An {\it ab initio} relativistic coupled-cluster theory of dipole and quadrupole polarizabilities: Applications to a few alkali atoms and alkaline earth ions

We present a general approach within the relativistic coupled-cluster theory framework to calculate exactly the first order wave functions due to any rank perturbation operators. Using this method, we calculate the static dipole and quadrupole polarizabilities in some alkali atoms and alkaline earth-metal ions. This may be a good test of the present theory for different rank and parity interaction operators. This shows a wide range of applications including precise calculations of both parity and CP violating amplitudes due to rank zero and rank one weak interaction Hamiltonians. We also give contributions from correlation effects and discuss them in terms of lower order many-body perturbation theory.Comment: Three tables and one figur

Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes

We set up the singular initial value problem for quasilinear hyperbolic Fuchsian systems of first order and establish an existence and uniqueness theory for this problem with smooth data and smooth coefficients (and with even lower regularity). We apply this theory in order to show the existence of smooth (generally not analytic) T2-symmetric solutions to the vacuum Einstein equations, which exhibit AVTD (asymptotically velocity term dominated) behavior in the neighborhood of their singularities and are polarized or half-polarized.Comment: 78 page

Defective synapse maturation and enhanced synaptic plasticity in Shank2 Δex7(-/-) mice

Autism spectrum disorders (ASDs) are neurodevelopmental disorders with a strong genetic etiology. Since mutations in human SHANK genes have been found in patients with autism, genetic mouse models are used for a mechanistic understanding of ASDs and the development of therapeutic strategies. SHANKs are scaffold proteins in the postsynaptic density of mammalian excitatory synapses with proposed functions in synaptogenesis, regulation of dendritic spine morphology, and instruction of structural synaptic plasticity. In contrast to all studies so far on the function of SHANK proteins, we have previously observed enhanced synaptic plasticity in Shank2 Δex7(-/-) mice. In a series of experiments, we now reproduce these results, further explore the synaptic phenotype, and directly compare our model to the independently generated Shank2 Δex6-7(-/-) mice. Minimal stimulation experiments reveal that Shank2 Δex7(-/-) mice possess an excessive fraction of silent (i.e., α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid, short, AMPA receptor lacking) synapses. The synaptic maturation deficit emerges during the third postnatal week and constitutes a plausible mechanistic explanation for the mutants' increased capacity for long-term potentiation, both in vivo and in vitro. A direct comparison with Shank2 Δex6-7(-/-) mice adds weight to the hypothesis that both mouse models show a different set of synaptic phenotypes, possibly due to differences in their genetic background. These findings add to the diversity of synaptic phenotypes in neurodevelopmental disorders and further support the supposed existence of "modifier genes" in the expression and inheritance of ASDs

Efficient Resolution of Anisotropic Structures

We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus on the solution of transport equations which exhibit propagation of singularities where, additionally, high-dimensionality enters when the convection field, and hence the solutions, depend on parameters varying over some compact set. Important constituents of our approach are directionally adaptive discretization concepts motivated by compactly supported shearlet systems, and well-conditioned stable variational formulations that support trial spaces with anisotropic refinements with arbitrary directionalities. We prove that they provide tight error-residual relations which are used to contrive rigorously founded adaptive refinement schemes which converge in $L_2$. Moreover, in the context of parameter dependent problems we discuss two approaches serving different purposes and working under different regularity assumptions. For frequent query problems, making essential use of the novel well-conditioned variational formulations, a new Reduced Basis Method is outlined which exhibits a certain rate-optimal performance for indefinite, unsymmetric or singularly perturbed problems. For the radiative transfer problem with scattering a sparse tensor method is presented which mitigates or even overcomes the curse of dimensionality under suitable (so far still isotropic) regularity assumptions. Numerical examples for both methods illustrate the theoretical findings

Tau Polarization Asymmetry in B→Xsτ+τ−B\to X_s\tau^+\tau^-

Rare $B$ decays provide an opportunity to probe for new physics beyond the Standard Model. In this paper, we propose to measure the tau polarization in the inclusive decay $B\to X_s\tau^+\tau^-$ and discuss how it can be used, in conjunction with other observables, to completely determine the parameters of the flavor-changing low-energy effective Hamiltonian. Both the Standard Model and several new physics scenarios are examined. This process has a large enough branching fraction, $\sim {\rm few}\times 10^{-7}$, such that sufficient statistics will be provided by the B-Factories currently under construction.Comment: 11 pages, LaTex file with psfig. Figures included via uufiles. Lengthened version. Includes new calculation of Monte Carlo fit to Wilson coefficient

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Probing exotic phenomena at the interface of nuclear and particle physics with the electric dipole moments of diamagnetic atoms: A unique window to hadronic and semi-leptonic CP violation

The current status of electric dipole moments of diamagnetic atoms which involves the synergy between atomic experiments and three different theoretical areas -- particle, nuclear and atomic is reviewed. Various models of particle physics that predict CP violation, which is necessary for the existence of such electric dipole moments, are presented. These include the standard model of particle physics and various extensions of it. Effective hadron level combined charge conjugation (C) and parity (P) symmetry violating interactions are derived taking into consideration different ways in which a nucleon interacts with other nucleons as well as with electrons. Nuclear structure calculations of the CP-odd nuclear Schiff moment are discussed using the shell model and other theoretical approaches. Results of the calculations of atomic electric dipole moments due to the interaction of the nuclear Schiff moment with the electrons and the P and time-reversal (T) symmetry violating tensor-pseudotensor electron-nucleus are elucidated using different relativistic many-body theories. The principles of the measurement of the electric dipole moments of diamagnetic atoms are outlined. Upper limits for the nuclear Schiff moment and tensor-pseudotensor coupling constant are obtained combining the results of atomic experiments and relativistic many-body theories. The coefficients for the different sources of CP violation have been estimated at the elementary particle level for all the diamagnetic atoms of current experimental interest and their implications for physics beyond the standard model is discussed. Possible improvements of the current results of the measurements as well as quantum chromodynamics, nuclear and atomic calculations are suggested.Comment: 46 pages, 19 tables and 16 figures. A review article accepted for EPJ