27,002 research outputs found
On the propagation of semiclassical Wigner functions
We establish the difference between the propagation of semiclassical Wigner
functions and classical Liouville propagation. First we re-discuss the
semiclassical limit for the propagator of Wigner functions, which on its own
leads to their classical propagation. Then, via stationary phase evaluation of
the full integral evolution equation, using the semiclassical expressions of
Wigner functions, we provide the correct geometrical prescription for their
semiclassical propagation. This is determined by the classical trajectories of
the tips of the chords defined by the initial semiclassical Wigner function and
centered on their arguments, in contrast to the Liouville propagation which is
determined by the classical trajectories of the arguments themselves.Comment: 9 pages, 1 figure. To appear in J. Phys. A. This version matches the
one set to print and differs from the previous one (07 Nov 2001) by the
addition of two references, a few extra words of explanation and an augmented
figure captio
Uniform approximation for the overlap caustic of a quantum state with its translations
The semiclassical Wigner function for a Bohr-quantized energy eigenstate is
known to have a caustic along the corresponding classical closed phase space
curve in the case of a single degree of freedom. Its Fourier transform, the
semiclassical chord function, also has a caustic along the conjugate curve
defined as the locus of diameters, i.e. the maximal chords of the original
curve. If the latter is convex, so is its conjugate, resulting in a simple fold
caustic. The uniform approximation through this caustic, that is here derived,
describes the transition undergone by the overlap of the state with its
translation, from an oscillatory regime for small chords, to evanescent
overlaps, rising to a maximum near the caustic. The diameter-caustic for the
Wigner function is also treated.Comment: 14 pages, 9 figure
Testing the Equivalence of Regular Languages
The minimal deterministic finite automaton is generally used to determine
regular languages equality. Antimirov and Mosses proposed a rewrite system for
deciding regular expressions equivalence of which Almeida et al. presented an
improved variant. Hopcroft and Karp proposed an almost linear algorithm for
testing the equivalence of two deterministic finite automata that avoids
minimisation. In this paper we improve the best-case running time, present an
extension of this algorithm to non-deterministic finite automata, and establish
a relationship between this algorithm and the one proposed in Almeida et al. We
also present some experimental comparative results. All these algorithms are
closely related with the recent coalgebraic approach to automata proposed by
Rutten
A percolation system with extremely long range connections and node dilution
We study the very long-range bond-percolation problem on a linear chain with
both sites and bonds dilution. Very long range means that the probability
for a connection between two occupied sites at a distance
decays as a power law, i.e. when , and
when . Site dilution means that the occupancy probability of a site
is . The behavior of this model results from the competition
between long-range connectivity, which enhances the percolation, and site
dilution, which weakens percolation. The case with is
well-known, being the exactly solvable mean-field model. The percolation order
parameter is investigated numerically for different values of
, and . We show that in the ranges
and the percolation order parameter depends only on
the average connectivity of sites, which can be explicitly computed in
terms of the three parameters , and
Orbit bifurcations and the scarring of wavefunctions
We extend the semiclassical theory of scarring of quantum eigenfunctions
psi_{n}(q) by classical periodic orbits to include situations where these
orbits undergo generic bifurcations. It is shown that |psi_{n}(q)|^{2},
averaged locally with respect to position q and the energy spectrum E_{n}, has
structure around bifurcating periodic orbits with an amplitude and length-scale
whose hbar-dependence is determined by the bifurcation in question.
Specifically, the amplitude scales as hbar^{alpha} and the length-scale as
hbar^{w}, and values of the scar exponents, alpha and w, are computed for a
variety of generic bifurcations. In each case, the scars are semiclassically
wider than those associated with isolated and unstable periodic orbits;
moreover, their amplitude is at least as large, and in most cases larger. In
this sense, bifurcations may be said to give rise to superscars. The
competition between the contributions from different bifurcations to determine
the moments of the averaged eigenfunction amplitude is analysed. We argue that
there is a resulting universal hbar-scaling in the semiclassical asymptotics of
these moments for irregular states in systems with a mixed phase-space
dynamics. Finally, a number of these predictions are illustrated by numerical
computations for a family of perturbed cat maps.Comment: 24 pages, 6 Postscript figures, corrected some typo
Neutral heavy lepton production at next high energy linear colliders
The discovery potential for detecting new heavy Majorana and Dirac neutrinos
at some recently proposed high energy colliders is discussed. These
new particles are suggested by grand unified theories and superstring-inspired
models. For these models the production of a single heavy neutrino is shown to
be more relevant than pair production when comparing cross sections and
neutrino mass ranges.
