10,488 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
Scaling in a continuous time model for biological aging
In this paper we consider a generalization to the asexual version of the
Penna model for biological aging, where we take a continuous time limit. The
genotype associated to each individual is an interval of real numbers over
which Dirac --functions are defined, representing genetically
programmed diseases to be switched on at defined ages of the individual life.
We discuss two different continuous limits for the evolution equation and two
different mutation protocols, to be implemented during reproduction. Exact
stationary solutions are obtained and scaling properties are discussed.Comment: 10 pages, 6 figure
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
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
Análise de uma potencial cadeia de exportação de feijões sob a ótica da nova economia institucional.
Tem como objetivo fazer uso da Nova Economia Institucional (NEI) com ferramenta de análise das possĂveis interações da cadeia produtiva do feijĂŁo para exportação.CONAFE
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
Cost efficiency of retrofit measures for typical masonry houses in Kosovo
A major challenge our society faces today is the buildings energy consumption. Building stock is responsible for about 40% of energy consumption worldwide. The same applies for Kosovo where large number of houses are poorly weatherized and inefficient in terms of energy consumption. Most of the energy consumption in the household sector in Kosovo is dedicated to the needs for heating purposes. Furthermore, many of these houses use wood or coal for heating releasing a lot of gases in the air and so contribute to an increased air pollution both indoors and outdoors. The Faculty of Civil Engineering and Architecture at the University of Prishtina ?Hasan Prishtina? aims to address the issue of energy efficiency for these houses. Specifically, in this study we intend to evaluate various retrofit measures applicable in the country for typical masonry houses and identify the cost-efficient solution. This paper reports for the initial results of the study and discusses related challenges.info:eu-repo/semantics/publishedVersio
Semiclassical theory for small displacements
Characteristic functions contain complete information about all the moments
of a classical distribution and the same holds for the Fourier transform of the
Wigner function: a quantum characteristic function, or the chord function.
However, knowledge of a finite number of moments does not allow for accurate
determination of the chord function. For pure states this provides the overlap
of the state with all its possible rigid translations (or displacements). We
here present a semiclassical approximation of the chord function for large
Bohr-quantized states, which is accurate right up to a caustic, beyond which
the chord function becomes evanescent. It is verified to pick out blind spots,
which are displacements for zero overlaps. These occur even for translations
within a Planck area of the origin. We derive a simple approximation for the
closest blind spots, depending on the Schroedinger covariance matrix, which is
verified for Bohr-quantized states.Comment: 16 pages, 4 figures
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
- …