255 research outputs found
Exponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics
Phase space representations of the dynamics of the quantal and classical cat
map are used to explore quantum--classical correspondence in a K-system: as
, the classical chaotic behavior is shown to emerge smoothly and
exactly. The quantum dynamics near the classical limit displays both
exponential separation of adjacent distributions and long time relaxation, two
characteristic features of classical chaotic motion.Comment: 10 pages, ReVTeX, to appear in Phys. Rev. Lett. 13 figures NOT
included. Available either as LARGE (uuencoded gzipped) postscript files or
hard-copies from [email protected]
Instability of the massive Klein-Gordon field on the Kerr spacetime
We investigate the instability of the massive scalar field in the vicinity of
a rotating black hole. The instability arises from amplification caused by the
classical superradiance effect. The instability affects bound states: solutions
to the massive Klein-Gordon equation which tend to zero at infinity. We
calculate the spectrum of bound state frequencies on the Kerr background using
a continued fraction method, adapted from studies of quasinormal modes. We
demonstrate that the instability is most significant for the ,
state, for . For a fast rotating hole () we find
a maximum growth rate of ,
at . The physical implications are discussed.Comment: Added references. 27 pages, 7 figure
From Heisenberg matrix mechanics to EBK quantization: theory and first applications
Despite the seminal connection between classical multiply-periodic motion and
Heisenberg matrix mechanics and the massive amount of work done on the
associated problem of semiclassical (EBK) quantization of bound states, we show
that there are, nevertheless, a number of previously unexploited aspects of
this relationship that bear on the quantum-classical correspondence. In
particular, we emphasize a quantum variational principle that implies the
classical variational principle for invariant tori. We also expose the more
indirect connection between commutation relations and quantization of action
variables. With the help of several standard models with one or two degrees of
freedom, we then illustrate how the methods of Heisenberg matrix mechanics
described in this paper may be used to obtain quantum solutions with a modest
increase in effort compared to semiclassical calculations. We also describe and
apply a method for obtaining leading quantum corrections to EBK results.
Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.
The XXL Survey: XII. Optical spectroscopy of X-ray-selected clusters and the frequency of AGN in superclusters
This article belongs to the first series of XXL publications. It presents
multifibre spectroscopic observations of three 0.55 sq.deg. fields in the XXL
Survey, which were selected on the basis of their high density of
X-ray-detected clusters. The observations were obtained with the
AutoFib2+WYFFOS (AF2) wide-field fibre spectrograph mounted on the 4.2m William
Herschel Telescope. The paper first describes the scientific rationale, the
preparation, the data reduction, and the results of the observations, and then
presents a study of active galactic nuclei (AGN) within three superclusters. We
obtained redshifts for 455 galaxies in total, 56 of which are counterparts of
X-ray point-like sources. We were able to determine the redshift of the merging
supercluster XLSSC-e, which consists of six individual clusters at z~0.43, and
we confirmed the redshift of supercluster XLSSC-d at z~0.3. More importantly,
we discovered a new supercluster, XLSSC-f, that comprises three galaxy clusters
also at z~0.3. We find a significant 2D overdensity of X-ray point-like sources
only around the supercluster XLSSC-f. This result is also supported by the
spatial (3D) analysis of XLSSC-f, where we find four AGN with compatible
spectroscopic redshifts and possibly one more with compatible photometric
redshift. In addition, we find two AGN (3D analysis) at the redshift of
XLSSC-e, but no AGN in XLSSC-d. Comparing these findings with the optical
galaxy overdensity we conclude that the total number of AGN in the area of the
three superclusters significantly exceeds the field expectations. The
difference in the AGN frequency between the three superclusters cannot be
explained by the present study because of small number statistics. Further
analysis of a larger number of superclusters within the 50 sq. deg. of the XXL
is needed before any conclusions on the effect of the supercluster environment
on AGN can be reached.Comment: 11 pages, published by A&
Galaxy pre-processing in substructures around z0.4 galaxy clusters
We present a detailed analysis of galaxy colours in two galaxy clusters at
\mbox{z 0.4}, \mbox{MACS J0416.1-2403} and \mbox{MACS J1206.2-0847},
drawn from the CLASH-VLT survey, to investigate the role of pre-processing in
the quenching of star formation. We estimate the fractions of red and blue
galaxies within the main cluster and the detected substructures and study the
trends of the colour fractions as a function of the projected distance from the
cluster and substructure centres. Our results show that the colours of cluster
and substructure members have consistent spatial distributions. In particular,
the colour fractions of galaxies inside substructures follow the same spatial
trends observed in the main clusters. Additionally, we find that at large
cluster-centric distances \mbox{()} the fraction of blue
galaxies in both the main clusters and in the substructures is always lower
than the average fraction of UVJ-selected star-forming galaxies in the field as
measured in the COSMOS/UltraVista data set. We finally estimate environmental
quenching efficiencies in the clusters and in the substructures and find that
at large distances from the cluster centres, the quenching efficiency of
substructures becomes comparable to the quenching efficiency of clusters. Our
results suggest that pre-processing plays a significant role in the formation
and evolution of passive galaxies in clusters at low redshifts.Comment: Accepted for publication in MNRAS. 28 pages, 14 figures, 20 table
Geometrical Models of the Phase Space Structures Governing Reaction Dynamics
Hamiltonian dynamical systems possessing equilibria of stability type display \emph{reaction-type
dynamics} for energies close to the energy of such equilibria; entrance and
exit from certain regions of the phase space is only possible via narrow
\emph{bottlenecks} created by the influence of the equilibrium points. In this
paper we provide a thorough pedagogical description of the phase space
structures that are responsible for controlling transport in these problems. Of
central importance is the existence of a \emph{Normally Hyperbolic Invariant
Manifold (NHIM)}, whose \emph{stable and unstable manifolds} have sufficient
dimensionality to act as separatrices, partitioning energy surfaces into
regions of qualitatively distinct behavior. This NHIM forms the natural
(dynamical) equator of a (spherical) \emph{dividing surface} which locally
divides an energy surface into two components (`reactants' and `products'), one
on either side of the bottleneck. This dividing surface has all the desired
properties sought for in \emph{transition state theory} where reaction rates
are computed from the flux through a dividing surface. In fact, the dividing
surface that we construct is crossed exactly once by reactive trajectories, and
not crossed by nonreactive trajectories, and related to these properties,
minimizes the flux upon variation of the dividing surface.
