6,715 research outputs found
Intermediate wave-function statistics
We calculate statistical properties of the eigenfunctions of two quantum
systems that exhibit intermediate spectral statistics: star graphs and Seba
billiards. First, we show that these eigenfunctions are not quantum ergodic,
and calculate the corresponding limit distribution. Second, we find that they
can be strongly scarred by short periodic orbits, and construct sequences of
states which have such a limit. Our results are illustrated by numerical
computations.Comment: 4 pages, 3 figures. Final versio
No quantum ergodicity for star graphs
We investigate statistical properties of the eigenfunctions of the
Schrodinger operator on families of star graphs with incommensurate bond
lengths. We show that these eigenfunctions are not quantum ergodic in the limit
as the number of bonds tends to infinity by finding an observable for which the
quantum matrix elements do not converge to the classical average. We further
show that for a given fixed graph there are subsequences of eigenfunctions
which localise on pairs of bonds. We describe how to construct such
subsequences explicitly. These constructions are analogous to scars on short
unstable periodic orbits.Comment: 26 pages, 5 figure
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
Nodal Domain Statistics for Quantum Maps, Percolation and SLE
We develop a percolation model for nodal domains in the eigenvectors of
quantum chaotic torus maps. Our model follows directly from the assumption that
the quantum maps are described by random matrix theory. Its accuracy in
predicting statistical properties of the nodal domains is demonstrated by
numerical computations for perturbed cat maps and supports the use of
percolation theory to describe the wave functions of general hamiltonian
systems, where the validity of the underlying assumptions is much less clear.
We also demonstrate that the nodal domains of the perturbed cat maps obey the
Cardy crossing formula and find evidence that the boundaries of the nodal
domains are described by SLE with close to the expected value of 6,
suggesting that quantum chaotic wave functions may exhibit conformal invariance
in the semiclassical limit.Comment: 4 pages, 5 figure
Quantum chaotic resonances from short periodic orbits
We present an approach to calculating the quantum resonances and resonance
wave functions of chaotic scattering systems, based on the construction of
states localized on classical periodic orbits and adapted to the dynamics.
Typically only a few of such states are necessary for constructing a resonance.
Using only short orbits (with periods up to the Ehrenfest time), we obtain
approximations to the longest living states, avoiding computation of the
background of short living states. This makes our approach considerably more
efficient than previous ones. The number of long lived states produced within
our formulation is in agreement with the fractal Weyl law conjectured recently
in this setting. We confirm the accuracy of the approximations using the open
quantum baker map as an example.Comment: 4 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
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