Strichartz estimates for the Schr\"odinger equation on polygonal domains

We prove Strichartz estimates with a loss of derivatives for the Schr\"odinger equation on polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions. Using a standard doubling procedure, estimates the on polygon follow from those on Euclidean surfaces with conical singularities. We develop a Littlewood-Paley squarefunction estimate with respect to the spectrum of the Laplacian on these spaces. This allows us to reduce matters to proving estimates at each frequency scale. The problem can be localized in space provided the time intervals are sufficiently small. Strichartz estimates then follow from a result of the second author regarding the Schr\"odinger equation on the Euclidean cone.Comment: 12 page

Universality of ac-conduction in anisotropic disordered systems: An effective medium approximation study

Anisotropic disordered system are studied in this work within the random barrier model. In such systems the transition probabilities in different directions have different probability density functions. The frequency-dependent conductivity at low temperatures is obtained using an effective medium approximation. It is shown that the isotropic universal ac-conduction law, $\sigma \ln \sigma=u$, is recovered if properly scaled conductivity ($\sigma$) and frequency ($u$) variables are used.Comment: 5 pages, no figures, final form (with corrected equations

Quantum entanglement and teleportation in pulsed cavity-optomechanics

Entangling a mechanical oscillator with an optical mode is an enticing and yet a very challenging goal in cavity optomechanics. Here we consider a pulsed scheme to create Einstein-Podolsky-Rosen-type entanglement between a traveling-wave light pulse and a mechanical oscillator. The entanglement can be verified unambiguously by a pump-probe sequence of pulses. In contrast to schemes that work in a steady-state regime under a continuous-wave drive, this protocol is not subject to stability requirements that normally limit the strength of achievable entanglement. We investigate the protocol's performance under realistic conditions, including mechanical decoherence, in full detail. We discuss the relevance of a high mechanical Qf product for entanglement creation and provide a quantitative statement on which magnitude of the Qf product is necessary for a successful realization of the scheme. We determine the optimal parameter regime for its operation and show it to work in current state-of-the-art systems.Comment: 10 pages, 2 figure

AAT Imaging and Microslit Spectroscopy in the Southern Hubble Deep Field

We present a deep photometric (B- and R-band) catalog and an associated spectroscopic redshift survey conducted in the vicinity of the Hubble Deep Field South. The spectroscopy yields 53 extragalactic redshifts in the range 0<z<1.4 substantially increasing the body of spectroscopic work in this field to over 200 objects. The targets are selected from deep AAT prime focus images complete to R<24 and spectroscopy is 50% complete at R=23. There is now strong evidence for a rich cluster at z\simeq 0.58 flanking the WFPC2 field which is consistent with a known absorber of the bright QSO in this field. We find that photometric redshifts of z<1 galaxies in this field based on HST data are accurate to \sigma_z/(1+z)=0.03 (albeit with small number statistics). The observations were carried out as a community service for Hubble Deep Field science, to demonstrate the first use of the `nod & shuffle' technique with a classical multi-object spectrograph and to test the use of `microslits' for ultra-high multiplex observations along with a new VPH grism and deep-depletion CCD. The reduction of this new type of data is also described.Comment: From the better late than never department: AJ in press (2006). 16 pages, 2 tables, 6 figures, final data release + Appendix at http://www.aao.gov.au/hdfs/Redshifts

Symmetry-allowed phase transitions realized by the two-dimensional fully frustrated XY class

A 2D Fully Frustrated XY(FFXY) class of models is shown to contain a new groundstate in addition to the checkerboard groundstates of the standard 2D FFXY model. The spin configuration of this additional groundstate is obtained. Associated with this groundstate there are additional phase transitions. An order parameter accounting for these new transitions is proposed. The transitions associated with the new order parameter are suggested to be similar to a 2D liquid-gas transition which implies Z_2-Ising like transitions. This suggests that the class of 2D FFXY models belongs within a U(1) x Z_2 x Z_2-designation of possible transitions, which implies that there are seven different possible single and combined transitions. MC-simulations for the generalized fully frustrated XY (GFFXY) model on a square lattice are used to investigate which of these possibilities can be realized in practice: five of the seven are encountered. Four critical points are deduced from the MC-simulations, three consistent with central charge c=3/2 and one with c=1. The implications for the standard 2D FFXY-model are discussed in particular with respect to the long standing controversy concerning the characteristics of its phase transitions.Comment: 8 pages, 8 figure

Considerations on the Unruh Effect: Causality and Regularization

This article is motivated by the observation, that calculations of the Unruh effect based on idealized particle detectors are usually made in a way that involves integrations along the {\em entire} detector trajectory up to the infinitely remote {\em future}. We derive an expression which allows time-dependence of the detector response in the case of a non-stationary trajectory and conforms more explicitely to the principle of causality, namely that the response at a given instant of time depends only on the detectors {\em past} movements. On trying to reproduce the thermal Unruh spectrum we are led to an unphysical result, which we trace down to the use of the standard regularization t\to t-i\eps of the correlation function. By consistently employing a rigid detector of finite extension, we are led to a different regularization which works fine with our causal response function.Comment: 19 pages, 2 figures, v2: some minor change