2,931 research outputs found
An efficient method for scattering problems in open billiards: Theory and applications
We present an efficient method to solve scattering problems in
two-dimensional open billiards with two leads and a complicated scattering
region. The basic idea is to transform the scattering region to a rectangle,
which will lead to complicated dynamics in the interior, but simple boundary
conditions. The method can be specialized to closed billiards, and it allows
the treatment of interacting particles in the billiard. We apply this method to
quantum echoes measured recently in a microwave cavity, and indicate, how it
can be used for interacting particles.Comment: 9 pages 6 figures submitted to PR
First experimental evidence for quantum echoes in scattering systems
A self-pulsing effect termed quantum echoes has been observed in experiments
with an open superconducting and a normal conducting microwave billiard whose
geometry provides soft chaos, i.e. a mixed phase space portrait with a large
stable island. For such systems a periodic response to an incoming pulse has
been predicted. Its period has been associated to the degree of development of
a horseshoe describing the topology of the classical dynamics. The experiments
confirm this picture and reveal the topological information.Comment: RevTex 4.0, 5 eps-figure
Self-pulsing effect in chaotic scattering
We study the quantum and classical scattering of Hamiltonian systems whose
chaotic saddle is described by binary or ternary horseshoes. We are interested
in parameters of the system for which a stable island, associated with the
inner fundamental periodic orbit of the system exists and is large, but chaos
around this island is well developed. In this situation, in classical systems,
decay from the interaction region is algebraic, while in quantum systems it is
exponential due to tunneling. In both cases, the most surprising effect is a
periodic response to an incoming wave packet. The period of this self-pulsing
effect or scattering echoes coincides with the mean period, by which the
scattering trajectories rotate around the stable orbit. This period of rotation
is directly related to the development stage of the underlying horseshoe.
Therefore the predicted echoes will provide experimental access to topological
information. We numerically test these results in kicked one dimensional models
and in open billiards.Comment: Submitted to New Journal of Physics. Two movies (not included) and
full-resolution figures are available at http://www.cicc.unam.mx/~mejia
Localization in Strongly Chaotic Systems
We show that, in the semiclassical limit and whenever the elements of the
Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic
time-independent systems in ordered bases can on average be exponentially
localized across the energy shell and decay faster than exponentially outside
the energy shell. Typically however, matrix elements are strongly correlated
leading to deviations from such behavior.Comment: RevTeX, 5 pages + 3 postscript figures, submitted to Phys. Rev. Let
Next-to-next-to-leading order fits to CCFR'97 data and infrared renormalons
We briefly summarize the outcomes of our recent improved fits to the
experimental data of CCFR collaboration for structure function of deep-inelastic scattering at the next-to-next-to-leading order. Special
attention is paid to the extraction of and the parameter of the
infrared renormalon model for -correction at different orders of
perturbation theory. The results can be of interest for planning similar
studies using possible future data of Neutrino Factories.Comment: 3 pages, presented at WG3 of 4th NuFact'02 Workshop, London 1-6 July,
200
Transition from Gaussian-orthogonal to Gaussian-unitary ensemble in a microwave billiard with threefold symmetry
Recently it has been shown that time-reversal invariant systems with discrete
symmetries may display in certain irreducible subspaces spectral statistics
corresponding to the Gaussian unitary ensemble (GUE) rather than to the
expected orthogonal one (GOE). A Kramers type degeneracy is predicted in such
situations. We present results for a microwave billiard with a threefold
rotational symmetry and with the option to display or break a reflection
symmetry. This allows us to observe the change from GOE to GUE statistics for
one subset of levels. Since it was not possible to separate the three
subspectra reliably, the number variances for the superimposed spectra were
studied. The experimental results are compared with a theoretical and numerical
study considering the effects of level splitting and level loss
Berry-Robnik level statistics in a smooth billiard system
Berry-Robnik level spacing distribution is demonstrated clearly in a generic
quantized plane billiard for the first time. However, this ultimate
semi-classical distribution is found to be valid only for extremely small
semi-classical parameter (effective Planck's constant) where the assumption of
statistical independence of regular and irregular levels is achieved. For
sufficiently larger semiclassical parameter we find (fractional power-law)
level repulsion with phenomenological Brody distribution providing an adequate
global fit.Comment: 10 pages in LaTeX with 4 eps figures include
Effective Lagrangians and Chiral Random Matrix Theory
Recently, sum rules were derived for the inverse eigenvalues of the Dirac
operator. They were obtained in two different ways: i) starting from the
low-energy effective Lagrangian and ii) starting from a random matrix theory
with the symmetries of the Dirac operator. This suggests that the effective
theory can be obtained directly from the random matrix theory. Previously, this
was shown for three or more colors with fundamental fermions. In this paper we
construct the effective theory from a random matrix theory for two colors in
the fundamental representation and for an arbitrary number of colors in the
adjoint representation. We construct a fermionic partition function for
Majorana fermions in Euclidean space time. Their reality condition is
formulated in terms of complex conjugation of the second kind.Comment: 27 page
Heavy Quark Initiated Contributions to Deep Inelastic Structure Functions
We present O(alpha_s^1) corrections to deep inelastic scattering amplitudes
on massive quarks obtained within the scheme of Aivazis, Collins, Olness and
Tung (ACOT). After identifying the correct subtraction term the convergence of
these contributions towards the analogous coefficient functions for massless
quarks, obtained within the modified minimal subtraction scheme (MSbar), is
demonstrated. Furthermore, the quantitative relevance of the contributions to
neutral current (NC) and charged current (CC) structure functions is
investigated for several choices of the factorization scale.Comment: 29 pages, 6 figures; uses epsfig.sty, amssymb.sty, axodraw.sty; minor
changes for publication in Phys. Rev.
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