Irrationality exponent, Hausdorff dimension and effectivization

We generalize the classical theorem by Jarnik and Besicovitch on the irrationality exponents of real numbers and Hausdorff dimension and show that the two notions are independent. For any real number a greater than or equal to 2 and any non-negative real b be less than or equal to 2 / a, we show that there is a Cantor-like set with Hausdorff dimension equal to b such that, with respect to its uniform measure, almost all real numbers have irrationality exponent equal to a. We give an analogous result relating the irrationality exponent and the effective Hausdorff dimension of individual real numbers. We prove that there is a Cantor-like set such that, with respect to its uniform measure, almost all elements in the set have effective Hausdorff dimension equal to b and irrationality exponent equal to a. In each case, we obtain the desired set as a distinguished path in a tree of Cantor sets.Fil: Becher, Veronica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Reimann, Jan. State University of Pennsylvania; Estados UnidosFil: Slaman, Theodore A.. University of California. Department of Mathematics; Estados Unido

Next-to-next-to-leading logarithmic resummation for transverse thrust

We obtain a prediction for the hadron-collider event-shape variable transverse thrust in which the terms enhanced in the dijet limit are resummed to next-to-next-to-leading logarithmic accuracy. Our method exploits universality properties made manifest in the factorized expression for the cross section and only requires one-loop calculations. The necessary two-loop ingredients are extracted using known results and existing numerical codes. Our technique is general and applicable to other observables as well.Comment: 6 pages, 2 figures. v2: Corrected values in Eq.(15); updated Figure 2 accordingl

Characterizing Few-Fermion Systems with Momentum Correlations

In this thesis I report on the experimental study of fermionic systems in two complementary experimental settings, i.e. large ensembles of dipolar erbium atoms and few-particle systems of fermionic lithium trapped in optical tweezers. Compared to alkali atoms, dipolar quantum gases offer new avenues to explore due to their long-range anisotropic interactions and a rich internal structure. Such richness comes at the cost of complexity and therefore requires precise investigations of the atomic properties as well as the development of new experimental methods. In the first part of this thesis we present measurements of the anisotropic light shift of erbium atoms and compare the results to semiempirical electronic-structure calculations. Measurements of scalar and tensor polarizabilies of the ground and one excited state show good agreement with calculated values. We furthermore present the first experimental realization of a two-component strongly-interacting Fermi gas with dipolar interactions. We identify several intra and interspin Feshbach resonances at low magnetic field and precisely map out the scattering length across one broad resonance. The second part of this thesis is dedicated to the characterization of small fermionic systems with momentum correlation measurements. Starting with systems of two or three indistinguishable fermions, we detect and discuss second and third-order momentum correlations that arise from quantum statistics alone. We then extend the study of correlation functions to interacting systems and develop a scheme to constrain large parts of the density matrix. Based on these constraints we reconstruct physical density matrices via Bayesian inference. We finally use the reconstructed states to address the influence of exchange symmetry on particle-particle entanglement in systems of identical fermions. Using the simple notion of an Antisymmetric Negativity we are able to separate entanglement from antisymmetrization from entanglement induced by interaction

Single-photon emission from Ni-related color centers in CVD diamond

Color centers in diamond are very promising candidates among the possible realizations for practical single-photon sources because of their long-time stable emission at room temperature. The popular nitrogen-vacancy center shows single-photon emission, but within a large, phonon-broadened spectrum (~100nm), which strongly limits its applicability for quantum communication. By contrast, Ni-related centers exhibit narrow emission lines at room temperature. We present investigations on single color centers consisting of Ni and Si created by ion implantation into single crystalline IIa diamond. We use systematic variations of ion doses between 10^8/cm^2 and 10^14/cm^2 and energies between 30keV and 1.8MeV. The Ni-related centers show emission in the near infrared spectral range (~770nm to 787nm) with a small line-width (~3nm FWHM). A measurement of the intensity correlation function proves single-photon emission. Saturation measurements yield a rather high saturation count rate of 77.9 kcounts/s. Polarization dependent measurements indicate the presence of two orthogonal dipoles.Comment: 8 pages, published in conference proceedings of SPIE Photonics Europe 201

