Local entanglement generation in the adiabatic regime

We study entanglement generation in a pair of qubits interacting with an initially correlated system. Using time independent perturbation theory and the adiabatic theorem, we show conditions under which the qubits become entangled as the joint system evolves into the ground state of the interacting theory. We then apply these results to the case of qubits interacting with a scalar quantum field. We study three different variations of this setup; a quantum field subject to Dirichlet boundary conditions, a quantum field interacting with a classical potential and a quantum field that starts in a thermal state.Comment: 9 pages, 6 figures. v2: reference [14] adde

Percolation model for nodal domains of chaotic wave functions

Nodal domains are regions where a function has definite sign. In recent paper [nlin.CD/0109029] it is conjectured that the distribution of nodal domains for quantum eigenfunctions of chaotic systems is universal. We propose a percolation-like model for description of these nodal domains which permits to calculate all interesting quantities analytically, agrees well with numerical simulations, and due to the relation to percolation theory opens the way of deeper understanding of the structure of chaotic wave functions.Comment: 4 pages, 6 figures, Late

Phase transitions with four-spin interactions

Using an extended Lee-Yang theorem and GKS correlation inequalities, we prove, for a class of ferromagnetic multi-spin interactions, that they will have a phase transition(and spontaneous magnetization) if, and only if, the external field $h=0$ (and the temperature is low enough). We also show the absence of phase transitions for some nonferromagnetic interactions. The FKG inequalities are shown to hold for a larger class of multi-spin interactions

Numerical indications of a q-generalised central limit theorem

We provide numerical indications of the $q$-generalised central limit theorem that has been conjectured (Tsallis 2004) in nonextensive statistical mechanics. We focus on $N$ binary random variables correlated in a {\it scale-invariant} way. The correlations are introduced by imposing the Leibnitz rule on a probability set based on the so-called $q$-product with $q \le 1$. We show that, in the large $N$ limit (and after appropriate centering, rescaling, and symmetrisation), the emerging distributions are $q_e$-Gaussians, i.e., $p(x) \propto [1-(1-q_e) \beta(N) x^2]^{1/(1-q_e)}$, with $q_e=2-\frac{1}{q}$, and with coefficients $\beta(N)$ approaching finite values $\beta(\infty)$. The particular case $q=q_e=1$ recovers the celebrated de Moivre-Laplace theorem.Comment: Minor improvements and corrections have been introduced in the new version. 7 pages including 4 figure

Positive Association of Cardiovascular Disease (CVD) with Chronic Exposure to Drinking Water Arsenic (As) at Concentrations below the WHO Provisional Guideline Value: A Systematic Review and Meta-Analysis.

To the best of our knowledge, a dose-response meta-analysis of the relationship between cardiovascular disease (CVD) and arsenic (As) exposure at drinking water As concentrations lower than the WHO provisional guideline value (10 µg/L) has not been published yet. We conducted a systematic review and meta-analyses to estimate the pooled association between the relative risk of each CVD endpoint and low-level As concentration in drinking water both linearly and non-linearly using a random effects dose-response model. In this study, a significant positive association was found between the risks of most CVD outcomes and drinking water As concentration for both linear and non-linear models (p-value for trend < 0.05). Using the preferred linear model, we found significant increased risks of coronary heart disease (CHD) mortality and CVD mortality as well as combined fatal and non-fatal CHD, CVD, carotid atherosclerosis disease and hypertension in those exposed to drinking water with an As concentration of 10 µg/L compared to the referent (drinking water As concentration of 1 µg/L) population. Notwithstanding limitations included, the observed significant increased risks of CVD endpoints arising from As concentrations in drinking water between 1 µg/L and the 10 µg/L suggests further lowering of this guideline value should be considered

Random walks on graphs: ideas, techniques and results

Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and new ideas have been introduced, which can be fruitfully extended to different areas and disciplines. Here we aim at giving a brief but comprehensive perspective of these progresses, with a particular emphasis on physical aspects.Comment: LateX file, 34 pages, 13 jpeg figures, Topical Revie

'Don't think in your head, think aloud': ICT and exploratory talk in the primary school mathematics classroom

This paper arises out of research into classroom activities conducted with Year 5 and Year 6 primary school students (9-10 year-olds). The study applied the ‘Thinking Together’ approach developed by Mercer and colleagues at the Open University in mathematics lessons involving the use of ICT. The study describes the use of mathematics software to promote collaborative thinking and exploratory talk in the mathematics classroom. Teachers were given training in the Thinking Together approach. They then conducted a series of lessons with students and explicitly taught them how to work and talk collaboratively to solve mathematical problems at the computer. These lessons were video-recorded and the transcripts analysed for evidence of ‘exploratory talk’. This paper reports on the role of the teacher, the students and the computer in developing exploratory talk

Symmetries of Abelian Orbifolds

Using the Polya Enumeration Theorem, we count with particular attention to C^3/Gamma up to C^6/Gamma, abelian orbifolds in various dimensions which are invariant under cycles of the permutation group S_D. This produces a collection of multiplicative sequences, one for each cycle in the Cycle Index of the permutation group. A multiplicative sequence is controlled by its values on prime numbers and their pure powers. Therefore, we pay particular attention to orbifolds of the form C^D/Gamma where the order of Gamma is p^alpha. We propose a generalization of these sequences for any D and any p.Comment: 75 pages, 13 figures, 30 table