6,269 research outputs found
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
Method and apparatus for attaching physiological monitoring electrodes Patent
Adhesive spray process for attaching biomedical skin electrode
Periodic orbit bifurcations and scattering time delay fluctuations
We study fluctuations of the Wigner time delay for open (scattering) systems
which exhibit mixed dynamics in the classical limit. It is shown that in the
semiclassical limit the time delay fluctuations have a distribution that
differs markedly from those which describe fully chaotic (or strongly
disordered) systems: their moments have a power law dependence on a
semiclassical parameter, with exponents that are rational fractions. These
exponents are obtained from bifurcating periodic orbits trapped in the system.
They are universal in situations where sufficiently long orbits contribute. We
illustrate the influence of bifurcations on the time delay numerically using an
open quantum map.Comment: 9 pages, 3 figures, contribution to QMC200
Spectral statistics for unitary transfer matrices of binary graphs
Quantum graphs have recently been introduced as model systems to study the
spectral statistics of linear wave problems with chaotic classical limits. It
is proposed here to generalise this approach by considering arbitrary, directed
graphs with unitary transfer matrices. An exponentially increasing contribution
to the form factor is identified when performing a diagonal summation over
periodic orbit degeneracy classes. A special class of graphs, so-called binary
graphs, is studied in more detail. For these, the conditions for periodic orbit
pairs to be correlated (including correlations due to the unitarity of the
transfer matrix) can be given explicitly. Using combinatorial techniques it is
possible to perform the summation over correlated periodic orbit pair
contributions to the form factor for some low--dimensional cases. Gradual
convergence towards random matrix results is observed when increasing the
number of vertices of the binary graphs.Comment: 18 pages, 8 figure
A self‐consistent model of helium in the thermosphere
We have found that consideration of neutral helium as a major species leads to a more complete physics‐based modeling description of the Earth's upper thermosphere. An augmented version of the composition equation employed by the Thermosphere‐Ionosphere‐Electrodynamic General Circulation Model (TIE‐GCM) is presented, enabling the inclusion of helium as the fourth major neutral constituent. Exospheric transport acting above the upper boundary of the model is considered, further improving the local time and latitudinal distributions of helium. The new model successfully simulates a previously observed phenomenon known as the “winter helium bulge,” yielding behavior very similar to that of an empirical model based on mass spectrometer observations. This inclusion has direct consequence on the study of atmospheric drag for low‐Earth‐orbiting satellites, as well as potential implications on exospheric and topside ionospheric research.Key PointsTIE‐GCM has been modified to account for neutral heliumSeasonal behavior is successfully capturedNeutral densities from the new model agree well with previous observationsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/113723/1/jgra51979.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/113723/2/jgra51979_am.pd
A new correlator in quantum spin chains
We propose a new correlator in one-dimensional quantum spin chains, the
Emptiness Formation Probability (EFP). This is a natural generalization
of the Emptiness Formation Probability (EFP), which is the probability that the
first spins of the chain are all aligned downwards. In the EFP we let
the spins in question be separated by sites. The usual EFP corresponds to
the special case when , and taking allows us to quantify non-local
correlations. We express the EFP for the anisotropic XY model in a
transverse magnetic field, a system with both critical and non-critical
regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find
that the magnetic field induces an interesting length scale.Comment: 6 pages, 1 figur
Quantization of multidimensional cat maps
In this work we study cat maps with many degrees of freedom. Classical cat
maps are classified using the Cayley parametrization of symplectic matrices and
the closely associated center and chord generating functions. Particular
attention is dedicated to loxodromic behavior, which is a new feature of
two-dimensional maps. The maps are then quantized using a recently developed
Weyl representation on the torus and the general condition on the Floquet
angles is derived for a particular map to be quantizable. The semiclassical
approximation is exact, regardless of the dimensionality or of the nature of
the fixed points.Comment: 33 pages, latex, 6 figures, Submitted to Nonlinearit
On the resonance eigenstates of an open quantum baker map
We study the resonance eigenstates of a particular quantization of the open
baker map. For any admissible value of Planck's constant, the corresponding
quantum map is a subunitary matrix, and the nonzero component of its spectrum
is contained inside an annulus in the complex plane, . We consider semiclassical sequences of eigenstates, such that the
moduli of their eigenvalues converge to a fixed radius . We prove that, if
the moduli converge to , then the sequence of eigenstates
converges to a fixed phase space measure . The same holds for
sequences with eigenvalue moduli converging to , with a different
limit measure . Both these limiting measures are supported on
fractal sets, which are trapped sets of the classical dynamics. For a general
radius , we identify families of eigenstates with
precise self-similar properties.Comment: 32 pages, 2 figure
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