Correlated random fields in dielectric and spin glasses

Both orientational glasses and dipolar glasses possess an intrinsic random field, coming from the volume difference between impurity and host ions. We show this suppresses the glass transition, causing instead a crossover to the low $T$ phase. Moreover the random field is correlated with the inter-impurity interactions, and has a broad distribution. This leads to a peculiar variant of the Imry-Ma mechanism, with 'domains' of impurities oriented by a few frozen pairs. These domains are small: predictions of domain size are given for specific systems, and their possible experimental verification is outlined. In magnetic glasses in zero field the glass transition survives, because the random fields are disallowed by time-reversal symmetry; applying a magnetic field then generates random fields, and suppresses the spin glass transition.Comment: minor modifications, final versio

Examples for the Infinite Dimensional Morse Lemma

Examples are presented which show how to use the Morse lemma in specific infinite dimensional examples and what can go wrong if various hypotheses are dropped. One of the examples shows that the version of the Morse lemma using singularity theory can hold, yet the hypotheses of the Morse–Palais and Morse–Tromba lemmas fail. Another example shows how to obtain a concrete normal form in infinite dimensions using the splitting lemma and hypotheses related to those in the Morse–Tromba lemma. An example of Dancer is given which shows that for the validity of the Morse lemma in Hilbert space, some hypotheses on the higher order terms must be made in addition to smoothness, if the quadratic term is only weakly nondegenerate. A general conjecture along these lines is made

Low temperature universality in disordered solids

The low temperature universal properties in disordered and amorphous solids are considered. We introduce a model that includes two types of two level systems (TLSs), which, based on their local symmetry, interact weakly or strongly with the phonon field. This accounts well for the experimental results, and addresses some long-standing questions: the nature of the TLSs; the smallness and universality of the phonon attenuation, and the energy scale of $3$K below which universality is observed. Our model describes disordered lattices; we also discuss its application to amorphous solids.Comment: 12 pages, 4 figures, published versio

Quantum spin glass in anisotropic dipolar systems

The spin-glass phase in the \LHx compound is considered. At zero transverse field this system is well described by the classical Ising model. At finite transverse field deviations from the transverse field quantum Ising model are significant, and one must take properly into account the hyperfine interactions, the off-diagonal terms in the dipolar interactions, and details of the full J=8 spin Hamiltonian to obtain the correct physical picture. In particular, the system is not a spin glass at finite transverse fields and does not show quantum criticality.Comment: 6 pages, 2 figures, to appear in J. Phys. Condens. Matter (proceedings of the HFM2006 conference

Analysis of error growth and stability for the numerical integration of the equations of chemical kinetics

Error growth and stability analyzed for numerical integration of differential equations in chemical kinetic

Deprojection of luminosity functions of galaxies in the Coma cluster

We use a simple analytic model to deproject 2-d luminosity functions (LF) of galaxies in the Coma cluster measured by Beijersbergen et al. 2002. We demonstrate that the shapes of the LFs change after deprojection. It is therefore essential to correct LFs for projection effects. The deprojected LFs of the central area have best-fitting Schechter parameters of M^{*}_U=-18.31^{+0.08}_{-0.08} and \alpha_U=-1.27^{+0.018}_{-0.018}, M^{*}_B=-19.79^{+0.14}_{-0.15} and \alpha_B=-1.44^{+0.016}_{-0.016} and M^{*}_r=-21.77^{+0.20}_{-0.28} and \alpha_r=-1.27^{+0.012}_{-0.012}. The corrections are not significant enough to change the previously observed trend of increasing faint end slopes with increasing distance to the cluster center. The weighted U, B, and r band slopes of the deprojected LFs show a slightly weaker steepening with increasing projected cluster radius.Comment: Accepted for publication in A&A as a Research Not

