Bowen Measure From Heteroclinic Points

We present a new construction of the entropy-maximizing, invariant probability measure on a Smale space (the Bowen measure). Our construction is based on points that are unstably equivalent to one given point, and stably equivalent to another: heteroclinic points. The spirit of the construction is similar to Bowen's construction from periodic points, though the techniques are very different. We also prove results about the growth rate of certain sets of heteroclinic points, and about the stable and unstable components of the Bowen measure. The approach we take is to prove results through direct computation for the case of a Shift of Finite type, and then use resolving factor maps to extend the results to more general Smale spaces

A deep sea docking station for ODYSSEY class autonomous underwater vehicles

Under subcontract to the Massachusetts Institute of Technology's (MIT) Sea Grant Autonomous Ocean Sampling Network (AOSN) program, engineers and researchers at the Woods Hole Oceanographic Institution (WHOI) designed, fabricated and operated a deep sea Docking Station for ODYSSEY-class autonomous underwater vehicles (AUVs). The docking station provides shelter as well as power transfer and data exchange services for an AUV that is between autonomous midwater missions. The Station is integrated into the main tension member of a deep sea mooring system. A large subsea flotation sphere supports the mass of the Station above the seafoor. A surface expression connected by an umbilcal to the Station was capable of bi-directional satellite or radio frequency communications. Primary subsystems of the Docking Station described in this report include a dock controller with multi-sensor support, long-duration battery packs, a docking pole with a moving carage, an inductive link for power and data transfer, and information about how the Station was deployed, operated and recovered.Funding was provided by the Offce of Naval Research under Grant No. NOOO-14-95-1-1316

Biased EPR entanglement and its application to teleportation

We consider pure continuous variable entanglement with non-equal correlations between orthogonal quadratures. We introduce a simple protocol which equates these correlations and in the process transforms the entanglement onto a state with the minimum allowed number of photons. As an example we show that our protocol transforms, through unitary local operations, a single squeezed beam split on a beam splitter into the same entanglement that is produced when two squeezed beams are mixed orthogonally. We demonstrate that this technique can in principle facilitate perfect teleportation utilising only one squeezed beam.Comment: 8 pages, 5 figure

Teleportation of continuous variable polarisation states

This paper discusses methods for the optical teleportation of continuous variable polarisation states. We show that using two pairs of entangled beams, generated using four squeezed beams, perfect teleportation of optical polarisation states can be performed. Restricting ourselves to 3 squeezed beams, we demonstrate that polarisation state teleportation can still exceed the classical limit. The 3-squeezer schemes involve either the use of quantum non-demolition measurement or biased entanglement generated from a single squeezed beam. We analyse the efficacies of these schemes in terms of fidelity, signal transfer coefficients and quantum correlations

Finite temperature bosonization

Finite temperature properties of a non-Fermi liquid system is one of the most challenging probelms in current understanding of strongly correlated electron systems. The paradigmatic arena for studying non-Fermi liquids is in one dimension, where the concept of a Luttinger liquid has arisen. The existence of a critical point at zero temperature in one dimensional systems, and the fact that experiments are all undertaken at finite temperature, implies a need for these one dimensional systems to be examined at finite temperature. Accordingly, we extended the well-known bosonization method of one dimensional electron systems to finite temperatures. We have used this new bosonization method to calculate finite temperature asymptotic correlation functions for linear fermions, the Tomonaga-Luttinger model, and the Hubbard model.Comment: REVTex, 48 page

