Nodal domain distributions for quantum maps

The statistics of the nodal lines and nodal domains of the eigenfunctions of quantum billiards have recently been observed to be fingerprints of the chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett., Vol. 88 (2002), 114101) and by Bogomolny and Schmit (Phys. Rev. Lett., Vol. 88 (2002), 114102). These statistics were shown to be computable from the random wave model of the eigenfunctions. We here study the analogous problem for chaotic maps whose phase space is the two-torus. We show that the distributions of the numbers of nodal points and nodal domains of the eigenvectors of the corresponding quantum maps can be computed straightforwardly and exactly using random matrix theory. We compare the predictions with the results of numerical computations involving quantum perturbed cat maps.Comment: 7 pages, 2 figures. Second version: minor correction

On the mean values of L-functions in orthogonal and symplectic families

Hybrid Euler-Hadamard products have previously been studied for the Riemann zeta function on its critical line and for Dirichlet L-functions in the context of the calculation of moments and connections with Random Matrix Theory. According to the Katz-Sarnak classification, these are believed to represent families of L-function with unitary symmetry. We here extend the formalism to families with orthogonal & symplectic symmetry. Specifically, we establish formulae for real quadratic Dirichlet L-functions and for the L-functions associated with primitive Hecke eigenforms of weight 2 in terms of partial Euler and Hadamard products. We then prove asymptotic formulae for some moments of these partial products and make general conjectures based on results for the moments of characteristic polynomials of random matrices

Comb entanglement in quantum spin chains

Bipartite entanglement in the ground state of a chain of $N$ quantum spins can be quantified either by computing pairwise concurrence or by dividing the chain into two complementary subsystems. In the latter case the smaller subsystem is usually a single spin or a block of adjacent spins and the entanglement differentiates between critical and non-critical regimes. Here we extend this approach by considering a more general setting: our smaller subsystem $S_A$ consists of a {\it comb} of $L$ spins, spaced $p$ sites apart. Our results are thus not restricted to a simple `area law', but contain non-local information, parameterized by the spacing $p$. For the XX model we calculate the von-Neumann entropy analytically when $N\to \infty$ and investigate its dependence on $L$ and $p$. We find that an external magnetic field induces an unexpected length scale for entanglement in this case.Comment: 6 pages, 4 figure

Pursuing Energy-Efficient Behavior in a Regulatory Environment: Motivating Policymakers, Program Administrators, and Program Implementers

This white paper examines how policymakers, program administrators, and program implementers can be motivated to pursue behavioral change in a regulatory environment. For the purposes of this report, behavior change is defined rather broadly, encompassing both behaviors associated with the purchase and installation of energy efficiency technologies as well as behaviors, decisions, and actions that might be thought of as more independent of technology. These include energy use habits, lifestyle choices, and consumption patterns. The insights and lessons discussed in this paper are drawn from a wide variety of sources including interviews with representatives from the energy and utility communities, and program documentation for energy-related programs and projects

Improved reference models for middle atmosphere ozone

Improvements are provided for the ozone reference model which is to be incorporated in the COSPAR International Reference Atmosphere (CIRA). The ozone reference model will provide considerable information on the global ozone distribution, including ozone vertical structure as a function of month and latitude from approximately 25 to 90 km, combining data from five recent satellite experiments (Nimbus 7 LIMS, Nimbus 7 SBUV, AE-2 SAGE, Solar Mesosphere Explorer (SME) UVS, and SME IR). The improved models are described and use reprocessed AE-2 SAGE data (sunset) and extend the use of SAGE data from 1981 to the period 1981-1983. Comparisons are shown between the ozone reference model and various nonsatellite measurements at different levels in the middle atmosphere

A keystone Methylobacterium strain in biofilm formation in drinking water

The structure of biofilms in drinking water systems is influenced by the interplay between biological and physical processes. Bacterial aggregates in bulk fluid are important in seeding biofilm formation on surfaces. In simple pure and co-cultures, certain bacteria, including Methylobacterium, are implicated in the formation of aggregates. However, it is unclear whether they help to form aggregates in complex mixed bacterial communities. Furthermore, different flow regimes could affect the formation and destination of aggregates. In this study, real drinking water mixed microbial communities were inoculated with the Methylobacterium strain DSM 18358. The propensity of Methylobacterium to promote aggregation was monitored under both stagnant and flow conditions. Under stagnant conditions, Methylobacterium enhanced bacterial aggregation even when it was inoculated in drinking water at 1% relative abundance. Laminar and turbulent flows were developed in a rotating annular reactor. Methylobacterium was found to promote a higher degree of aggregation in turbulent than laminar flow. Finally, fluorescence in situ hybridisation images revealed that Methylobacterium aggregates had distinct spatial structures under the different flow conditions. Overall, Methylobacterium was found to be a key strain in the formation of aggregates in bulk water and subsequently in the formation of biofilms on surfaces

Europe as a multilevel federation

Peer reviewedPublisher PD