The strain gap in a system of weakly and strongly interacting two-level systems

Many disordered lattices exhibit remarkable universality in their low temperature properties, similar to that found in amorphous solids. Recently a two-TLS (two-level system) model was derived based on the microscopic characteristics of disordered lattices. Within the two-TLS model the quantitative universality of phonon attenuation, and the energy scale of $1-3$ K below which universality is observed, are derived as a consequence of the existence of two types of TLSs, differing by their interaction with the phonon field. In this paper we calculate analytically and numerically the densities of states (DOS) of the weakly and strongly interacting TLSs. We find that the DOS of the former can be well described by a Gaussian function, whereas the DOS of the latter have a power law correlation gap at low energies, with an intriguing dependence of the power on the short distance cutoff of the interaction. Both behaviors are markedly different from the logarithmic gap exhibited by a single species of interacting TLSs. Our results support the notion that it is the weakly interacting $\tau$-TLSs that dictate the standard low temperature glassy physics. Yet, the power-law DOS we find for the $S$-TLSs enables the prediction of a number of deviations from the universal glassy behavior that can be tested experimentally. Our results carry through to the analogous system of electronic and nuclear spins, implying that electronic spin flip rate is significantly reduced at temperatures smaller than the magnitude of the hyperfine interaction.Comment: Version submitted to EPJ S

External Shear in Quadruply Imaged Lens Systems

We use publicly available N-body simulations and semi-analytic models of galaxy formation to estimate the levels of external shear due to structure near the lens in gravitational lens systems. We also describe two selection effects, specific to four-image systems, that enhance the probability of observing systems to have higher external shear. Ignoring additional contributions from "cosmic shear" and assuming that lens galaxies are not significantly flattened, we find that the mean shear at the position of a quadruple lens galaxy is 0.11, the rms shear is roughly 0.15, and there is roughly a 45% likelihood of external shear greater than 0.1. This is much larger than previous estimates and in good agreement with typical measured external shear. The higher shear primarily stems from the tendency of early-type galaxies, which are the majority of lenses, to reside in overdense regions.Comment: 5 pages, 2 figures, ApJ in press, minor revision

On the active site of elastase: Partial mapping by means of specific peptide substrates

AbstractRNase-S peptide as well as some related octa- and hexapeptides were found to be highly, reactive substrates of porcine elastase (e.g. Ala4-Lys-Phe: Km = 4500 M−1, kcat = 32 sec−1, C = 1.4 × 105 M−1 sec−1). Comparison of the various peptides led to the conclusion that the active site of porcine elastase is composed of 6–7 subsites (c.f. [1]). Preliminary mapping shows that subsites S2, S′1 and S′2 have hydrophobic character. Occupation of subsite S4 by the substrate is important for efficient hydrolysis. Binding at this subsite was found to be stereospecific

CP-violating Majorana phases, lepton-conserving processes and final state interactions

The CP-violating phases associated with Majorana neutrinos can give rise to CP-violating effects even in processes that conserve total Lepton number, such as \mu -> eee+, \mu + e -> e + e and others. After explaining the reasons that make this happen, we consider the calculation of the rates for the process of the form \ell_a + \ell_b -> \ell_a + \ell_c, and its conjugate \bar\ell_a + \bar\ell_b -> \bar\ell_a + \bar\ell_c, where \ell_a, \ell_b and \ell_c denote charged leptons of different flavors. In the context of the Standard Model with Majorana neutrinos, we show that the difference in the rates depends on such phases. Our calculations illustrate in detail the mechanics that operate behind the scene, and set the stage for carrying out the analogous, more complicated (as we explain), calculations for other processes such as \mu -> eee+ and its conjugate.Comment: Latex, axodraw, 24 page

Reactor mixing angle from hybrid neutrino masses

In terms of its eigenvector decomposition, the neutrino mass matrix (in the basis where the charged lepton mass matrix is diagonal) can be understood as originating from a tribimaximal dominant structure with small deviations, as demanded by data. If neutrino masses originate from at least two different mechanisms, referred to as "hybrid neutrino masses", the experimentally observed structure naturally emerges provided one mechanism accounts for the dominant tribimaximal structure while the other is responsible for the deviations. We demonstrate the feasibility of this picture in a fairly model-independent way by using lepton-number-violating effective operators, whose structure we assume becomes dictated by an underlying $A_4$ flavor symmetry. We show that if a second mechanism is at work, the requirement of generating a reactor angle within its experimental range always fixes the solar and atmospheric angles in agreement with data, in contrast to the case where the deviations are induced by next-to-leading order effective operators. We prove this idea is viable by constructing an $A_4$-based ultraviolet completion, where the dominant tribimaximal structure arises from the type-I seesaw while the subleading contribution is determined by either type-II or type-III seesaw driven by a non-trivial $A_4$ singlet (minimal hybrid model). After finding general criteria, we identify all the $\mathbb{Z}_N$ symmetries capable of producing such $A_4$-based minimal hybrid models.Comment: 18 pages, 5 figures. v3: section including sum rules added, accepted by JHE

Spin and Charge Correlations in Quantum Dots: An Exact Solution

The inclusion of charging and spin-exchange interactions within the Universal Hamiltonian description of quantum dots is challenging as it leads to a non-Abelian action. Here we present an {\it exact} analytical solution of the probem, in particular, in the vicinity of the Stoner instabilty point. We calculate several observables, including the tunneling density of states (TDOS) and the spin susceptibility. Near the instability point the TDOS exhibits a non-monotonous behavior as function of the tunneling energy, even at temperatures higher than the exchange energy. Our approach is generalizable to a broad set of observables, including the a.c. susceptibility and the absorption spectrum for anisotropic spin interaction. Our results could be tested in nearly ferromagnetic materials.Comment: JETPL class, 6 pages, 2 figure

Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications

Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.Comment: 16 pages, 0 figure

Chandra X-ray Observations of the Quadruply Lensed Quasar RX J0911.4+0551

We present results from X-ray observations of the quadruply lensed quasar RX J0911.4+0551 using data obtained with the Advanced CCD Imaging Spectrometer (ACIS) on board the Chandra X-ray Observatory. The 29 ks observation detects a total of ~404 X-ray photons (0.3 to 7.0 keV) from the four images of the lensed quasar. Deconvolution of the aspect corrected data resolves all four lensed images, with relative positions in good agreement with optical measurements. When compared to contemporaneous optical data, one of the lensed images (component A3) is dimmer by a factor of ~6 in X-rays with respect to the 2 brighter images (components A1 and A2). Spectral fitting for the combined images shows significant intrinsic absorption in the soft (0.2 to 2.4 keV) energy band, consistent with the mini-BAL nature of this quasar, while a comparison with ROSAT PSPC observations from 1990 shows a drop of ~6.5 in the total soft bandpass flux. The observations also detect ~157 X-ray photons arising from extended emission of the nearby cluster (peaked ~42" SW of RXJ0911.4+0551) responsible for the large external shear present in the system. The Chandra observation reveals the cluster emission to be complex and non-spherical, and yields a cluster temperature of kT = 2.3^{+1.8}_{-0.8} keV and a 2.0 to 10 keV cluster luminosity within a 1 Mpc radius of L_X = 7.6_{-0.2}^{+0.6} x 10^{43} ergs/s (error bars denote 90% confidence limits). Our mass estimate of the cluster within its virial radius is 2.3^{+1.8}_{-0.7} x 10^{14} solar, and is a factor of 2 smaller than, although consistent with, previous mass estimates based on the observed cluster velocity dispersion.Comment: 16 pages, 3 figures (figure 1 is color ps). Accepted by Ap