Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping

Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive $1/r$ interaction, we point out that the instance of self-trapping of the condensate, without external trap potential, is physically best understood by introducing appropriate "atomic" units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters $N^2 a/a_u$ and $\gamma/N^2$, where $N$ is the particle number, $a$ the scattering length, $a_u$ the "Bohr" radius and $\gamma$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, for energies, sizes and peak densities, and compare with previous variational results. As a novel feature we point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.Comment: 7 pages, 7 figures, to appear in Phys. Rev.

Hidden geometric correlations in real multiplex networks

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the individual layers. We find that these correlations are strong in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate: (i) the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers; (ii) accurate trans-layer link prediction, where connections in one layer can be predicted by observing the hidden geometric space of another layer; and (iii) efficient targeted navigation in the multilayer system using only local knowledge, which outperforms navigation in the single layers only if the geometric correlations are sufficiently strong. Our findings uncover fundamental organizing principles behind real multiplexes and can have important applications in diverse domains.Comment: Supplementary Materials available at http://www.nature.com/nphys/journal/v12/n11/extref/nphys3812-s1.pd

Alfven modes driven non-linearly by metric perturbations in anisotropic magnetized cosmologies

We consider anisotropic magnetized cosmologies filled with conductive plasma fluid and study the implications of metric perturbations that propagate parallel to the ambient magnetic field. It is known that in the first order (linear) approximation with respect to the amplitude of the perturbations no electric field and density perturbations arise. However, when we consider the non-linear coupling of the metric perturbations with their temporal derivatives, certain classes of solutions can induce steeply increasing in time electric field perturbations. This is verified both numerically and analytically. The source of these perturbations can be either high-frequency quantum vacuum fluctuations, driven by the cosmological pump field, in the early stages of the evolution of the Universe or astrophysical processes or a non-linear isotropization process of an initially anisotropic cosmological spacetime.Comment: 7 pages, RevTex, 3 figures ps, accepted for publication to IJMP

The spinorial geometry of supersymmetric backgrounds

We propose a new method to solve the Killing spinor equations of eleven-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1,10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for N=2 backgrounds provided that one of the spinors represents the orbit of Spin(1,10) with stability subgroup SU(5). We directly solve the Killing spinor equations of N=1 and some N=2, N=3 and N=4 backgrounds. In the N=2 case, we investigate backgrounds with SU(5) and SU(4) invariant Killing spinors and compute the associated spacetime forms. We find that N=2 backgrounds with SU(5) invariant Killing spinors admit a timelike Killing vector and that the space transverse to the orbits of this vector field is a Hermitian manifold with an SU(5)-structure. Furthermore, N=2 backgrounds with SU(4) invariant Killing spinors admit two Killing vectors, one timelike and one spacelike. The space transverse to the orbits of the former is an almost Hermitian manifold with an SU(4)-structure and the latter leaves the almost complex structure invariant. We explore the canonical form of Killing spinors for backgrounds with extended, N>2, supersymmetry. We investigate a class of N=3 and N=4 backgrounds with SU(4) invariant spinors. We find that in both cases the space transverse to a timelike vector field is a Hermitian manifold equipped with an SU(4)-structure and admits two holomorphic Killing vector fields. We also present an application to M-theory Calabi-Yau compactifications with fluxes to one-dimension.Comment: Latex, 54 pages, v2: clarifications made and references added. v3: minor changes. v4: minor change

Scalar field induced oscillations of neutron stars and gravitational collapse

We study the interaction of massless scalar fields with self-gravitating neutron stars by means of fully dynamic numerical simulations of the Einstein-Klein-Gordon perfect fluid system. Our investigation is restricted to spherical symmetry and the neutron stars are approximated by relativistic polytropes. Studying the nonlinear dynamics of isolated neutron stars is very effectively performed within the characteristic formulation of general relativity, in which the spacetime is foliated by a family of outgoing light cones. We are able to compactify the entire spacetime on a computational grid and simultaneously impose natural radiative boundary conditions and extract accurate radiative signals. We study the transfer of energy from the scalar field to the fluid star. We find, in particular, that depending on the compactness of the neutron star model, the scalar wave forces the neutron star either to oscillate in its radial modes of pulsation or to undergo gravitational collapse to a black hole on a dynamical timescale. The radiative signal, read off at future null infinity, shows quasi-normal oscillations before the setting of a late time power-law tail.Comment: 12 pages, 13 figures, submitted to Phys. Rev.

Measurement-based analysis of the dynamic performance of microgrids using system identification techniques

The dynamic performance of microgrids is of crucial importance, due to the increased complexity introduced by the combined effect of inverter interfaced and rotating distributed generation. This paper presents a methodology for the investigation of the dynamic behavior of microgrids based on measurements using Prony analysis and state-space black-box modeling techniques. Both methods are compared and evaluated using real operating conditions data obtained by a laboratory microgrid system. The recorded responses and the calculated system eigenvalues are used to analyze the system dynamics and interactions among the distributed generation units. The proposed methodology can be applied to any real-world microgrid configuration, taking advantage of the future smart grid technologies and features

Operator monotones, the reduction criterion and the relative entropy

We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures.Comment: Final version accepted for publication, added references in reference [1] and [13

Dynamic performance of a low voltage microgrid with droop controlled distributed generation

Microgrids are small-scale highly controlled networks designed to supply electrical energy. From the operational point of view, microgrids are active distribution networks, facilitating the integration of distributed generation units. Major technical issues in this concept include system stability and protection coordination which are significantly influenced by the high penetration of inverter-interfaced distributed energy sources. These units often adopt the frequency-active power and voltage-reactive power droop control strategy to participate in the load sharing of an islanded microgrid. The scope of the paper is to investigate the dynamic performance of a low voltage laboratory-scale microgrid system, using experimental results and introduce the concept of Prony analysis for understanding the connected components. Several small disturbance test cases are conducted and the investigations focus on the influence of the droop controlled distributed generation sources

Matter flows around black holes and gravitational radiation

We develop and calibrate a new method for estimating the gravitational radiation emitted by complex motions of matter sources in the vicinity of black holes. We compute numerically the linearized curvature perturbations induced by matter fields evolving in fixed black hole backgrounds, whose evolution we obtain using the equations of relativistic hydrodynamics. The current implementation of the proposal concerns non-rotating holes and axisymmetric hydrodynamical motions. As first applications we study i) dust shells falling onto the black hole isotropically from finite distance, ii) initially spherical layers of material falling onto a moving black hole, and iii) anisotropic collapse of shells. We focus on the dependence of the total gravitational wave energy emission on the flow parameters, in particular shell thickness, velocity and degree of anisotropy. The gradual excitation of the black hole quasi-normal mode frequency by sufficiently compact shells is demonstrated and discussed. A new prescription for generating physically reasonable initial data is discussed, along with a range of technical issues relevant to numerical relativity.Comment: 27 pages, 12 encapsulated figures, revtex, amsfonts, submitted to Phys. Rev.