Quantum transport with coupled cavities on the Apollonian network

We study the dynamics of single photonic and atomic excitations in the Jaynes-Cummings-Hubbard (JCH) model where the cavities are arranged in an Apollonian network (AN). The existence of a gapped field normal frequency spectrum along with strongly localized eigenstates on the AN highlights many of the features provided by the model. By numerically diagonalizing the JCH Hamiltonian in the single excitation subspace, we evaluate the time evolution of fully localized initial states, for many energy regimes. We provide a detailed description of the photonic quantum walk on the AN and also address how an effective Jaynes-Cummings interaction can be achieved at the strong hopping regime. When the hopping rate and the atom-field coupling strength is of the same order, the excitation is relatively allowed to roam between atomic and photonic degrees of freedom as it propagates. However, different cavities will contribute mostly to one of these components, depending on the detuning and initial conditions, in contrast to the strong atom-field coupling regime, where atomic and photonic modes propagate identically.Comment: 10 pages, 10 figure

Preliminary EoS for core-collapse supernova simulations with the QMC model

In this work we present the preliminary results of a complete equation of state (EoS) for core-collapse supernova simulations. We treat uniform matter made of nucleons using the the quark-meson coupling (QMC) model. We show a table with a variety of thermodynamic quantities, which covers the proton fraction range $Y_{p}=0-0.65$ with the linear grid spacing $\Delta Y_{p}=0.01$ ($66$ points) and the density range $\rho_{B}=10^{14}-10^{16}$g.cm$^{-3}$ with the logarithmic grid spacing $\Delta log_{10}(\rho_{B}/[$g.cm$^{-3}])=0.1$ ($21$ points). This preliminary study is performed at zero temperature and our results are compared with the widely used EoS already available in the literature

On the Combinatorial Complexity of Approximating Polytopes

Approximating convex bodies succinctly by convex polytopes is a fundamental problem in discrete geometry. A convex body $K$ of diameter $\mathrm{diam}(K)$ is given in Euclidean $d$-dimensional space, where $d$ is a constant. Given an error parameter $\varepsilon > 0$, the objective is to determine a polytope of minimum combinatorial complexity whose Hausdorff distance from $K$ is at most $\varepsilon \cdot \mathrm{diam}(K)$. By combinatorial complexity we mean the total number of faces of all dimensions of the polytope. A well-known result by Dudley implies that $O(1/\varepsilon^{(d-1)/2})$ facets suffice, and a dual result by Bronshteyn and Ivanov similarly bounds the number of vertices, but neither result bounds the total combinatorial complexity. We show that there exists an approximating polytope whose total combinatorial complexity is $\tilde{O}(1/\varepsilon^{(d-1)/2})$, where $\tilde{O}$ conceals a polylogarithmic factor in $1/\varepsilon$. This is a significant improvement upon the best known bound, which is roughly $O(1/\varepsilon^{d-2})$. Our result is based on a novel combination of both old and new ideas. First, we employ Macbeath regions, a classical structure from the theory of convexity. The construction of our approximating polytope employs a new stratified placement of these regions. Second, in order to analyze the combinatorial complexity of the approximating polytope, we present a tight analysis of a width-based variant of B\'{a}r\'{a}ny and Larman's economical cap covering. Finally, we use a deterministic adaptation of the witness-collector technique (developed recently by Devillers et al.) in the context of our stratified construction.Comment: In Proceedings of the 32nd International Symposium Computational Geometry (SoCG 2016) and accepted to SoCG 2016 special issue of Discrete and Computational Geometr

Unified Superfluid Dark Sector

We present a novel theory of a unified dark sector, where late-time cosmic acceleration emerges from the dark matter superfluid framework. The system is described by a superfluid mixture consisting of two distinguishable states with a small energy gap, such as the ground state and an excited state of dark matter. Given their contact in the superfluid, interaction between those states can happen, converting one state into the other. This long range interaction within the superfluid couples the two superfluid phonon species through a cosine potential motivated by Josephson/Rabi interactions. As a consequence of this potential, a new dynamics of late-time accelerated expansion emerges in this system, without the need of dark energy, coming from a universe containing only this two-state DM superfluid. Because the superfluid species are non-relativistic, their sound speeds remain suitably small throughout the evolution. We calculate the expansion history and growth of linear perturbations, and compare the results to $\Lambda$CDM cosmology. For the fiducial parameters studied here, the predicted expansion and growth function are close to those of $\Lambda$CDM, but the difference in the predicted growth rate is significant at late times. The present theory nicely complements the recent proposal of dark matter superfluidity to explain the empirical success of MOdified Newtonian Dynamics (MOND) on galactic scales, thus offering a unified framework for dark matter, dark energy, and MOND phenomenology.Comment: 27 pages, 4 figures. v2: Version accepted in JCA

Asymmetric dynamics and critical behavior in the Bak-Sneppen model

We investigate, using mean-field theory and simulation, the effect of asymmetry on the critical behavior and probability density of Bak-Sneppen models. Two kinds of anisotropy are investigated: (i) different numbers of sites to the left and right of the central (minimum) site are updated and (ii) sites to the left and right of the central site are renewed in different ways. Of particular interest is the crossover from symmetric to asymmetric scaling for weakly asymmetric dynamics, and the collapse of data with different numbers of updated sites but the same degree of asymmetry. All non-symmetric rules studied fall, independent of the degree of asymmetry, in the same universality class. Conversely, symmetric variants reproduce the exponents of the original model. Our results confirm the existence of two symmetry-based universality classes for extremal dynamics.Comment: 14 pages, 8 figures, 1 tabl

Search and Placement in Tiered Cache Networks

Content distribution networks have been extremely successful in today's Internet. Despite their success, there are still a number of scalability and performance challenges that motivate clean slate solutions for content dissemination, such as content centric networking. In this paper, we address two of the fundamental problems faced by any content dissemination system: content search and content placement. We consider a multi-tiered, multi-domain hierarchical system wherein random walks are used to cope with the tradeoff between exploitation of known paths towards custodians versus opportunistic exploration of replicas in a given neighborhood. TTL-like mechanisms, referred to as reinforced counters, are used for content placement. We propose an analytical model to study the interplay between search and placement. The model yields closed form expressions for metrics of interest such as the average delay experienced by users and the load placed on custodians. Then, leveraging the model solution we pose a joint placement-search optimization problem. We show that previously proposed strategies for optimal placement, such as the square-root allocation, follow as special cases of ours, and that a bang-bang search policy is optimal if content allocation is given