10,077 research outputs found
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
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
Comb entanglement in quantum spin chains
Bipartite entanglement in the ground state of a chain of 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 consists of a {\it comb} of spins, spaced sites apart.
Our results are thus not restricted to a simple `area law', but contain
non-local information, parameterized by the spacing . For the XX model we
calculate the von-Neumann entropy analytically when and
investigate its dependence on and . We find that an external magnetic
field induces an unexpected length scale for entanglement in this case.Comment: 6 pages, 4 figure
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
Ozone reference models for the middle atmosphere (new CIRA)
Models of ozone vertical structure were generated that were based on multiple data sets from satellites. The very good absolute accuracy of the individual data sets allowed the data to be directly combined to generate these models. The data used for generation of these models are from some of the most recent satellite measurements over the period 1978 to 1983. A discussion is provided of validation and error analyses of these data sets. Also, inconsistencies in data sets brought about by temporal variations or other factors are indicated. The models cover the pressure range from from 20 to 0.003 mb (25 to 90 km). The models for pressures less than 0.5 mb represent only the day side and are only provisional since there was limited longitudinal coverage at these levels. The models start near 25 km in accord with previous COSPAR international reference atmosphere (CIRA) models. Models are also provided of ozone mixing ratio as a function of height. The monthly standard deviation and interannual variations relative to zonal means are also provided. In addition to the models of monthly latitudinal variations in vertical structure based on satellite measurements, monthly models of total column ozone and its characteristic variability as a function of latitude based on four years of Nimbus 7 measurements, models of the relationship between vertical structure and total column ozone, and a midlatitude annual mean model are incorporated in this set of ozone reference atmospheres. Various systematic variations are discussed including the annual, semiannual, and quasibiennial oscillations, and diurnal, longitudinal, and response to solar activity variations
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