599 research outputs found
Long Arm of the Law
Once again, the Long Arm of the Law session lights the Charleston Conference stage! In this year\u27s presentation we will continue to inform the audience about the latest court cases and rulings that impact us in libraries and the information industry. As always, there are many new legal developments that will intrigue the Charleston audience
Periodic Orbits and Spectral Statistics of Pseudointegrable Billiards
We demonstrate for a generic pseudointegrable billiard that the number of
periodic orbit families with length less than increases as , where is a constant and is the average area occupied by these families. We also find that
increases with before saturating. Finally, we show
that periodic orbits provide a good estimate of spectral correlations in the
corresponding quantum spectrum and thus conclude that diffraction effects are
not as significant in such studies.Comment: 13 pages in RevTex including 5 figure
Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2
The spectral correlation of a chaotic system with spin 1/2 is universally
described by the GSE (Gaussian Symplectic Ensemble) of random matrices in the
semiclassical limit. In semiclassical theory, the spectral form factor is
expressed in terms of the periodic orbits and the spin state is simulated by
the uniform distribution on a sphere. In this paper, instead of the uniform
distribution, we introduce Brownian motion on a sphere to yield the parametric
motion of the energy levels. As a result, the small time expansion of the form
factor is obtained and found to be in agreement with the prediction of
parametric random matrices in the transition within the GSE universality class.
Moreover, by starting the Brownian motion from a point distribution on the
sphere, we gradually increase the effect of the spin and calculate the form
factor describing the transition from the GOE (Gaussian Orthogonal Ensemble)
class to the GSE class.Comment: 25 pages, 2 figure
Mutual Coherence of Polarized Light in Disordered Media: Two-Frequency Method Extended
The paper addresses the two-point correlations of electromagnetic waves in
general random, bi-anisotropic media whose constitutive tensors are complex
Hermitian, positive- or negative-definite matrices. A simplified version of the
two-frequency Wigner distribution (2f-WD) for polarized waves is introduced and
the closed form Wigner-Moyal equation is derived from the Maxwell equations. In
the weak-disorder regime with an arbitrarily varying background the
two-frequency radiative transfer (2f-RT) equations for the associated coherence matrices are derived from the Wigner-Moyal equation by using the
multiple scale expansion. In birefringent media, the coherence matrix becomes a
scalar and the 2f-RT equations take the scalar form due to the absence of
depolarization. A paraxial approximation is developed for spatialy anisotropic
media. Examples of isotropic, chiral, uniaxial and gyrotropic media are
discussed
The three-body problem and the Hannay angle
The Hannay angle has been previously studied for a celestial circular
restricted three-body system by means of an adiabatic approach. In the present
work, three main results are obtained. Firstly, a formal connection between
perturbation theory and the Hamiltonian adiabatic approach shows that both lead
to the Hannay angle; it is thus emphasised that this effect is already
contained in classical celestial mechanics, although not yet defined nor
evaluated separately. Secondly, a more general expression of the Hannay angle,
valid for an action-dependent potential is given; such a generalised expression
takes into account that the restricted three-body problem is a time-dependent,
two degrees of freedom problem even when restricted to the circular motion of
the test body. Consequently, (some of) the eccentricity terms cannot be
neglected {\it a priori}. Thirdly, we present a new numerical estimate for the
Earth adiabatically driven by Jupiter. We also point out errors in a previous
derivation of the Hannay angle for the circular restricted three-body problem,
with an action-independent potential.Comment: 11 pages. Accepted by Nonlinearit
Periodic Orbits in Polygonal Billiards
We review some properties of periodic orbit families in polygonal billiards
and discuss in particular a sum rule that they obey. In addition, we provide
algorithms to determine periodic orbit families and present numerical results
that shed new light on the proliferation law and its variation with the genus
of the invariant surface. Finally, we deal with correlations in the length
spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure
Notes on Conformal Invisibility Devices
As a consequence of the wave nature of light, invisibility devices based on
isotropic media cannot be perfect. The principal distortions of invisibility
are due to reflections and time delays. Reflections can be made exponentially
small for devices that are large in comparison with the wavelength of light.
Time delays are unavoidable and will result in wave-front dislocations. This
paper considers invisibility devices based on optical conformal mapping. The
paper shows that the time delays do not depend on the directions and impact
parameters of incident light rays, although the refractive-index profile of any
conformal invisibility device is necessarily asymmetric. The distortions of
images are thus uniform, which reduces the risk of detection. The paper also
shows how the ideas of invisibility devices are connected to the transmutation
of force, the stereographic projection and Escheresque tilings of the plane
Geometric Phase, Hannay's Angle, and an Exact Action Variable
Canonical structure of a generalized time-periodic harmonic oscillator is
studied by finding the exact action variable (invariant). Hannay's angle is
defined if closed curves of constant action variables return to the same curves
in phase space after a time evolution. The condition for the existence of
Hannay's angle turns out to be identical to that for the existence of a
complete set of (quasi)periodic wave functions. Hannay's angle is calculated,
and it is shown that Berry's relation of semiclassical origin on geometric
phase and Hannay's angle is exact for the cases considered.Comment: Submitted to Phys. Rev. Lett. (revised version
Universal spectral form factor for chaotic dynamics
We consider the semiclassical limit of the spectral form factor of
fully chaotic dynamics. Starting from the Gutzwiller type double sum over
classical periodic orbits we set out to recover the universal behavior
predicted by random-matrix theory, both for dynamics with and without time
reversal invariance. For times smaller than half the Heisenberg time
, we extend the previously known -expansion to
include the cubic term. Beyond confirming random-matrix behavior of individual
spectra, the virtue of that extension is that the ``diagrammatic rules'' come
in sight which determine the families of orbit pairs responsible for all orders
of the -expansion.Comment: 4 pages, 1 figur
The maximally entangled symmetric state in terms of the geometric measure
The geometric measure of entanglement is investigated for permutation
symmetric pure states of multipartite qubit systems, in particular the question
of maximum entanglement. This is done with the help of the Majorana
representation, which maps an n qubit symmetric state to n points on the unit
sphere. It is shown how symmetries of the point distribution can be exploited
to simplify the calculation of entanglement and also help find the maximally
entangled symmetric state. Using a combination of analytical and numerical
results, the most entangled symmetric states for up to 12 qubits are explored
and discussed. The optimization problem on the sphere presented here is then
compared with two classical optimization problems on the S^2 sphere, namely
Toth's problem and Thomson's problem, and it is observed that, in general, they
are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and
reference
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