5,139 research outputs found
Method and apparatus for attaching physiological monitoring electrodes Patent
Adhesive spray process for attaching biomedical skin electrode
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
Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function
We argue that the freezing transition scenario, previously explored in the
statistical mechanics of 1/f-noise random energy models, also determines the
value distribution of the maximum of the modulus of the characteristic
polynomials of large N x N random unitary (CUE) matrices. We postulate that our
results extend to the extreme values taken by the Riemann zeta-function zeta(s)
over sections of the critical line s=1/2+it of constant length and present the
results of numerical computations in support. Our main purpose is to draw
attention to possible connections between the statistical mechanics of random
energy landscapes, random matrix theory, and the theory of the Riemann zeta
function.Comment: published version with a few misprints corrected and references adde
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
On the duality between periodic orbit statistics and quantum level statistics
We discuss consequences of a recent observation that the sequence of periodic
orbits in a chaotic billiard behaves like a poissonian stochastic process on
small scales. This enables the semiclassical form factor to
agree with predictions of random matrix theories for other than infinitesimal
in the semiclassical limit.Comment: 8 pages LaTe
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 Nodal Count Statistics for Separable Systems in any Dimension
We consider the statistics of the number of nodal domains aka nodal counts
for eigenfunctions of separable wave equations in arbitrary dimension. We give
an explicit expression for the limiting distribution of normalised nodal counts
and analyse some of its universal properties. Our results are illustrated by
detailed discussion of simple examples and numerical nodal count distributions.Comment: 21 pages, 4 figure
Signatures of homoclinic motion in quantum chaos
Homoclinic motion plays a key role in the organization of classical chaos in
Hamiltonian systems. In this Letter, we show that it also imprints a clear
signature in the corresponding quantum spectra. By numerically studying the
fluctuations of the widths of wavefunctions localized along periodic orbits we
reveal the existence of an oscillatory behavior, that is explained solely in
terms of the primary homoclinic motion. Furthermore, our results indicate that
it survives the semiclassical limit.Comment: 5 pages, 4 figure
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