On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces

We study the recurrence and ergodicity for the billiard on noncompact polygonal surfaces with a free, cocompact action of $\Z$ or $\Z^2$. In the $\Z$-periodic case, we establish criteria for recurrence. In the more difficult $\Z^2$-periodic case, we establish some general results. For a particular family of $\Z^2$-periodic polygonal surfaces, known in the physics literature as the wind-tree model, assuming certain restrictions of geometric nature, we obtain the ergodic decomposition of directional billiard dynamics for a dense, countable set of directions. This is a consequence of our results on the ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure

'An outsider in our midst': narratives of Neil Lennon, soccer and ethno-religious igotry in the Scottish press

This essay offers a critique of media narratives concerning soccer and those of 'difference' in contemporary Scotland, in particular those who have Irishness as their different identity. It examines certain newspaper narratives concerning Neil Lennon of Celtic FC during autumn 2005. During this period Lennon was characterized as a soccer villain. The commentaries drew on existing perceptions concerning his personality and style of play. More importantly Lennon's national identity (Irish) and his religious background (Catholic) were integrated into the narratives, marking him as an outsider in Scotland. These narratives resonate with public and private discourses of 'otherness' concerning the Irish Catholic diaspora community in Scotland. These broader discourses are manifest as ethno-religious prejudices directed against this community. The discourses of 'outsider' and 'otherness' that surround Lennon, Celtic FC and the Irish Catholic community expose the myth of Scotland's collective self-image as an egalitarian and inclusive society

Celtic FC’s 1967 Lisbon Lions:Why the European Cup victory of the first club from Britain was a defining moment for the Irish diaspora in Scotland

In 1967, in Lisbon, Celtic Football Club, won the European Cup becoming the first club outside of Portugal, Spain and Italy to win it. The win was and is totemic for the Irish Catholic immigrant community in Scotland that has historically supported Celtic. We suggest the significance of the win reveals intersections of ethnicity, religion, nationalism, and the politics of ‘sectarianism’ in Scotland. During a period of discriminatory practices and attitudes towards Irish descended Catholics in Scotland, this iconic win for a Scottish based club born of Irish Catholics personified for this diaspora that (on one level) their day had arrived. This article explores the socio-cultural significance and legacy of ‘Lisbon 67ʹ for insider and outsider groups in Scotland. We reveal that soccer remains a central component of group memory connecting the past, present and future. We suggest Celtic’s win offered confidence and hope to a marginalized group within Scotland

Just a wind-up? Ethnicity, religion and prejudice in Scottish football-related comedy

This article probes how media representations of football in Scotland sustain the hegemonic ideologies associated with ethnicity and religion. The paper probes the football-related comedy output of one radio programme; radio output and football comedy are both neglected cultural material in studies of sport in Scotland. It argues that ambiguity and allusive language in comedy construct multiple interpretative possibilities that can demean the social and cultural identity of particular groups in society. The discussion analyses specific sketches from the Scottish radio comedy show Watson's Wind Up. It is concluded that although humorous, these sketches reveal how ideas, myths and stereotypes that coalesce round Celtic FC and the Irish-descended and Catholic communities in Scotland reinforce and sustain anti-Irish and anti-Catholic bigotry

Quantum state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience - using gravitational-wave detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer's classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the classical noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum state preparation, and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses, and the performance of the planned Advanced LIGO interferometers in quantum-state preparation

Searching for a Stochastic Background of Gravitational Waves with LIGO

The Laser Interferometer Gravitational-wave Observatory (LIGO) has performed the fourth science run, S4, with significantly improved interferometer sensitivities with respect to previous runs. Using data acquired during this science run, we place a limit on the amplitude of a stochastic background of gravitational waves. For a frequency independent spectrum, the new limit is $\Omega_{\rm GW} < 6.5 \times 10^{-5}$. This is currently the most sensitive result in the frequency range 51-150 Hz, with a factor of 13 improvement over the previous LIGO result. We discuss complementarity of the new result with other constraints on a stochastic background of gravitational waves, and we investigate implications of the new result for different models of this background.Comment: 37 pages, 16 figure

Search for gravitational wave bursts in LIGO's third science run

We report on a search for gravitational wave bursts in data from the three LIGO interferometric detectors during their third science run. The search targets subsecond bursts in the frequency range 100-1100 Hz for which no waveform model is assumed, and has a sensitivity in terms of the root-sum-square (rss) strain amplitude of hrss ~ 10^{-20} / sqrt(Hz). No gravitational wave signals were detected in the 8 days of analyzed data.Comment: 12 pages, 6 figures. Amaldi-6 conference proceedings to be published in Classical and Quantum Gravit

Upper limits on the strength of periodic gravitational waves from PSR J1939+2134

The first science run of the LIGO and GEO gravitational wave detectors presented the opportunity to test methods of searching for gravitational waves from known pulsars. Here we present new direct upper limits on the strength of waves from the pulsar PSR J1939+2134 using two independent analysis methods, one in the frequency domain using frequentist statistics and one in the time domain using Bayesian inference. Both methods show that the strain amplitude at Earth from this pulsar is less than a few times $10^{-22}$.Comment: 7 pages, 1 figure, to appear in the Proceedings of the 5th Edoardo Amaldi Conference on Gravitational Waves, Tirrenia, Pisa, Italy, 6-11 July 200

Improving the sensitivity to gravitational-wave sources by modifying the input-output optics of advanced interferometers

We study frequency dependent (FD) input-output schemes for signal-recycling interferometers, the baseline design of Advanced LIGO and the current configuration of GEO 600. Complementary to a recent proposal by Harms et al. to use FD input squeezing and ordinary homodyne detection, we explore a scheme which uses ordinary squeezed vacuum, but FD readout. Both schemes, which are sub-optimal among all possible input-output schemes, provide a global noise suppression by the power squeeze factor, while being realizable by using detuned Fabry-Perot cavities as input/output filters. At high frequencies, the two schemes are shown to be equivalent, while at low frequencies our scheme gives better performance than that of Harms et al., and is nearly fully optimal. We then study the sensitivity improvement achievable by these schemes in Advanced LIGO era (with 30-m filter cavities and current estimates of filter-mirror losses and thermal noise), for neutron star binary inspirals, and for narrowband GW sources such as low-mass X-ray binaries and known radio pulsars. Optical losses are shown to be a major obstacle for the actual implementation of these techniques in Advanced LIGO. On time scales of third-generation interferometers, like EURO/LIGO-III (~2012), with kilometer-scale filter cavities, a signal-recycling interferometer with the FD readout scheme explored in this paper can have performances comparable to existing proposals. [abridged]Comment: Figs. 9 and 12 corrected; Appendix added for narrowband data analysi