Mesoscopic pinning forces in neutron star crusts

The crust of a neutron star is thought to be comprised of a lattice of nuclei immersed in a sea of free electrons and neutrons. As the neutrons are superfluid their angular momentum is carried by an array of quantized vortices. These vortices can pin to the nuclear lattice and prevent the neutron superfluid from spinning down, allowing it to store angular momentum which can then be released catastrophically, giving rise to a pulsar glitch. A crucial ingredient for this model is the maximum pinning force that the lattice can exert on the vortices, as this allows us to estimate the angular momentum that can be exchanged during a glitch. In this paper we perform, for the first time, a detailed and quantitative calculation of the pinning force \emph{per unit length} acting on a vortex immersed in the crust and resulting from the mesoscopic vortex-lattice interaction. We consider realistic vortex tensions, allow for displacement of the nuclei and average over all possible orientation of the crystal with respect to the vortex. We find that, as expected, the mesoscopic pinning force becomes weaker for longer vortices and is generally much smaller than previous estimates, based on vortices aligned with the crystal. Nevertheless the forces we obtain still have maximum values of order $f_{\rm{pin}}\approx 10^{15}$ dyn/cm, which would still allow for enough angular momentum to be stored in the crust to explain large Vela glitches, if part of the star is decoupled during the event.Comment: 17 pages, 16 figures, 5 table

p-adic families of modular forms and p-adic Abel-Jacobi maps

We show that p-adic families of modular forms give rise to certain p-adic Abel-Jacobi maps at their p-new specializations. We introduce the concept of differentiation of distributions, using it to give a new description of the Coleman-Teitelbaum cocycle that arises in the context of the LL -invariant.Nous associons certaines applications p-adiques d\u2019Abel-Jacobi aux familles analytiques de formes modulaires \ue0 ses poids nouveaux en p. Nous introduisons le concept de la d\ue9riv\ue9e d\u2019une distribution. Utilisant ce concept, nous donnons une nouvelle perspective sur le cocycle de Coleman-Teitelbaum dans le contexte de l\u2019invariant LL

Triple product p-adic L-functions for balanced weights

We construct p-adic triple product L-functions that interpolate (square roots of) central critical L-values in the balanced region. Thus, our construction complements that of Harris and Tilouine. There are four central critical regions for the triple product L-functions and two opposite settings, according to the sign of the functional equation. In the first case, three of these regions are of interpolation, having positive sign; they are called the unbalanced regions and one gets three p-adic L-functions, one for each region of interpolation (this is the Harris-Tilouine setting). In the other setting there is only one region of interpolation, called the balanced region: we produce the corresponding p-adic L-function. Our triple product p-adic L-function arises as p-adic period integrals interpolating normalizations of the local archimedean period integrals. The latter encode information about classical representation theoretic branching laws. The main step in our construction of p-adic period integrals is showing that these branching laws vary in a p-adic analytic fashion. This relies crucially on the Ash-Stevens theory of highest weight representations over affinoid algebras

Diagonal classes and the Bloch–Kato conjecture

The aim of this note is twofold. Firstly, we prove an explicit reciprocity law for certain diagonal classes in the \ub4etale cohomology of the triple product of a modular curve, stated in [8] and used there as a crucial ingredient in the proof of the main results. Secondly, we apply the aforementioned reciprocity law to address the rank-zero case of the equivariant Bloch\u2013Kato conjecture for the self-dual motive of an elliptic newform of weight k > 2. In the special case k = 2, our result gives a self-contained and simpler proof of the main result of [15]

Modular p-adic L-functions attached to real quadratic fields and arithmetic applications

Let f 08 Sk0+2(\u3930(Np)) be a normalized N-new eigenform with p 24 N and such that ap2 60 pk0+1 and ordp(ap) < k0 + 1. By Coleman's theory, there is a p-adic family of eigenforms whose weight k0 + 2 specialization is f. Let K be a real quadratic field and let \u3c8 be an unramified character of Gal(K\u305 /K). Under mild hypotheses on the discriminant of K and the factorization of N, we construct a p-adic L-function \u2112/K,\u3c8 interpolating the central critical values of the Rankin L-functions associated to the base change to K of the specializations of in classical weight, twisted by \u3c8. When the character \u3c8 is quadratic, \u2112/K,\u3c8 factors into a product of two Mazur-Kitagawa p-adic L-functions. If, in addition, has p-new specialization in weight k0 + 2, then under natural parity hypotheses we may relate derivatives of each of the Mazur-Kitagawa factors of \u2112/K,\u3c8 at k0 to Bloch\u2013Kato logarithms of Heegner cycles. On the other hand the derivatives of our p-adic L-functions encodes the position of the so called Darmon cycles