We discuss three presentations of the energy surface and the phase space
structures contained in it for 2-degree-of-freedom (DoF) systems in the
threedimensional space , and two schematic models which capture many of
the essential features of the dynamics for -DoF systems. In addition, we
elucidate the structure of the NHIM.Comment: 44 pages, 38 figures, PDFLaTe
Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape
Lobe dynamics and escape from a potential well are general frameworks
introduced to study phase space transport in chaotic dynamical systems. While
the former approach studies how regions of phase space are transported by
reducing the flow to a two-dimensional map, the latter approach studies the
phase space structures that lead to critical events by crossing periodic orbit
around saddles. Both of these frameworks require computation with curves
represented by millions of points-computing intersection points between these
curves and area bounded by the segments of these curves-for quantifying the
transport and escape rate. We present a theory for computing these intersection
points and the area bounded between the segments of these curves based on a
classification of the intersection points using equivalence class. We also
present an alternate theory for curves with nontransverse intersections and a
method to increase the density of points on the curves for locating the
intersection points accurately.The numerical implementation of the theory
presented herein is available as an open source software called Lober. We used
this package to demonstrate the application of the theory to lobe dynamics that
arises in fluid mechanics, and rate of escape from a potential well that arises
in ship dynamics.Comment: 33 pages, 17 figure
Diffuse-Charge Dynamics in Electrochemical Systems
The response of a model micro-electrochemical system to a time-dependent
applied voltage is analyzed. The article begins with a fresh historical review
including electrochemistry, colloidal science, and microfluidics. The model
problem consists of a symmetric binary electrolyte between parallel-plate,
blocking electrodes which suddenly apply a voltage. Compact Stern layers on the
electrodes are also taken into account. The Nernst-Planck-Poisson equations are
first linearized and solved by Laplace transforms for small voltages, and
numerical solutions are obtained for large voltages. The ``weakly nonlinear''
limit of thin double layers is then analyzed by matched asymptotic expansions
in the small parameter , where is the
screening length and the electrode separation. At leading order, the system
initially behaves like an RC circuit with a response time of
(not ), where is the ionic diffusivity, but nonlinearity
violates this common picture and introduce multiple time scales. The charging
process slows down, and neutral-salt adsorption by the diffuse part of the
double layer couples to bulk diffusion at the time scale, . In the
``strongly nonlinear'' regime (controlled by a dimensionless parameter
resembling the Dukhin number), this effect produces bulk concentration
gradients, and, at very large voltages, transient space charge. The article
concludes with an overview of more general situations involving surface
conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference
GASP - XVII. H I imaging of the jellyfish galaxy JO206:Gas stripping and enhanced star formation
We present VLA HI observations of JO206, a prototypical ram-pressure stripped
galaxy in the GASP sample. This massive galaxy (M 8.5
10 M) is located at a redshift of 0.0513, near the
centre of the low-mass galaxy cluster, IIZw108 ( km/s). JO206
is characterised by a long tail (90 kpc) of ionised gas stripped away by
ram-pressure. We find a similarly long HI tail in the same direction as the
ionised gas tail and measure a total HI mass of
M. This is about half the expected HI mass given the stellar mass and
surface density of JO206. A total of M (60%) of
the detected HI is in the gas stripped tail. An analysis of the star formation
rate shows that the galaxy is forming more stars compared to galaxies with the
same stellar and HI mass. On average we find a HI gas depletion time of
0.5 Gyr which is about four times shorter than that of "normal" spiral
galaxies. We performed a spatially resolved analysis of the relation between
star formation rate density and gas density in the disc and tail of the galaxy
at the resolution of our HI data. The star formation efficiency of the disc is
about 10 times higher than that of the tail at fixed HI surface densities. Both
the inner and outer parts of JO206 show an enhanced star formation compared to
regions of similar HI surface density in field galaxies. The enhanced star
formation is due to ram-pressure stripping during the galaxy's first infall
into the cluster.Comment: 13 pages, 12 figures, Accepted for publication in MNRA
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