Quantum Nondemolition Squeezing of a Nanomechanical Resonator

We show that the nanoresonator position can be squeezed significantly below the ground state level by measuring the nanoresonator with a quantum point contact or a single-electron transistor and applying a periodic voltage across the detector. The mechanism of squeezing is basically a generalization of quantum nondemolition measurement of an oscillator to the case of continuous measurement by a weakly coupled detector. The quantum feedback is necessary to prevent the ``heating'' due to measurement back-action. We also discuss a procedure of experimental verification of the squeezed state.Comment: 9 pages, 3 figure

Mesoscopic Mechanical Resonators as Quantum Non-Inertial Reference Frames

An atom attached to a micrometer-scale wire that is vibrating at a frequency of 100 MHz and with displacement amplitude 1 nm experiences an acceleration magnitude 10^9 ms^-2, approaching the surface gravity of a neutron star. As one application of such extreme non-inertial forces in a mesoscopic setting, we consider a model two-path atom interferometer with one path consisting of the 100 MHz vibrating wire atom guide. The vibrating wire guide serves as a non-inertial reference frame and induces an in principle measurable phase shift in the wave function of an atom traversing the wire frame. We furthermore consider the effect on the two-path atom wave interference when the vibrating wire is modeled as a quantum object, hence functioning as a quantum non-inertial reference frame. We outline a possible realization of the vibrating wire, atom interferometer using a superfluid helium quantum interference setup.Comment: Published versio

Multilevel Monte Carlo for Random Degenerate Scalar Convection Diffusion Equation

We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous dependence of weak solutions on data in the deterministic case, we develop a definition of random entropy solution. We establish existence, uniqueness, measurability and integrability results for these random entropy solutions, generalizing \cite{Mishr478,MishSch10a} to possibly degenerate hyperbolic-parabolic problems with random data. We next address the numerical approximation of random entropy solutions, specifically the approximation of the deterministic first and second order statistics. To this end, we consider explicit and implicit time discretization and Finite Difference methods in space, and single as well as Multi-Level Monte-Carlo methods to sample the statistics. We establish convergence rate estimates with respect to the discretization parameters, as well as with respect to the overall work, indicating substantial gains in efficiency are afforded under realistic regularity assumptions by the use of the Multi-Level Monte-Carlo method. Numerical experiments are presented which confirm the theoretical convergence estimates.Comment: 24 Page

Flavor Changing Neutral Current Effects and CP Violation in the Minimal 3-3-1 Model

We investigate in detail the flavor structure of the minimal 331 model and its implications for several flavor changing neutral current (FCNC) processes. In this model, where the weak SU(2)_L gauge group of the Standard Model is extended to a SU(3)_L, the by far dominant new contributions come from an additional neutral Z' gauge boson, that can transmit FCNCs at tree-level. At the same time, electroweak precision observables receive new contributions only at the loop level and do not constrain the model very strongly. In our analysis, we take into account new CP violating effects that have been neglected in earlier analyses, and account for a general flavor structure without reference to a certain parameterization of the new mixing matrix. We begin by studying the bounds obtained from quantities such as Delta M_K, epsilon_K, Delta M_{d/s} as well as sin 2 beta|_{J/psi K_S}, and go on to explore the implications for several clean rare decay channels, namely the decays K+->pi+ nu nu, K_L -> pi0 nu nu, B_{d/s} -> mu+ mu- and K_L -> pi0 l+l-. We find sizeable effects in all these decays, but the most interesting quantity turns out to be the B_s - bar B_s mixing phase beta_s, as measured in the mixing induced CP asymmetry of B_s -> J/psi phi, which can be large. In general, we find effects in purely hadronic channels to be larger than in (semi-)leptonic ones, due to a suppression of the Z'-lepton couplings.Comment: 29 pages, 11 figures, Some Comments and References added, version to appear in Phys Rev

Palaeolimnology of Lake Sapanca and identification of historic earthquake signals, Northern Anatolian Fault Zone (Turkey)

Lake Sapanca is located on a strand of the Northern Anatolian Fault Zone (NAFZ, Turkey), where a series of strong earthquakes (Ms >6.0) have occurred over the past hundred years. Identifying prehistoric earthquakes in and around Lake Sapanca is key to a better understanding of plate movements along the NAFZ. This study contributes to the development of palaeolimnological tools to identify past earthquakes in Lake Sapanca. To this end several promising proxies were investigated, specifically lithology, magnetic susceptibility, grain size (thin-section and laser analysis), geochemistry, pollen concentration, diatom assemblages, 137Cs and 210Pb. Sedimentological indicators provided evidence for reworked, turbidite-like or homogeneous facies (event layers) in several short cores (<45 cm). Other indicators of sediment input and the historical chronicles available for the area suggest that three of these event layers likely originated from the AD 1957, 1967 and 1999 earthquakes. Recent changes in sediment deposition and nutrient levels have also been identified, but are probably not related to earthquakes. This study demonstrates that a combination of indicators can be used to recognize earthquake-related event layers in cores that encompass a longer period of time

Numerical methods for Lévy processes

We survey the use and limitations of some numerical methods for pricing derivative contracts in multidimensional geometric Lévy model

On Kolmogorov equations for anisotropic multivariate Lévy processes

For d-dimensional exponential Lévy models, variational formulations of the Kolmogorov equations arising in asset pricing are derived. Well-posedness of these equations is verified. Particular attention is paid to pure jump, d-variate Lévy processes built from parametric, copula dependence models in their jump structure. The domains of the associated Dirichlet forms are shown to be certain anisotropic Sobolev spaces. Singularity-free representations of the Dirichlet forms are given which remain bounded for piecewise polynomial, continuous functions of finite element type. We prove that the variational problem can be localized to a bounded domain with explicit localization error bounds. Furthermore, we collect several analytical tools for further numerical analysi

Antibody response to streptococcal cell wall antigens associated with experimental arthritis in rats.

The antibody response to group A streptococcal cell wall components was measured in rats during the development of chronic, remittent experimental arthritis. The arthritis was induced by a single intraperitoneal injection of an aqueous suspension of group A streptococcal cell wall fragments and antibodies were measured by a radioactive antigen-binding assay. Antibodies in serum against both peptidoglycan and A polysaccharide reached maximum levels at 1 or 2 weeks and declined to preimmunization levels by day 63. The kinetics and magnitude of the antibody responses were similar in neonatally thymectomized and non-thymectomized rats. A relationship between chronic joint lesions and anti-peptidoglycan concentration in serum was indicated, since all rats which produced high levels of antibody developed severe chronic arthritis. However, 46% of the rats which produced very low levels of antibody also developed moderate to severe arthritis. There was no correlation between anti-A polysaccharide antibodies and joint disease, although the concentration of this antibody was 10- to 100-fold greater than the anti-peptidoglycan. We conclude that antibody can be a component in the pathogenesis of this experimental model of arthritis, but its role requires further elucidation