3,391 research outputs found
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
Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs
Physicists have argued that periodic orbit bunching leads to universal
spectral fluctuations for chaotic quantum systems. To establish a more detailed
mathematical understanding of this fact, it is first necessary to look more
closely at the classical side of the problem and determine orbit pairs
consisting of orbits which have similar actions. In this paper we specialize to
the geodesic flow on compact factors of the hyperbolic plane as a classical
chaotic system. We prove the existence of a periodic partner orbit for a given
periodic orbit which has a small-angle self-crossing in configuration space
which is a `2-encounter'; such configurations are called `Sieber-Richter pairs'
in the physics literature. Furthermore, we derive an estimate for the action
difference of the partners. In the second part of this paper [13], an inductive
argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit
Intensity distribution in rotational line spectra
Completely resolved Doppler-free rotational line spectra of six vibronic two-photon bands in benzene C6 H6 and C6 D6 are presented. The excited final states possess different excess energies in S1 (1567 to 2727 cm−1 ) and are embedded in dense manifolds of background states with differing densities of states (1<rho<60 1/cm−1 ). The bands are analyzed by a statistical procedure. The intensity distribution of several hundreds of lines of each band is investigated. It is found that all weakly perturbed bands display a similar, peaked intensity distribution while in strongly perturbed bands the number of lines decreases monotonically with increasing intensity. The origin of this difference is discussed in terms of coupling to the many background states. The Journal of Chemical Physics is copyrighted by The American Institute of Physics
Semiclassical structure of chaotic resonance eigenfunctions
We study the resonance (or Gamow) eigenstates of open chaotic systems in the
semiclassical limit, distinguishing between left and right eigenstates of the
non-unitary quantum propagator, and also between short-lived and long-lived
states. The long-lived left (right) eigenstates are shown to concentrate as
on the forward (backward) trapped set of the classical dynamics.
The limit of a sequence of eigenstates is found
to exhibit a remarkably rich structure in phase space that depends on the
corresponding limiting decay rate. These results are illustrated for the open
baker map, for which the probability density in position space is observed to
have self-similarity properties.Comment: 4 pages, 4 figures; some minor corrections, some changes in
presentatio
A generic map has no absolutely continuous invariant probability measure
Let be a smooth compact manifold (maybe with boundary, maybe
disconnected) of any dimension . We consider the set of maps
which have no absolutely continuous (with respect to Lebesgue)
invariant probability measure. We show that this is a residual (dense
C^1$ topology.
In the course of the proof, we need a generalization of the usual Rokhlin
tower lemma to non-invariant measures. That result may be of independent
interest.Comment: 12 page
Pulsar Magnetospheric Emission Mapping: Images and Implications of Polar-Cap Weather
The beautiful sequences of ``drifting'' subpulses observed in some radio
pulsars have been regarded as among the most salient and potentially
instructive characteristics of their emission, not least because they have
appeared to represent a system of subbeams in motion within the emission zone
of the star. Numerous studies of these ``drift'' sequences have been published,
and a model of their generation and motion articulated long ago by Ruderman &
Sutherland (1975); but efforts thus far have failed to establish an
illuminating connection between the drift phemomenon and the actual sites of
radio emission. Through a detailed analysis of a nearly coherent sequence of
``drifting'' pulses from pulsar B0943+10, we have in fact identified a system
of subbeams circulating around the magnetic axis of the star. A mapping
technique, involving a ``cartographic'' transform and its inverse, permits us
to study the character of the polar-cap emission ``map'' and then to confirm
that it, in turn, represents the observed pulse sequence. On this basis, we
have been able to trace the physical origin of the ``drifting-subpulse''
emission to a stably rotating and remarkably organized configuration of
emission columns, in turn traceable possibly to the magnetic polar-cap ``gap''
region envisioned by some theories.Comment: latex with five eps figure
On the Form Factor for the Unitary Group
We study the combinatorics of the contributions to the form factor of the
group U(N) in the large limit. This relates to questions about
semiclassical contributions to the form factor of quantum systems described by
the unitary ensemble.Comment: 35 page
Physical inactivity amplifies the negative association between sleep quality and depressive symptoms.
Poor sleep quality and physical inactivity are known risk factors for depressive symptoms. Yet, whether these factors differently contribute to depressive symptoms and whether they interact with one another remains unclear. Here, we examined how sleep quality and physical activity influence depressive symptoms in 79,274 adults 50 years of age or older (52.4% women) from the Survey of Health, Aging and Retirement in Europe (SHARE) study. Sleep quality (poor vs. good), physical activity (inactive vs. active), and depressive symptoms (0 to 12 score) were repeatedly collected (7 waves of data collection) between 2004 and 2017. Results showed that sleep quality and physical activity were associated with depressive symptoms. Specifically, participants with poorer sleep quality reported more depressive symptoms than participants with better sleep quality (b = 1.85, 95% CI = 1.83-1.86, p < .001). Likewise, compared to physically active participants, physically inactive participants reported more depressive symptoms (b = 0.44, 95% CI = 0.42-0.45, p < .001). Moreover, sleep quality and physical activity showed an interactive association with depressive symptoms (b = 0.17, 95% CI = 0.13-0.20, p < .001). The negative association between poor sleep quality and higher depressive symptoms was stronger in physically inactive than active participants. These findings suggest that, in adults 50 years of age or older, both poor sleep quality and physical inactivity are related to an increase in depressive symptoms. Moreover, the detrimental association between poor sleep quality and depressive symptoms is amplified in physically inactive individuals
Semiclassical Theory of Quantum Chaotic Transport: Phase-Space Splitting, Coherent Backscattering and Weak Localization
We investigate transport properties of quantized chaotic systems in the short
wavelength limit. We focus on non-coherent quantities such as the Drude
conductance, its sample-to-sample fluctuations, shot-noise and the transmission
spectrum, as well as coherent effects such as weak localization. We show how
these properties are influenced by the emergence of the Ehrenfest time scale
\tE. Expressed in an optimal phase-space basis, the scattering matrix
acquires a block-diagonal form as \tE increases, reflecting the splitting of
the system into two cavities in parallel, a classical deterministic cavity
(with all transmission eigenvalues either 0 or 1) and a quantum mechanical
stochastic cavity. This results in the suppression of the Fano factor for
shot-noise and the deviation of sample-to-sample conductance fluctuations from
their universal value. We further present a semiclassical theory for weak
localization which captures non-ergodic phase-space structures and preserves
the unitarity of the theory. Contrarily to our previous claim [Phys. Rev. Lett.
94, 116801 (2005)], we find that the leading off-diagonal contribution to the
conductance leads to the exponential suppression of the coherent backscattering
peak and of weak localization at finite \tE. This latter finding is
substantiated by numerical magnetoconductance calculations.Comment: Typos in central eqns corrected (this paper supersedes
cond-mat/0509186) 20page
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