancy between the measured absorption lengths of the density of shower muons and the predicted ones at large distances from the EAS core. The studied deficiencies show that all four considered hadronic interaction models fail to describe consistently the zenith angle evolution of the muon content of EAS in the aforesaid energy regime.

In this study, we revisit the Schwinger-Dyson equation for the electron propagator in QED in three and four space-time dimensions. Our analysis addresses the non-perturbative phenomenon of dynamical chiral symmetry breaking, which requires a critical value of the coupling for the dynamical generation of electron masses, encoded in the infrared behavior of the corresponding Green function. With a minimalistic truncation of the infinite tower of equations and adopting standard assumptions, the resulting gap equation is linearized and transformed into a Schrödinger-like equation with an auxiliary potential barrier (or well) subjected to boundary conditions for both high and low momenta. The dynamical mass is then associated with the zero mode of the corresponding Schrödinger-like operator and follows the Miransky scaling law, as expected.

We present a general strategy to solve the stationary Schrödinger-Poisson (SP) system of equations for multistates with axial symmetry. The approach allows us to obtain the well known single and multistate solutions with spherical symmetry, Newtonian multistate $\ell-$boson stars and axially symmetric multistate configurations. For each case we construct particular examples that illustrate the method, whose stability properties are studied by numerically solving the time-dependent SP system. Among the stable configurations there are the mixed-two-state configurations including spherical and dipolar components, which might have an important value as potential anisotropic dark matter halos in the context of ultralight bosonic dark matter scenarios. This is the reason why we also present a possible process of formation of these mixed-two-state configurations that could open the door to the exploration of more general multistate structure formation scenarios.

The 2016 Physics Nobel Prize honors a variety of discoveries related to topological phases and phase transitions. Here we sketch two exciting facets: the groundbreaking works by John Kosterlitz and David Thouless on phase transitions of infinite order, and by Duncan Haldane on the energy gaps in quantum spin chains. These insights came as surprises in the 1970s and 1980s, respectively, and they have both initiated new fields of research in theoretical and experimental physics.

In this paper we investigate the localization and mass spectra of matter fields with spin 0, 1 and 1/2 on a geometric thick brane generated by pure 4D and 5D positive cosmological constants without bulk scalar fields. This model possesses a 4D cosmological constant that can be made as small as one desires without fine-tuning it with the bulk cosmological constant. The RS model is obtained as an analytic continuation of the flat brane limit of this braneworld configuration when the Hubble parameter disappears. Within this inflating braneworld model it is possible to formulate a mechanism for obtaining TeV mass scales from Planck ones by adding a positive thin brane, where the Standard Model fields are trapped, at a distance y_2 from the origin, where the Planck thick brane resides. The brane separation must be of the same order than the inverse thickness parameter of the model in order for the mechanism to generate the desired hierarchy. This result is obtained by imposing the recovery of both the correct 4D gravitational couplings and the actually observed accelerated expansion of the universe in our de Sitter braneworld. Regarding the localization of matter in the purely geometric thick braneworld, for spin 0 massless and massive scalar fields as well as for spin 1 vector fields, the potentials of the Kaluza--Klein (KK) modes in thecorresponding Schroedinger equations are modified Poeschl-Teller potentials, which lead to the localization of the scalar and vector zero modes on the brane as well as to mass gaps in the mass spectra. We also compute the corrections to Coulomb's law coming from massive KK vector modes. For spin 1/2 fermions, we introduce the bulk mass term MF(z)\bar{\Psi}\Psi in the action and show that localization of the massless left-chiral fermion zero mode is feasible for two mass functions MF(z) with a finite/infinite number of massive KK bound states.

We discuss mean field theory of Quarkyonic matter at zero temperature. We treat the nucleons with contact interactions in mean field approximation, discussing both vector and scalar mean field interactions. We treat the quarks without mean field vector interactions, but allow mass terms to be generated consistent from a scalar mean field consistent with the additive quark model for quark masses. Quarkyonic matter is composed of a shell of nucleons that under-occupy the total available phase space associated with the underlying quark degrees of freedom. The fully occupied Fermi sphere beneath this shell of nucleons at high densities is thought of as quarks, but when this fully occupied distribution of states first appears, although the phase space is filled, the matter is at low density. For the transition between this low density and high density saturated matter, we advocate a dual description of the fully filled Fermi sea in terms of hadrons, and make a phenomenological hypothesis for the equation of state of this matter. We then proceed to an example where the mean field interactions are all vector and only associated with the nucleons, ignoring the effects of mass change associated with the scalar interactions. Except for the effects of Pauli blocking, the nucleons and quarks do not interact. To get a reasonable transition to Quarkyonic matter the interaction of the quarks among themselves are assumed to be non-perturbative, and a simple phenomenological relation between quark Fermi energy and density is introduced.

We summarize recent progress in applying the worldline formalism to the analytic calculation of one-loop N-point amplitudes. This string-inspired approach is well-adapted to avoiding some of the calculational inefficiencies of the standard Feynman diagram approach, most notably by providing master formulas that sum over diagrams differing only by the position of external legs and/or internal propagators. We illustrate the mathematical challenge involved with the low-energy limit of the N-photon amplitudes in scalar and spinor QED, and then present an algorithm that, in principle, solves this problem for the much more difficult case of the N-point amplitudes at full momentum in phi^3 theory. The method is based on the algebra of inverse derivatives in the Hilbert space of periodic functions orthogonal to the constant ones, in which the Bernoulli numbers and polynomials play a central role.