Impact of recycling and lateral sediment input on grain size fining trends – implications for reconstructing tectonic and climate forcings in ancient sedimentary systems

Grain size trends in basin stratigraphy are thought to preserve a rich record of the climatic and tectonic controls on landscape evolution. Stratigraphic models assume that over geological timescales, the downstream profile of sediment deposition is in dynamic equilibrium with the spatial distribution of tectonic subsidence in the basin, sea level and the flux and calibre of sediment supplied from mountain catchments. Here, we demonstrate that this approach in modelling stratigraphic responses to environmental change is missing a key ingredient: the dynamic geomorphology of the sediment routing system. For three large alluvial fans in the Iglesia basin, Argentine Andes we measured the grain size of modern river sediment from fan apex to toe and characterise the spatial distribution of differential subsidence for each fan by constructing a 3D model of basin stratigraphy from seismic data. We find, using a self-similar grain size fining model, that the profile of grain size fining on all three fans cannot be reproduced given the subsidence profile measured and for any sediment supply scenario. However, by adapting the self-similar model, we demonstrate that the grain size trends on each fan can be effectively reproduced when sediment is not only sourced from a single catchment at the apex of the system, but also laterally, from tributary catchments and through fan surface recycling. Without constraint on the dynamic geomorphology of these large alluvial systems, signals of tectonic and climate forcing in grain size data are masked and would be indecipherable in the geological record. This has significant implications for our ability to make sensitive, quantitative reconstructions of external boundary conditions from the sedimentary record

Coarse-grained entanglement classification through orthogonal arrays

Classification of entanglement in multipartite quantum systems is an open problem solved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in systems consisting of $N$ subsystems with an arbitrary number of internal levels each, based on properties of orthogonal arrays with $N$ columns. In particular, we investigate in detail a subset of highly entangled pure states which contains all states defining maximum distance separable codes. To illustrate the methods presented, we analyze systems of four and five qubits, as well as heterogeneous tripartite systems consisting of two qubits and one qutrit or one qubit and two qutrits.Comment: 38 pages, 1 figur

Geometry and Dynamics of a Coupled 4D-2D Quantum Field Theory

Geometric and dynamical aspects of a coupled 4D-2D interacting quantum field theory - the gauged nonAbelian vortex - are investigated. The fluctuations of the internal 2D nonAbelian vortex zeromodes excite the massless 4D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2D CP(N-1) zeromodes associated with a nonAbelian vortex become nonnormalizable. Moreover, all sorts of global, topological 4D effects such as the nonAbelian Aharonov-Bohm effect come into play. These topological global features and the dynamical properties associated with the fluctuation of the 2D vortex moduli modes are intimately correlated, as shown concretely here in a U(1) x SU(N) x SU(N) model with scalar fields in a bifundamental representation of the two SU(N) factor gauge groups.Comment: Latex, 39 pages, 5 figure

The effect of realistic equations of state and general relativity on the "snowplow" model for pulsar glitches

Many pulsars are observed to "glitch", i.e. show sudden jumps in their rotational frequency $\nu$, some of which can be as large as $\Delta \nu/\nu\approx 10^{-6}-10^{-5}$ in a subset of pulsars known as giant glitchers. Recently Pizzochero (2011) has shown that an analytic model based on realistic values for the pinning forces in the crust and for the angular momentum transfer in the star can describe the average properties of giant glitches, such as the inter-glitch waiting time, the step in frequency and that in frequency derivative. In this paper we extend the model (originally developed in Newtonian gravity and for a polytropic equation of state) to realistic backgrounds obtained by integrating the relativistic equations of stellar structure and using physically motivated equations of state to describe matter in the neutron star. We find that this more detailed treatment still reproduces the main features of giant glitches in the Vela pulsar and allows us to set constraints on the equation of state. In particular we find that stiffer equations of state are favoured and that it is unlikely that the Vela pulsar has a high mass (larger than $M\approx 1.5 M_\odot$).Comment: 15 pages, 8 figures, submitted to MNRA