Monotones and invariants for multi-particle quantum states

We introduce new entanglement monotones which generalize, to the case of many parties, those which give rise to the majorization-based partial ordering of bipartite states' entanglement. We give some examples of restrictions they impose on deterministic and probabilistic conversion between multipartite states via local actions and classical communication. These include restrictions which do not follow from any bipartite considerations. We derive supermultiplicativity relations between each state's monotones and the monotones for collective processing when the parties share several states. We also investigate polynomial invariants under local unitary transformations, and show that a large class of these are invariant under collective unitary processing and also multiplicative, putting restrictions, for example, on the exact conversion of multiple copies of one state to multiple copies of another.Comment: 25 pages, LaTe

"There Were Only Friendly People and Love in the Air": Fans, Tourism and the Eurovision Song Contest

This chapter will give some insight into the Eurovision Song Contest (ESC) as an event that attracts a particular group of tourists – fans. Fan tourism is a growing field and the travel industries are increasingly viewing fans as a key market segment. What makes the ESC unique both as an event and a fandom is that the fans are firstly fans of the competition, and not of a particular artist. With a television audience of around 200 million the ESC can be regarded as a mega event, but despite its size it has maintained a certain intimacy – which may be partly due to the friendly atmosphere among the traveling fans (many of whom are regular ESC attendees). The ESC as a media event is sometimes prone to stereotyping, and perhaps constructing simplified European identities, but the corporal event experience adds other aspects and dimensions. While watching from the sofa and following social media comments may reinforce old-fashioned dichotomies, traveling to attend the event and mixing with fans from other countries foster a greater sense of respect for other cultures

Spectra and eigenstates of spin chain Hamiltonians

We prove that translationally invariant Hamiltonians of a chain of $n$ qubits with nearest-neighbour interactions have two seemingly contradictory features. Firstly in the limit $n\rightarrow\infty$ we show that any translationally invariant Hamiltonian of a chain of $n$ qubits has an eigenbasis such that almost all eigenstates have maximal entanglement between fixed-size sub-blocks of qubits and the rest of the system; in this sense these eigenstates are like those of completely general Hamiltonians (i.e. Hamiltonians with interactions of all orders between arbitrary groups of qubits). Secondly in the limit $n\rightarrow\infty$ we show that any nearest-neighbour Hamiltonian of a chain of $n$ qubits has a Gaussian density of states; thus as far as the eigenvalues are concerned the system is like a non-interacting one. The comparison applies to chains of qubits with translationally invariant nearest-neighbour interactions, but we show that it is extendible to much more general systems (both in terms of the local dimension and the geometry of interaction). Numerical evidence is also presented which suggests that the translational invariance condition may be dropped in the case of nearest-neighbour chains.Comment: Updated figures, as accepted in 'Communications in Mathematical Physics' on 5 January 201

Gamma Rays From The Galactic Center and the WMAP Haze

Recently, an analysis of data from the Fermi Gamma Ray Space Telescope has revealed a flux of gamma rays concentrated around the inner ~0.5 degrees of the Milky Way, with a spectrum that is sharply peaked at 2-4 GeV. If interpreted as the products of annihilating dark matter, this signal implies that the dark matter consists of particles with a mass between 7.3 and 9.2 GeV annihilating primarily to charged leptons. This mass range is very similar to that required to accommodate the signals reported by CoGeNT and DAMA/LIBRA. In addition to gamma rays, the dark matter is predicted to produce energetic electrons and positrons in the Inner Galaxy, which emit synchrotron photons as a result of their interaction with the galactic magnetic field. In this letter, we calculate the flux and spectrum of this synchrotron emission assuming that the gamma rays from the Galactic Center originate from dark matter, and compare the results to measurements from the WMAP satellite. We find that a sizable flux of hard synchrotron emission is predicted in this scenario, and that this can easily account for the observed intensity, spectrum, and morphology of the "WMAP Haze".Comment: 5 pages, 4 figure

Random matrices and quantum spin chains

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the density of states when $n \rightarrow\infty$, giving explicit bounds on the rate of approach to the limit. Universality within a class of probability measures and the extension to more general interaction geometries are established. The level spacing distributions of the Gaussian Orthogonal, Unitary and Symplectic Ensembles are observed numerically for the energy levels in these ensembles.Comment: Updated figures, as accepted in 'Markov Processes and Related Fields' on 3 March 201

Unstable coronal loops : numerical simulations with predicted observational signatures

We present numerical studies of the nonlinear, resistive magnetohydrodynamic (MHD) evolution of coronal loops. For these simulations we assume that the loops carry no net current, as might be expected if the loop had evolved due to vortex flows. Furthermore the initial equilibrium is taken to be a cylindrical flux tube with line-tied ends. For a given amount of twist in the magnetic field it is well known that once such a loop exceeds a critical length it becomes unstableto ideal MHD instabilities. The early evolution of these instabilities generates large current concentrations. Firstly we show that these current concentrations are consistent with the formation of a current sheet. Magnetic reconnection can only occur in the vicinity of these current concentrations and we therefore couple the resistivity to the local current density. This has the advantage of avoiding resistive diffusion in regions where it should be negligible. We demonstrate the importance of this procedure by comparison with simulations based on a uniform resistivity. From our numerical experiments we are able to estimate some observational signatures for unstable coronal loops. These signatures include: the timescale of the loop brightening; the temperature increase; the energy released and the predicted observable flow speeds. Finally we discuss to what extent these observational signatures are consistent with the properties of transient brightening loops.Comment: 13 pages, 9 figure

Optimal Entanglement Enhancement for Mixed States

We consider the actions of protocols involving local quantum operations and classical communication (LQCC) on a single system consisting of two separated qubits. We give a complete description of the orbits of the space of states under LQCC and characterise the representatives with maximal entanglement of formation. We thus obtain a LQCC entanglement concentration protocol for a single given state (pure or mixed) of two qubits which is optimal in the sense that the protocol produces, with non-zero probability, a state of maximal possible entanglement of formation. This defines a new entanglement measure, the maximum extractable entanglement.Comment: Final version: to appear in Phys. Rev. Let