Random Matrix Theory and Entanglement in Quantum Spin Chains

We compute the entropy of entanglement in the ground states of a general class of quantum spin-chain Hamiltonians - those that are related to quadratic forms of Fermi operators - between the first N spins and the rest of the system in the limit of infinite total chain length. We show that the entropy can be expressed in terms of averages over the classical compact groups and establish an explicit correspondence between the symmetries of a given Hamiltonian and those characterizing the Haar measure of the associated group. These averages are either Toeplitz determinants or determinants of combinations of Toeplitz and Hankel matrices. Recent generalizations of the Fisher-Hartwig conjecture are used to compute the leading order asymptotics of the entropy as N --> infinity . This is shown to grow logarithmically with N. The constant of proportionality is determined explicitly, as is the next (constant) term in the asymptotic expansion. The logarithmic growth of the entropy was previously predicted on the basis of numerical computations and conformal-field-theoretic calculations. In these calculations the constant of proportionality was determined in terms of the central charge of the Virasoro algebra. Our results therefore lead to an explicit formula for this charge. We also show that the entropy is related to solutions of ordinary differential equations of Painlev\'e type. In some cases these solutions can be evaluated to all orders using recurrence relations.Comment: 39 pages, 1 table, no figures. Revised version: minor correction

Reconstruction d'ensemble des événements spatio-temporels d'étiage extrême en France depuis 1871

International audienceThe length of streamflow observations is generally limited to the last 50 years even in data-rich countries like France. It therefore offers too small a sample of extreme low-flow events to properly explore the long-term evolution of their characteristics and associated impacts. To overcome this limit, this work first presents a daily 140-year ensemble reconstructed streamflow dataset for a reference network of near-natural catchments in France. This dataset, called SCOPE Hydro (Spatially COherent Probabilistic Extended Hydrological dataset), is based on (1) a probabilistic precipitation, temperature, and reference evapotranspiration downscaling of the Twentieth Century Reanalysis over France, called SCOPE Climate, and (2) continuous hydrological modelling using SCOPE Climate as forcings over the whole period. This work then introduces tools for defining spatio-temporal extreme low-flow events. Extreme low-flow events are first locally defined through the sequent peak algorithm using a novel combination of a fixed threshold and a daily variable threshold. A dedicated spatial matching procedure is then established to identify spatio-temporal events across France. This procedure is furthermore adapted to the SCOPE Hydro 25-member ensemble to characterize in a probabilistic way unrecorded historical events at the national scale. Extreme low-flow events are described and compared in a spatially and temporally homogeneous way over 140 years on a large set of catchments. Results highlight well-known recent events like 1976 or 1989-1990, but also older and relatively forgotten ones like the 1878 and 1893 events. These results contribute to improving our knowledge of historical events and provide a selection of benchmark events for climate change adaptation purposes. Moreover, this study allows for further detailed analyses of the effect of climate variability and anthropogenic climate change on low-flow hydrology at the scale of France

Entangled Light in Moving Frames

We calculate the entanglement between a pair of polarization-entangled photon beams as a function of the reference frame, in a fully relativistic framework. We find the transformation law for helicity basis states and show that, while it is frequency independent, a Lorentz transformation on a momentum-helicity eigenstate produces a momentum-dependent phase. This phase leads to changes in the reduced polarization density matrix, such that entanglement is either decreased or increased, depending on the boost direction, the rapidity, and the spread of the beam.Comment: 4 pages and 3 figures. Minor corrections, footnote on optimal basis state