Using Lewis-Riesenfeld theory, we derive an exact non-adiabatic master equation describing the time evolution of the QED Schwinger pair production rate for a general time-varying electric field. This equation can be written equivalently as a first-order matrix equation, as a Vlasov type integral equation, or as a third-order differential equation. In the last version it relates to the KdV equation, which allows us to construct an exact solution using the well-known one-soliton solution to that equation. The case of time-like delta function pulse fields is also shortly considered. We compare with previous approaches to the purely time-dependent field case.

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.

We derive an exact solution representing a Bondi-type stationary accretion of a kinetic (Vlasov) gas onto the Kerr black hole. The solution is exact in the sense that relevant physical quantities, such as the particle current density or the accretion rates, are expressed as explicit integrals, which can be evaluated numerically. Whereas the angular momentum accretion rate is shown to vanish exactly, we provide an analytic approximation which allows us to obtain simple formulas for the mass and energy accretion rates. These formulas are used to derive characteristic time scales of the black hole mass growth and the associated spin-down in two different scenarios: assuming that the ambient energy density is either constant or decreases on a cosmological scale.

Ultrahigh energy cosmic ray air showers probe particle physics at energies beyond the reach of accelerators. Here we introduce a new method to test hadronic interaction models without relying on the absolute energy calibration, and apply it to events with primary energy 6-16 EeV (E_CM = 110-170 TeV), whose longitudinal development and lateral distribution were simultaneously measured by the Pierre Auger Observatory. The average hadronic shower is 1.33 +- 0.16 (1.61 +- 0.21) times larger than predicted using the leading LHC-tuned models EPOS-LHC (QGSJetII-04), with a corresponding excess of muons.

The purpose of the present study is to extend the simple concept of apparent coefficient of restitution, widely approached in the literature for the case of a single-contact-point between a sphere and a wall, to the case of bouncing whose complexity is increased due to the shape of the contacting object. Experiments are carried out with a finite-length cylinder, freely falling in a liquid at rest. Complex 3D motions of the cylinder with respect to the wall occur during bouncing, including multi-contact-points between the cylinder and the bottom as well as cavitation. We investigate numerical modelling of an idealized situation (2D infinite cylinder falling parallel to the wall) with 2D simulations where the fluid equations of motion were coupled to the particle equation of motion through an Immersed Boundary Method. The particle equation of motion is coupled to an elastic force to model bouncing, requiring a parameterization of the cut-off length (interpreted as a roughness) and the contact time (associated with the contact elasticity) used here to capture the experimental observations. The simulations confirmed that i) the departure of the coefficient of restitution from 0 is strictly dependent on the apparent roughness and ii) the coefficient of restitution depends on the contact time. Finally, we model the coefficient of restitution as the product of two contributions to the mechanical loss of energy: the collision-to-terminal velocity ratio ($V_c/V_t$) of the approach-phase and the rebound-to-collision velocity ratio ($-V_r/V_c$) of the contact-phase. This leads to a reasonably good prediction of the coefficient of restitution in the intermediate regime in $St$. This suggests the relevance of lumping the complex details of physical phenomena involved during contact into a simple concept based on the contact apparent roughness and elasticity.

We analyze the steady radial accretion of matter into a nonrotating black hole. Neglecting the self-gravity of the accreting matter, we consider a rather general class of static, spherically symmetric and asymptotically flat background spacetimes with a regular horizon. In addition to the Schwarzschild metric, this class contains certain deformation of it which could arise in alternative gravity theories or from solutions of the classical Einstein equations in the presence of external matter fields. Modeling the ambient matter surrounding the black hole by a relativistic perfect fluid, we reformulate the accretion problem as a dynamical system, and under rather general assumptions on the fluid equation of state, we determine the local and global qualitative behavior of its phase flow. Based on our analysis and generalizing previous work by Michel, we prove that for any given positive particle density number at infinity, there exists a unique radial, steady-state accretion flow which is regular at the horizon. We determine the physical parameters of the flow, including its accretion and compression rates, and discuss their dependency on the background metric.

In this work we revisit the steady state, spherically symmetric gas accretion problem from the non-relativistic regime to the ultra-relativistic one. We first perform a detailed comparison between the Bondi and Michel models, and show how the mass accretion rate in the Michel solution approaches a constant value as the fluid temperature increases, whereas the corresponding Bondi value continually decreases, the difference between these two predicted values becoming arbitrarily large at ultra-relativistic temperatures. Additionally, we extend the Michel solution to the case of a fluid with an equation of state corresponding to a monoatomic, relativistic gas. Finally, using general relativistic hydrodynamic simulations, we study spherical accretion onto a rotating black hole, exploring the influence of the black hole spin on the mass accretion rate, the flow morphology and characteristics, and the sonic surface. The effect of the black hole spin becomes more significant as the gas temperature increases and as the adiabatic index $\gamma$ stiffens. For an ideal gas in the ultra-relativistic limit ($\gamma=4/3$), we find a reduction of 10 per cent in the mass accretion rate for a maximally rotating black hole as compared to a non-rotating one, while this reduction is of up to 50 per cent for a stiff fluid ($\gamma=2$).

We use the worldline formalism for calculating the one-loop effective action for the Einstein-Maxwell background induced by charged scalars or spinors, in the limit of low energy and weak gravitational field but treating the electromagnetic field nonperturbatively. The effective action is obtained in a form which generalizes the standard proper-time representation of the Euler-Heisenberg Lagrangian. We compare with previous work and discuss possible applications.