Finite type approximations of Gibbs measures on sofic subshifts

Consider a H\"older continuous potential $\phi$ defined on the full shift A^\nn, where $A$ is a finite alphabet. Let X\subset A^\nn be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$ associated to $\phi$. Besides, there is a natural nested sequence of subshifts of finite type $(X_m)$ converging to the sofic subshift $X$. To this sequence we can associate a sequence of Gibbs measures $(\mu_{\phi}^m)$. In this paper, we prove that these measures weakly converge at exponential speed to $\mu_\phi$ (in the classical distance metrizing weak topology). We also establish a strong mixing property (ensuring weak Bernoullicity) of $\mu_\phi$. Finally, we prove that the measure-theoretic entropy of $\mu_\phi^m$ converges to the one of $\mu_\phi$ exponentially fast. We indicate how to extend our results to more general subshifts and potentials. We stress that we use basic algebraic tools (contractive properties of iterated matrices) and symbolic dynamics.Comment: 18 pages, no figure

A Near-Solar Metallicity, Nitrogen-Deficient Lyman Limit Absorber Associated with two S0 Galaxies

From UV spectra of the bright quasar PHL 1811 recorded by FUSE and the E140M configuration on STIS, we have determined the abundances of various atomic species in a Lyman limit system at z = 0.0809 with log N(H I) = 17.98. Considerably more hydrogen may be in ionized form, since the abundances of C II, Si II, S II and Fe II are very large compared to that of O I, when compared to their respective solar abundance ratios. Our determination [O/H] = -0.19 in the H I-bearing gas indicates that the chemical enrichment of the gas is unusually high for an extragalactic QSO absorption system. However, this same material has an unusually low abundance of nitrogen, [N/O] < -0.59, indicating that there may not have been enough time during this enrichment for secondary nitrogen to arise from low and intermediate mass stars. In an earlier investigation we found two galaxies at nearly the same redshift as this absorption system and displaced by 34 and 87 kpc from the line of sight. An r-band image recorded by the ACS on HST indicates these are S0 galaxies. One or both of these galaxies may be the source of the gas, which might have been expelled in a fast wind, by tidal stripping, or by ram-pressure stripping. Subtraction of the ACS point-spread function from the image of the QSO reveals the presence of a face-on spiral galaxy under the glare of the quasar; although it is possible that this galaxy may be responsible for the Lyman limit absorption, the exact alignment of the QSO with the center of the galaxy suggests that the spiral is the quasar host.Comment: 74 pages, 14 figures; to be published in the Astrophysical Journal (Part 1) May 1, 2005 issue. A version of the paper with figures of better quality may be found at http://www.astro.princeton.edu/~ebj/PHL1811_paper.ps (postscript) or http://www.astro.princeton.edu/~ebj/PHL1811_paper.pdf (pdf

Understanding initial data for black hole collisions

Numerical relativity, applied to collisions of black holes, starts with initial data for black holes already in each other's strong field. The initial hypersurface data typically used for computation is based on mathematical simplifying prescriptions, such as conformal flatness of the 3-geometry and longitudinality of the extrinsic curvature. In the case of head on collisions of equal mass holes, there is evidence that such prescriptions work reasonably well, but it is not clear why, or whether this success is more generally valid. Here we study these questions by considering the ``particle limit'' for head on collisions of nonspinning holes. Einstein's equations are linearized in the mass of the small hole, and described by a single gauge invariant spacetime function psi, for each multipole. The resulting equations have been solved by numerical evolution for collisions starting from various initial separations, and the evolution is studied on a sequence of hypersurfaces. In particular, we extract hypersurface data, that is psi and its time derivative, on surfaces of constant background Schwarzschild time. These evolved data can then be compared with ``prescribed'' data, evolved data can be replaced by prescribed data on any hypersurface, and evolved further forward in time, a gauge invariant measure of deviation from conformal flatness can be evaluated, etc. The main findings of this study are: (i) For holes of unequal mass the use of prescribed data on late hypersurfaces is not successful. (ii) The failure is likely due to the inability of the prescribed data to represent the near field of the smaller hole. (iii) The discrepancy in the extrinsic curvature is more important than in the 3-geometry. (iv) The use of the more general conformally flat longitudinal data does not notably improve this picture.Comment: 20 pages, REVTEX, 26 PS figures include