Creature forcing and large continuum: The joy of halving

For $f,g\in\omega^\omega$ let $c^\forall_{f,g}$ be the minimal number of uniform $g$-splitting trees needed to cover the uniform $f$-splitting tree, i.e., for every branch $\nu$ of the $f$-tree, one of the $g$-trees contains $\nu$. Let $c^\exists_{f,g}$ be the dual notion: For every branch $\nu$, one of the $g$-trees guesses $\nu(m)$ infinitely often. We show that it is consistent that $c^\exists_{f_\epsilon,g_\epsilon}=c^\forall_{f_\epsilon,g_\epsilon}=\kappa_\epsilon$ for continuum many pairwise different cardinals $\kappa_\epsilon$ and suitable pairs $(f_\epsilon,g_\epsilon)$. For the proof we introduce a new mixed-limit creature forcing construction

Noisy independent component analysis of auto-correlated components

We present a new method for the separation of superimposed, independent, auto-correlated components from noisy multi-channel measurement. The presented method simultaneously reconstructs and separates the components, taking all channels into account and thereby increases the effective signal-to-noise ratio considerably, allowing separations even in the high noise regime. Characteristics of the measurement instruments can be included, allowing for application in complex measurement situations. Independent posterior samples can be provided, permitting error estimates on all desired quantities. Using the concept of information field theory, the algorithm is not restricted to any dimensionality of the underlying space or discretization scheme thereof

Semi-inclusive structure functions in the spectator model

We establish the relationship between distribution and fragmentation functions and the structure functions appearing in the cross section of polarized 1-particle inclusive deep-inelastic scattering. We present spectator model evaluations of these structure functions focusing on the case of an outgoing spin-1/2 baryon. Distribution functions obtained in the spectator model are known to fairly agree at low energy scales with global parameterizations extracted, for instance, from totally inclusive DIS data. Therefore, we expect it to give good hints on the functional dependence of the structure functions on the scaling variables x(Bjorken), z and on the transverse momentum of the observed outgoing hadron, P_{h\perp}. Presently, this dependence is not very well known, but experiments are planned in the near future.Comment: 19 pages, 16 figures, submitted to Eur. Phys. J.

Electroelasticity of Charged Black Branes

We present the first-order corrected dynamics of fluid branes carrying higher-form charge by obtaining the general form of their equations of motion to pole-dipole order. Assuming linear response theory, we characterize the corresponding effective theory of stationary bent charged (an)isotropic fluid branes in terms of two sets of response coefficients, the Young modulus and the piezoelectric moduli. We subsequently find large classes of examples in gravity of this effective theory, by constructing stationary strained charged black brane solutions to first order in a derivative expansion. Using solution generating techniques and bent neutral black branes as a seed solution, we obtain a class of charged black brane geometries carrying smeared Maxwell charge in Einstein-Maxwell-dilaton gravity. In the specific case of ten-dimensional space-time we furthermore use T-duality to generate bent black branes with higher-form charge, including smeared D-branes of type II string theory. By subsequently measuring the bending moment and the electric dipole moment which these geometries acquire due to the strain, we uncover that their form is captured by classical electroelasticity theory. In particular, we find that the Young modulus and the piezoelectric moduli of our strained charged black brane solutions are parameterized by a total of 4 response coefficients, both for the isotropic as well as anisotropic cases.Comment: v2: 40pp; typos fixe

Disordered Bose Einstein Condensates with Interaction

We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the interval.Comment: Contribution to the proceedings of ICMP12, Aalborg, Denmark, August 6-11, 2012. Minor amendments; subsection 4.4 on the thermodynamic limit adde

Towards a bulk description of higher spin SYK

We consider on the bulk side extensions of the Sachdev--Ye--Kitaev (SYK) model to Yang--Mills and higher spins. To this end we study generalizations of the Jackiw--Teitelboim (JT) model in the BF formulation. Our main goal is to obtain generalizations of the Schwarzian action, which we achieve in two ways: by considering the on-shell action supplemented by suitable boundary terms compatible with all symmetries, and by applying the Lee--Wald--Zoupas formalism to analyze the symplectic structure of dilaton gravity. We conclude with a discussion of the entropy (including log-corrections from higher spins) and a holographic dictionary for the generalized SYK/JT correspondence.Comment: 42 pages; v2: Typos correcte