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

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

Shor-Preskill Type Security-Proofs for Concatenated Bennett-Brassard 1984 Quantum Key Distribution Protocol

We discuss long code problems in the Bennett-Brassard 1984 (BB84) quantum key distribution protocol and describe how they can be overcome by concatenation of the protocol. Observing that concatenated modified Lo-Chau protocol finally reduces to the concatenated BB84 protocol, we give the unconditional security of the concatenated BB84 protocol.Comment: 4 pages, RevTe

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

Uniqueness and Nondegeneracy of Ground States for (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page

Status of the PICASSO Project

The Picasso project is a dark matter search experiment based on the superheated droplet technique. Preliminary runs performed at the Picasso Lab in Montreal have showed the suitability of this detection technique to the search for weakly interacting cold dark matter particles. In July 2002, a new phase of the project started. A batch of six 1-liter detectors with an active mass of approximately 40g was installed in a gallery of the SNO observatory in Sudbury, Ontario, Canada at a depth of 6,800 feet (2,070m). We give a status report on the new experimental setup, data analysis, and preliminary limits on spin-dependent neutralino interaction cross section.Comment: 3 pages, 2 figures. To appear in the Proceedings of the TAUP 2003 conference, 5-9 September, 2003, University of Washington, Seattle, US

A small universe after all?

The cosmic microwave background radiation allows us to measure both the geometry and topology of the universe. It has been argued that the COBE-DMR data already rule out models that are multiply connected on scales smaller than the particle horizon. Here we show the opposite is true: compact (small) hyperbolic universes are favoured over their infinite counterparts. For a density parameter of Omega_o=0.3, the compact models are a better fit to COBE-DMR (relative likelihood ~20) and the large-scale structure data (sigma_8 increases by ~25%).Comment: 4 pages, RevTeX, 7 Figure

Open inflationary universes in a brane world cosmology

In this paper, we study a type of one-field model for open inflationary universe models in the context of the brane world models. In the scenario of a one-bubble universe model, we determine and characterize the existence of the Coleman-De Lucia instanton, together with the period of inflation after tunneling has occurred. Our results are compared to those found in the Einstein theory of Relativistic Models.Comment: 8 pages, 4 Figures, accepted in Physical Review

Gammaherpesvirus infection modulates the temporal and spatial expression of SCGB1A1 (CCSP) and BPIFA1 (SPLUNC1) in the respiratory tract

Murine γ-herpesvirus 68 (MHV-68) infection of Mus musculus-derived strains of mice is an established model of γ-herpesvirus infection. We have previously developed an alternative system using a natural host, the wood mouse (Apodemus sylvaticus), and shown that the MHV-68 M3 chemokine-binding protein contributes significantly to MHV-68 pathogenesis. Here we demonstrate in A. sylvaticus using high-density micro-arrays that M3 influences the expression of genes involved in the host response including Scgb1a1 and Bpifa1 that encode potential innate defense proteins secreted into the respiratory tract. Further analysis of MHV-68-infected animals showed that the levels of both protein and RNA for SCGB1A1 and BPIFA1 were decreased at day 7 post infection (p.i.) but increased at day 14 p.i. as compared with M3-deficient and mock-infected animals. The modulation of expression was most pronounced in bronchioles but was also present in the bronchi and trachea. Double staining using RNA in situ hybridization and immunohistology demonstrated that much of the BPIFA1 expression occurs in club cells along with SCGB1A1 and that BPIFA1 is stored within granules in these cells. The increase in SCGB1A1 and BPIFA1 expression at day 14 p.i. was associated with the differentiation of club cells into mucus-secreting cells. Our data highlight the role of club cells and the potential of SCGB1A1 and BPIFA1 as innate defense mediators during respiratory virus infection

Non-stoichiometric oxide and metal interfaces and reactions

We have employed a combination of experimental surface science techniques and density functional calculations to study the reduction of TiO2(110) surfaces through the doping with submonolayer transition metals. We concentrate on the role of Ti adatoms in self doping of rutile and contrast the behaviour to that of Cr. DFT+U calculations enable identification of probable adsorption structures and their spectroscopic characteristics. Adsorption of both metals leads to a broken symmetry and an asymmetric charge transfer localised around the defect site of a mixed localised/delocalised character. Charge transfer creates defect states with Ti 3d character in the band gap at similar to 1-eV binding energy. Cr adsorption, however, leads to a very large shift in the valence-band edge to higher binding energy and the creation of Cr 3d states at 2.8-eV binding energy. Low-temperature oxidation lifts the Ti-derived band-gap states and modifies the intensity of the Cr features, indicative of a change of oxidation state from Cr3+ to Cr4+. Higher temperature processing leads to a loss of Cr from the surface region, indicative of its substitution into the bulk