1,205 research outputs found
Elastic Cross-Section and Luminosity Measurement in ATLAS at LHC
Recently the ATLAS experiment was complemented with a set of
ultra-small-angle detectors located in ``Roman Pot'' inserts at 240m on either
side of the interaction point, aiming at the absolute determination of the LHC
luminosity by measuring the elastic scattering rate at the Coulomb Nuclear
Interference region. Details of the proposed measurement the detector
construction and the expected performance as well as the challenges involved
are discussed here.Comment: EDS05, Blois, France, May 15-20, 200
The speed of Arnold diffusion
A detailed numerical study is presented of the slow diffusion (Arnold
diffusion) taking place around resonance crossings in nearly integrable
Hamiltonian systems of three degrees of freedom in the so-called `Nekhoroshev
regime'. The aim is to construct estimates regarding the speed of diffusion
based on the numerical values of a truncated form of the so-called remainder of
a normalized Hamiltonian function, and to compare them with the outcomes of
direct numerical experiments using ensembles of orbits. In this comparison we
examine, one by one, the main steps of the so-called analytic and geometric
parts of the Nekhoroshev theorem. We are led to two main results: i) We
construct in our concrete example a convenient set of variables, proposed first
by Benettin and Gallavotti (1986), in which the phenomenon of Arnold diffusion
in doubly resonant domains can be clearly visualized. ii) We determine, by
numerical fitting of our data the dependence of the local diffusion coefficient
"D" on the size "||R_{opt}||" of the optimal remainder function, and we compare
this with a heuristic argument based on the assumption of normal diffusion. We
find a power law "D\propto ||R_{opt}||^{2(1+b)}", where the constant "b" has a
small positive value depending also on the multiplicity of the resonance
considered.Comment: 39 pages, 11 figure
Secondary resonances and the boundary of effective stability of Trojan motions
One of the most interesting features in the libration domain of co-orbital
motions is the existence of secondary resonances. For some combinations of
physical parameters, these resonances occupy a large fraction of the domain of
stability and rule the dynamics within the stable tadpole region. In this work,
we present an application of a recently introduced `basic Hamiltonian model' Hb
for Trojan dynamics, in Paez and Efthymiopoulos (2015), Paez, Locatelli and
Efthymiopoulos (2016): we show that the inner border of the secondary resonance
of lowermost order, as defined by Hb, provides a good estimation of the region
in phase-space for which the orbits remain regular regardless the orbital
parameters of the system. The computation of this boundary is straightforward
by combining a resonant normal form calculation in conjunction with an
`asymmetric expansion' of the Hamiltonian around the libration points, which
speeds up convergence. Applications to the determination of the effective
stability domain for exoplanetary Trojans (planet-sized objects or asteroids)
which may accompany giant exoplanets are discussed.Comment: 21 pages, 9 figures. Accepted for publication in Celestial Mechanics
and Dynamical Astronom
Bohmian trajectories in an entangled two-qubit system
In this paper we examine the evolution of Bohmian trajectories in the
presence of quantum entanglement. We study a simple two-qubit system composed
of two coherent states and investigate the impact of quantum entanglement on
chaotic and ordered trajectories via both numerical and analytical
calculations.Comment: 12 Figures, corrected typos, replaced figure 10 and revised captions
in figures 8 and 1
Effective power-law dependence of Lyapunov exponents on the central mass in galaxies
Using both numerical and analytical approaches, we demonstrate the existence
of an effective power-law relation between the mean Lyapunov
exponent of stellar orbits chaotically scattered by a supermassive black
hole in the center of a galaxy and the mass parameter , i.e. ratio of the
mass of the black hole over the mass of the galaxy. The exponent is found
numerically to obtain values in the range --. We propose a
theoretical interpretation of these exponents, based on estimates of local
`stretching numbers', i.e. local Lyapunov exponents at successive transits of
the orbits through the black hole's sphere of influence. We thus predict
with --. Our basic model refers to elliptical
galaxy models with a central core. However, we find numerically that an
effective power law scaling of with holds also in models with central
cusp, beyond a mass scale up to which chaos is dominated by the influence of
the cusp itself. We finally show numerically that an analogous law exists also
in disc galaxies with rotating bars. In the latter case, chaotic scattering by
the black hole affects mainly populations of thick tube-like orbits surrounding
some low-order branches of the family of periodic orbits, as well as its
bifurcations at low-order resonances, mainly the Inner Lindbland resonance and
the 4/1 resonance. Implications of the correlations between and to
determining the rate of secular evolution of galaxies are discussed.Comment: 27 pages, 19 figure
Analytical description of the structure of chaos
We consider analytical formulae that describe the chaotic regions around the
main periodic orbit of the H\'{e}non map. Following our previous
paper (Efthymiopoulos, Contopoulos, Katsanikas ) we introduce new
variables in which the product (constant) gives
hyperbolic invariant curves. These hyperbolae are mapped by a canonical
transformation to the plane , giving "Moser invariant curves". We
find that the series are convergent up to a maximum value of
. We give estimates of the errors due to the finite truncation of
the series and discuss how these errors affect the applicability of analytical
computations. For values of the basic parameter of the H\'{e}non map
smaller than a critical value, there is an island of stability, around a stable
periodic orbit , containing KAM invariant curves. The Moser curves for are completely outside the last KAM curve around , the curves
with intersect the last KAM curve and the curves with are completely inside the last KAM curve. All orbits in
the chaotic region around the periodic orbit , although they seem
random, belong to Moser invariant curves, which, therefore define a "structure
of chaos". Orbits starting close and outside the last KAM curve remain close to
it for a stickiness time that is estimated analytically using the series
. We finally calculate the periodic orbits that accumulate close to the
homoclinic points, i.e. the points of intersection of the asymptotic curves
from , exploiting a method based on the self-intersections of the
invariant Moser curves. We find that all the computed periodic orbits are
generated from the stable orbit for smaller values of the H\'{e}non
parameter , i.e. they are all regular periodic orbits.Comment: 22 pages, 9 figure
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