A microlensing measurement of dark matter fractions in three lensing galaxies

Direct measurements of dark matter distributions in galaxies are currently only possible through the use of gravitational lensing observations. Combinations of lens modelling and stellar velocity dispersion measurements provide the best constraints on dark matter distributions in individual galaxies, however they can be quite complex. In this paper, we use observations and simulations of gravitational microlensing to measure the smooth (dark) matter mass fraction at the position of lensed images in three lens galaxies: MG 0414+0534, SDSS J0924+0219 and Q2237+0305. The first two systems consist of early-type lens galaxies, and both display a flux ratio anomaly in their close image pair. Anomalies such as these suggest a high smooth matter percentage is likely, and indeed we prefer ~50 per cent smooth matter in MG 0414+0534, and ~80 per cent in SDSS J0924+0219 at the projected locations of the lensed images. Q2237+0305 differs somewhat in that its lensed images lie in the central kiloparsec of the barred spiral lens galaxy, where we expect stars to dominate the mass distribution. In this system, we find a smooth matter percentage that is consistent with zero.Comment: 7 pages, 4 figures. Accepted for publication in Ap

CTQ 839: Candidate for the Smallest Projected Separation Binary Quasar

We report the discovery of the new double quasar CTQ 839. This B = 18.3, radio quiet quasar pair is separated by 2.1" in BRIH filters with magnitude differences of delta m_B = 2.5, delta m_R = delta m_I = 1.9, and delta m_H = 2.3. Spectral observations reveal both components to be z = 2.24 quasars, with relative redshifts that agree at the 100 km/s level, but exhibit pronounced differences in the equivalent widths of related emission features, as well as an enhancement of blue continuum flux in the brighter component longward of the Ly alpha emission feature. In general, similar redshift double quasars can be the result of a physical binary pair, or a single quasar multiply imaged by gravitational lensing. Empirical PSF subtraction of R and H band images of CTQ 839 reveal no indication of a lensing galaxy, and place a detection limit of R = 22.5 and H = 17.4 for a third component in the system. For an Einstein-de Sitter cosmology and SIS model, the R band detection limit constrains the characteristics of any lensing galaxy to z_lens >= 1 with a corresponding luminosity of L >~ 5 L_*, while an analysis based on the redshift probability distribution for the lensing galaxy argues against the existence of a z_lens >~ 1 lens at the 2 sigma level. A similar analysis for a Lambda dominated cosmology, however, does not significantly constrain the existence of any lensing galaxy. The broadband flux differences, spectral dissimilarities, and failure to detect a lensing galaxy make the lensing hypothesis for CTQ 839 unlikely. The similar redshifts of the two components would then argue for a physical quasar binary. At a projected separation of 8.3/h kpc (Omega_matter = 1), CTQ 839 would be the smallest projected separation binary quasar currently known.Comment: Latex, 23 pages including 5 ps figures; accepted for publication in A

Neutrino Mass from Triplet and Doublet Scalars at the TeV Scale

If the minimal standard model of particle interactions is extended to include a scalar triplet with lepton number $L=-2$ and a scalar doublet with $L=-1$, neutrino masses $m_\nu \sim \mu_{12}^4 v^2/M^5 \sim 10^{-2}$ eV is possible, where $v \sim 10^2$ GeV is the electroweak symmetry breaking scale, $M \sim 1$ TeV is the typical mass of the new scalars, and $\mu_{12} \sim 1$ GeV is a soft lepton-number-violating parameter.Comment: 6 pages, no figur

What are the interactions in quantum glasses?

The form of the low-temperature interactions between defects in neutral glasses is reconsidered. We analyse the case where the defects can be modelled either as simple 2-level tunneling systems, or tunneling rotational impurities. The coupling to strain fields is determined up to 2nd order in the displacement field. It is shown that the linear coupling generates not only the usual $1/r^3$ Ising-like interaction between the rotational tunneling defect modes, which cause them to freeze around a temperature $T_G$, but also a random field term. At lower temperatures the inversion symmetric tunneling modes are still active - however the coupling of these to the frozen rotational modes, now via the 2nd-order coupling to phonons, generates another random field term acting on the inversion symmetric modes (as well as shorter-range $1/r^5$ interactions between them). Detailed expressions for all these couplings are given.Comment: 12 pages, 2 figures. Minor modifications, published versio