Rapid angular expansion of the ionized core of CRL 618

Context. During the transition from the asymptotic giant branch (AGB) to the planetary nebulae phase the circumstellar envelopes of most low- and intermediate-mass stars experience a dramatic change in morphology. CRL 618 exhibits characteristics of both an AGB and post-AGB star. It also displays a spectacular array of bipolar lobes with a dense equatorial region, which makes it an excellent object for studying the development of asymmetries in evolved stars. In recent decades, an elliptical compact HII region located in the center of the nebula has been seen to be increasing in size and flux. This seems to be due to the ionization of the circumstellar envelope by the central star, and it probably indicates the beginning of the planetary nebula phase for CRL 618. Aims. We aim to determine the physical conditions under which the ionization of the circumstellar envelope of CRL 618 began to take place as well as the subsequent propagation of the ionization front. Methods. We analyzed interferometric radio continuum data at ~5 and 22 GHz from observations carried out at seven epochs with the VLA. We traced the flux increase of the ionized region over a period of ~26 years. We measured the dimensions of the HII region directly from the brightness distribution images to determine the increase of its size over time. For one of the epochs we analyzed observations at six frequencies from which we estimated the electron density distribution. We carried out model calculations of the spectral energy distribution at two different epochs to corroborate our observational results. Results. We found that the radio continuum flux and the size of the ionized region have been increasing monotonically in the past three decades. The size of the major axis of the HII region shows a dependance on frequency, which has been interpreted as a result of the gradient of the electron density in this direction. The growth of the HII region is due to the expansion of an ionized wind whose mass-loss rate increased continuously for a period of ~100 years until a few decades ago, when the mass-loss rate experienced a sudden decline. Our results indicate that the circumstellar envelope began to be ionized around 1971, which marks the start of the planetary nebula phase of CRL 618. © ESO, 2013

Entanglement entropy in quantum spin chains with finite range interaction

We study the entropy of entanglement of the ground state in a wide family of one-dimensional quantum spin chains whose interaction is of finite range and translation invariant. Such systems can be thought of as generalizations of the XY model. The chain is divided in two parts: one containing the first consecutive L spins; the second the remaining ones. In this setting the entropy of entanglement is the von Neumann entropy of either part. At the core of our computation is the explicit evaluation of the leading order term as L tends to infinity of the determinant of a block-Toeplitz matrix whose symbol belongs to a general class of 2 x 2 matrix functions. The asymptotics of such determinant is computed in terms of multi-dimensional theta-functions associated to a hyperelliptic curve of genus g >= 1, which enter into the solution of a Riemann-Hilbert problem. Phase transitions for thes systems are characterized by the branch points of the hyperelliptic curve approaching the unit circle. In these circumstances the entropy diverges logarithmically. We also recover, as particular cases, the formulae for the entropy discovered by Jin and Korepin (2004) for the XX model and Its, Jin and Korepin (2005,2006) for the XY model.Comment: 75 pages, 10 figures. Revised version with minor correction

Non-ohmic critical fluctuation conductivity of layered superconductors in magnetic field

Thermal fluctuation conductivity for a layered superconductor in perpendicular magnetic field is treated in the frame of the self-consistent Hartree approximation for an arbitrarily strong in-plane electric field. The simultaneous application of the two fields results in a slightly stronger suppression of the superconducting fluctuations, compared to the case when the fields are applied individually.Comment: 4 pages, 1 figure, to be published in Phys. Rev.

Numerical study of jets produced by conical wire arrays on the Magpie pulsed power generator

The aim of this work is to model the jets produced by conical wire arrays on the MAGPIE generator, and to design and test new setups to strengthen the link between laboratory and astrophysical jets. We performed the modelling with direct three-dimensional magneto-hydro-dynamic numerical simulations using the code GORGON. We applied our code to the typical MAGPIE setup and we successfully reproduced the experiments. We found that a minimum resolution of approximately 100 is required to retrieve the unstable character of the jet. We investigated the effect of changing the number of wires and found that arrays with less wires produce more unstable jets, and that this effect has magnetic origin. Finally, we studied the behaviour of the conical array together with a conical shield on top of it to reduce the presence of unwanted low density plasma flows. The resulting jet is shorter and less dense.Comment: Accepted for publication in Astrophysics & Space Science. HEDLA 2010 conference procedings. Final pubblication will be available on Springe