2,150 research outputs found
Spectral statistics in chaotic systems with a point interaction
We consider quantum systems with a chaotic classical limit that are perturbed
by a point-like scatterer. The spectral form factor K(tau) for these systems is
evaluated semiclassically in terms of periodic and diffractive orbits. It is
shown for order tau^2 and tau^3 that off-diagonal contributions to the form
factor which involve diffractive orbits cancel exactly the diagonal
contributions from diffractive orbits, implying that the perturbation by the
scatterer does not change the spectral statistic. We further show that
parametric spectral statistics for these systems are universal for small
changes of the strength of the scatterer.Comment: LaTeX, 21 pages, 7 figures, small corrections, new references adde
Semiclassical expansion of parametric correlation functions of the quantum time delay
We derive semiclassical periodic orbit expansions for a correlation function
of the Wigner time delay. We consider the Fourier transform of the two-point
correlation function, the form factor , that depends on the
number of open channels , a non-symmetry breaking parameter , and a
symmetry breaking parameter . Several terms in the Taylor expansion about
, which depend on all parameters, are shown to be identical to those
obtained from Random Matrix Theory.Comment: 21 pages, no figure
Geometrical theory of diffraction and spectral statistics
We investigate the influence of diffraction on the statistics of energy
levels in quantum systems with a chaotic classical limit. By applying the
geometrical theory of diffraction we show that diffraction on singularities of
the potential can lead to modifications in semiclassical approximations for
spectral statistics that persist in the semiclassical limit . This
result is obtained by deriving a classical sum rule for trajectories that
connect two points in coordinate space.Comment: 14 pages, no figure, to appear in J. Phys.
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
Form factor for large quantum graphs: evaluating orbits with time-reversal
It has been shown that for a certain special type of quantum graphs the
random-matrix form factor can be recovered to at least third order in the
scaled time \tau using periodic-orbit theory. Two types of contributing pairs
of orbits were identified, those which require time-reversal symmetry and those
which do not. We present a new technique of dealing with contribution from the
former type of orbits.
The technique allows us to derive the third order term of the expansion for
general graphs. Although the derivation is rather technical, the advantages of
the technique are obvious: it makes the derivation tractable, it identifies
explicitly the orbit configurations which give the correct contribution, it is
more algorithmical and more system-independent, making possible future
applications of the technique to systems other than quantum graphs.Comment: 25 pages, 14 figures, accepted to Waves in Random Media (special
issue on Quantum Graphs and their Applications). Fixed typos, removed an
overly restrictive condition (appendix), shortened introductory section
Randomly incomplete spectra and intermediate statistics
By randomly removing a fraction of levels from a given spectrum a model is
constructed that describes a crossover from this spectrum to a Poisson
spectrum. The formalism is applied to the transitions towards Poisson from
random matrix theory (RMT) spectra and picket fence spectra. It is shown that
the Fredholm determinant formalism of RMT extends naturally to describe
incomplete RMT spectra.Comment: 9 pages, 2 figures. To appear in Physical Review
Semiclassical Treatment of Diffraction in Billiard Systems with a Flux Line
In billiard systems with a flux line semiclassical approximations for the
density of states contain contributions from periodic orbits as well as from
diffractive orbits that are scattered on the flux line. We derive a
semiclassical approximation for diffractive orbits that are scattered once on a
flux line. This approximation is uniformly valid for all scattering angles. The
diffractive contributions are necessary in order that semiclassical
approximations are continuous if the position of the flux line is changed.Comment: LaTeX, 17 pages, 4 figure
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 stability of periodic orbits in delay equations with large delay
We prove a necessary and sufficient criterion for the exponential stability
of periodic solutions of delay differential equations with large delay. We show
that for sufficiently large delay the Floquet spectrum near criticality is
characterized by a set of curves, which we call asymptotic continuous spectrum,
that is independent on the delay.Comment: postprint versio
Leading off-diagonal contribution to the spectral form factor of chaotic quantum systems
We semiclassically derive the leading off-diagonal correction to the spectral
form factor of quantum systems with a chaotic classical counterpart. To this
end we present a phase space generalization of a recent approach for uniformly
hyperbolic systems (M. Sieber and K. Richter, Phys. Scr. T90, 128 (2001); M.
Sieber, J. Phys. A: Math. Gen. 35, L613 (2002)). Our results coincide with
corresponding random matrix predictions. Furthermore, we study the transition
from the Gaussian orthogonal to the Gaussian unitary ensemble.Comment: 8 pages, 2 figures; J. Phys. A: Math. Gen. (accepted for publication
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