The process is calculated
including on-shell and off-shell heavy neutrino effects.
We present a detailed study of cross sections and distributions that shows a
clear separation between the signal and standard model contributions, even
after including hadronization effects.Comment: 4 pages including 15 figures, 1 table. RevTex. Accepted in Physical
Review
Local quantum ergodic conjecture
The Quantum Ergodic Conjecture equates the Wigner function for a typical
eigenstate of a classically chaotic Hamiltonian with a delta-function on the
energy shell. This ensures the evaluation of classical ergodic expectations of
simple observables, in agreement with Shnirelman's theorem, but this putative
Wigner function violates several important requirements. Consequently, we
transfer the conjecture to the Fourier transform of the Wigner function, that
is, the chord function. We show that all the relevant consequences of the usual
conjecture require only information contained within a small (Planck) volume
around the origin of the phase space of chords: translations in ordinary phase
space. Loci of complete orthogonality between a given eigenstate and its nearby
translation are quite elusive for the Wigner function, but our local conjecture
stipulates that their pattern should be universal for ergodic eigenstates of
the same Hamiltonian lying within a classically narrow energy range. Our
findings are supported by numerical evidence in a Hamiltonian exhibiting soft
chaos. Heavily scarred eigenstates are remarkable counter-examples of the
ergodic universal pattern.Comment: 4 figure
Scarring by homoclinic and heteroclinic orbits
In addition to the well known scarring effect of periodic orbits, we show
here that homoclinic and heteroclinic orbits, which are cornerstones in the
theory of classical chaos, also scar eigenfunctions of classically chaotic
systems when associated closed circuits in phase space are properly quantized,
thus introducing strong quantum correlations. The corresponding quantization
rules are also established. This opens the door for developing computationally
tractable methods to calculate eigenstates of chaotic systems.Comment: 5 pages, 4 figure
Decoherence of Semiclassical Wigner Functions
The Lindblad equation governs general markovian evolution of the density
operator in an open quantum system. An expression for the rate of change of the
Wigner function as a sum of integrals is one of the forms of the Weyl
representation for this equation. The semiclassical description of the Wigner
function in terms of chords, each with its classically defined amplitude and
phase, is thus inserted in the integrals, which leads to an explicit
differential equation for the Wigner function. All the Lindblad operators are
assumed to be represented by smooth phase space functions corresponding to
classical variables. In the case that these are real, representing hermitian
operators, the semiclassical Lindblad equation can be integrated. There results
a simple extension of the unitary evolution of the semiclassical Wigner
function, which does not affect the phase of each chord contribution, while
dampening its amplitude. This decreases exponentially, as governed by the time
integral of the square difference of the Lindblad functions along the classical
trajectories of both tips of each chord. The decay of the amplitudes is shown
to imply diffusion in energy for initial states that are nearly pure.
Projecting the Wigner function onto an orthogonal position or momentum basis,
the dampening of long chords emerges as the exponential decay of off-diagonal
elements of the density matrix.Comment: 23 pg, 2 fi
The Phoenix Deep Survey: spectroscopic catalog
The Phoenix Deep Survey is a multi-wavelength survey based on deep 1.4 GHz
radio imaging, reaching well into the sub-100 microJy level. One of the aims of
this survey is to characterize the sub-mJy radio population, exploring its
nature and evolution. In this paper we present the catalog and results of the
spectroscopic observations aimed at characterizing the optically ``bright''
(R<~ 21.5 mag) counterparts of faint radio sources. Out of 371 sources with
redshift determination, 21% have absorption lines only, 11% show AGN
signatures, 32% are star-forming galaxies, 34% show narrow emission lines that
do not allow detailed spectral classification (due to poor signal-to-noise
ratio and/or lack of diagnostic emission lines) and the remaining 2% are
identified with stars. For the star-forming galaxies with a Balmer decrement
measurement we find a median extinction of A(Ha)=1.9 mag, higher than that of
optically selected samples. This is a result of the radio selection, which is
not biased against dusty systems. Using the available spectroscopic
information, we estimate the radio luminosity function of star-forming galaxies
in two independent redshift bins at z~0.1 and 0.3 respectively. We find direct
evidence for strong luminosity evolution of these systems consistent with L(1.4
GHz) ~ (1+z)^(2.7).Comment: 39 pages, 12 figures. References added, and minor changes to reflect
published versio
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