3,361 research outputs found
Nonstatistical dynamics on potentials exhibiting reaction path bifurcations and valley-ridge inflection points
We study reaction dynamics on a model potential energy surface exhibiting
post-transition state bifurcation in the vicinity of a valley ridge inflection
point. We compute fractional yields of products reached after the VRI region is
traversed, both with and without dissipation. It is found that apparently minor
variations in the potential lead to significant changes in the reaction
dynamics. Moreover, when dissipative effects are incorporated, the product
ratio depends in a complicated and highly non-monotonic fashion on the
dissipation parameter. Dynamics in the vicinity of the VRI point itself play
essentially no role in determining the product ratio, except in the highly
dissipative regime.Comment: 33 pages, 10 figures, corrected the author name in reference [6
Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
Many natural and social systems develop complex networks, that are usually
modelled as random graphs. The eigenvalue spectrum of these graphs provides
information about their structural properties. While the semi-circle law is
known to describe the spectral density of uncorrelated random graphs, much less
is known about the eigenvalues of real-world graphs, describing such complex
systems as the Internet, metabolic pathways, networks of power stations,
scientific collaborations or movie actors, which are inherently correlated and
usually very sparse. An important limitation in addressing the spectra of these
systems is that the numerical determination of the spectra for systems with
more than a few thousand nodes is prohibitively time and memory consuming.
Making use of recent advances in algorithms for spectral characterization, here
we develop new methods to determine the eigenvalues of networks comparable in
size to real systems, obtaining several surprising results on the spectra of
adjacency matrices corresponding to models of real-world graphs. We find that
when the number of links grows as the number of nodes, the spectral density of
uncorrelated random graphs does not converge to the semi-circle law.
Furthermore, the spectral densities of real-world graphs have specific features
depending on the details of the corresponding models. In particular, scale-free
graphs develop a triangle-like spectral density with a power law tail, while
small-world graphs have a complex spectral density function consisting of
several sharp peaks. These and further results indicate that the spectra of
correlated graphs represent a practical tool for graph classification and can
provide useful insight into the relevant structural properties of real
networks.Comment: 14 pages, 9 figures (corrected typos, added references) accepted for
Phys. Rev.
State-space Geometry, Statistical Fluctuations and Black Holes in String Theory
We study the state-space geometry of various extremal and nonextremal black
holes in string theory. From the notion of the intrinsic geometry, we offer a
new perspective of black hole vacuum fluctuations. For a given black hole
entropy, we explicate the intrinsic state-space geometric meaning of the
statistical fluctuations, local and global stability conditions and long range
statistical correlations. We provide a set of physical motivations pertaining
to the extremal and nonextremal black holes, \textit{viz.}, the meaning of the
chemical geometry and physics of correlation. We illustrate the state-space
configurations for general charge extremal black holes. In sequel, we extend
our analysis for various possible charge and anticharge nonextremal black
holes. From the perspective of statistical fluctuation theory, we offer general
remarks, future directions and open issues towards the intrinsic geometric
understanding of the vacuum fluctuations and black holes in string theory.
Keywords: Intrinsic Geometry; String Theory; Physics of black holes;
Classical black holes; Quantum aspects of black holes, evaporation,
thermodynamics; Higher-dimensional black holes, black strings, and related
objects; Statistical Fluctuation; Flow Instability.
PACS: 02.40.Ky; 11.25.-w; 04.70.-s; 04.70.Bw; 04.70.Dy; 04.50.Gh; 5.40.-a;
47.29.KyComment: 28 pages. arXiv admin note: substantial text overlap with
arXiv:1102.239
Semiclassical Casimir Energies at Finite Temperature
We study the dependence on the temperature T of Casimir effects for a range
of systems, and in particular for a pair of ideal parallel conducting plates,
separated by a vacuum. We study the Helmholtz free energy, combining
Matsubara's formalism, in which the temperature appears as a periodic Euclidean
fourth dimension of circumference 1/T, with the semiclassical periodic orbital
approximation of Gutzwiller. By inspecting the known results for the Casimir
energy at T=0 for a rectangular parallelepiped, one is led to guess at the
expression for the free energy of two ideal parallel conductors without
performing any calculation. The result is a new form for the free energy in
terms of the lengths of periodic classical paths on a two-dimensional cylinder
section. This expression for the free energy is equivalent to others that have
been obtained in the literature. Slightly extending the domain of applicability
of Gutzwiller's semiclassical periodic orbit approach, we evaluate the free
energy at T>0 in terms of periodic classical paths in a four-dimensional cavity
that is the tensor product of the original cavity and a circle. The validity of
this approach is at present restricted to particular systems. We also discuss
the origin of the classical form of the free energy at high temperatures.Comment: 17 pages, no figures, Late
Iron fluorescence from within the innermost stable orbit of black hole accretion disks
The fluorescent iron Ka line is a powerful observational probe of the inner
regions of black holes accretion disks. Previous studies have assumed that only
material outside the radius of marginal stability can contribute to the
observed line emission. Here, we show that fluorescence by material inside the
radius of marginal stability, which is in the process of spiralling towards the
event horizon, can have a observable influence on the iron line profile and
equivalent width. For concreteness, we consider the case of a geometrically
thin accretion disk, around a Schwarzschild black hole, in which fluorescence
is excited by an X-ray source placed at some height above the disk and on the
axis of the disk. Fully relativistic line profiles are presented for various
source heights and efficiencies. It is found that the extra line flux generally
emerges in the extreme red wing of the iron line, due to the large
gravitational redshift experienced by photons from the region within the radius
of marginal stability. We apply our models to the variable iron line seen in
the ASCA spectrum of the Seyfert nucleus MCG-6-30-15. It is found that the
change in the line profile, equivalent width, and continuum normalization, can
be well explained as being due to a change in the height of the source above
the disk. We discuss the implications of these results for distinguishing
rapidly-rotating black holes from slowly rotating holes using iron line
diagnostics.Comment: 20 pages, LaTeX. Accepted for publication in Astrophysical Journal.
Figures 3 to 7 replaced with corrected versions (previous figures affected by
calculational error). Some changes in the best fitting parameter
From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
The AdS/CFT correspondence between Sasaki-Einstein spaces and quiver gauge
theories is studied from the perspective of massless BPS geodesics. The
recently constructed toric Lpqr geometries are considered: we determine the
dual superconformal quivers and the spectrum of BPS mesons. The conformal
anomaly is compared with the volumes of the manifolds. The U(1)^2_F x U(1)_R
global symmetry quantum numbers of the mesonic operators are successfully
matched with the conserved momenta of the geodesics, providing a test of
AdS/CFT duality. The correspondence between BPS mesons and geodesics allows to
find new precise relations between the two sides of the duality. In particular
the parameters that characterize the geometry are mapped directly to the
parameters used for a-maximization in the field theory. The analysis simplifies
for the special case of the Lpqq models, which are shown to correspond to the
known "generalized conifolds". These geometries can break conformal invariance
through toric deformations of the complex structure.Comment: 30 pages, 8 figures, LaTeX. v2: One more figure. References added,
typos correcte
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