Do Carpets Impair Indoor Air Quality and Cause Adverse Health Outcomes: A Review

Several earlier studies have shown the presence of more dust and allergens in carpets compared with non-carpeted floors. At the same time, adverse effects of carpeted floors on perceived indoor air quality as well as worsening of symptoms in individuals with asthma and allergies were reported. Avoiding extensive carpet use in offices, schools, kindergartens and bedrooms has therefore been recommended by several health authorities. More recently, carpet producers have argued that former assessments were obsolete and that modern rugs are unproblematic, even for those with asthma and allergies. To investigate whether the recommendation to be cautious with the use of carpets is still valid, or whether there are new data supporting that carpet flooring do not present a problem for indoor air quality and health, we have reviewed the literature on this matter. We have not found updated peer reviewed evidence that carpeted floor is unproblematic for the indoor environment. On the contrary, also more recent data support that carpets may act as a repository for pollutants which may become resuspended upon activity in the carpeted area. Also, the use of carpets is still linked to perception of reduced indoor air quality as well as adverse health effects as previously reported. To our knowledge, there are no publications that report on deposition of pollutants and adverse health outcomes associated with modern rugs. However, due to the three-dimensional structure of carpets, any carpet will to some extent act like a sink. Thus, continued caution should still be exercised when considering the use of wall-to-wall carpeted floors in schools, kindergartens and offices, as well as in children’s bedrooms unless special needs indicate that carpets are preferableAcknowledgments: This study has not received any funding or grants. NIPH cover the costs for publishing in open access.publishedVersio

Visible-to-telecom quantum frequency conversion of light from a single quantum emitter

Quantum frequency conversion (QFC), a nonlinear optical process in which the frequency of a quantum light field is altered while conserving its non-classical correlations, was first demonstrated 20 years ago. Meanwhile, it is considered an essential tool for the implementation of quantum repeaters since it allows for interfacing quantum memories with telecom-wavelength photons as quantum information carriers. Here we demonstrate efficient (>30%) QFC of visible single photons (711 nm) emitted by a quantum dot (QD) to a telecom wavelength (1,313 nm). Analysis of the first and second-order coherence before and after wavelength conversion clearly proves that important properties, such as the coherence time and photon antibunching, are fully conserved during the frequency translation process. Our findings underline the great potential of single photon sources on demand in combination with QFC as a promising technique for quantum repeater schemes.Comment: 11 pages, 4 figure

Biomarkers of Human Exposure to Acrylamide and Relation to Polymorphisms in Metabolizing Genes

Acrylamide (AA) is formed in heat treated carbohydrate rich foods in the so-called Maillard reaction. AA is readily absorbed in the body and converted to glycidamide (GA) by epoxidation by the CYP2E1 (cytochrome P450 2E) enzyme. Both AA and GA may be detoxified through direct conjunction to glutathione by glutathione-S-transferases and GA by hydrolysis to glyceramide. Recently, we reported that biomarkers of AA exposure reflect intake of major food sources of AA; there were large interindividual variations in the blood ratio of GA-Hb/AA-Hb (GA- and AA-hemoglobin adducts). In this study we investigated whether the ratio of GA-Hb/AA-Hb in subjects could be related to polymorphic differences in genes coding for metabolizing enzymes CYP2E1, EPHX1 (microsomal epoxide hydrolase), GSTM1, GSTT1, and GSTP1, all being expected to be involved in the activation and detoxification of AA-associated adducts. We found significant associations between GSTM1 and GSTT1 genotypes and the ratio of GA-Hb/AA-Hb (p = 0.039 and p = 0.006, respectively). The ratio of GA-Hb/AA-Hb in individuals with the combined GSTM1- and GSTT1-null variants was significantly (p = 0.029) higher than those with the wild-type genotypes. Although the number of subjects was small, there were also significant associations with other combinations; CYP2E1 (Val179Val) plus GSTM1-null (p = 0.022); CYP2E1 (Val/Val), GSTM1-null plus GSTT1-null (p = 0.047); and CYP2E1 (Val/Val), GSTT1 null, EPHX1 (Tyr113Tyr) plus EPHX1 (His139Arg) (p = 0.018). Individuals with these combined genotypes had significantly higher blood ratio of GA-Hb/AA-Hb than other combinations. The observed associations correspond with what would be expected from the relative roles of these enzymes in activation and detoxification of AA, except for individuals with the EPHX1 (His139Arg) variant. The internal dose of genotoxic metabolite and also the concentration of AA in blood seem to be affected by these polymorphic genes. The genotypes and their combination may constitute useful biomarkers for the assessment of individual susceptibility to AA intake, and could add to the precision of epidemiological studies of dietary cancer