493 research outputs found
Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models
We compute exactly the distribution of the occupation time in a discrete {\em
non-Markovian} toy sequence which appears in various physical contexts such as
the diffusion processes and Ising spin glass chains. The non-Markovian property
makes the results nontrivial even for this toy sequence. The distribution is
shown to have non-Gaussian tails characterized by a nontrivial large deviation
function which is computed explicitly. An exact mapping of this sequence to an
Ising spin glass chain via a gauge transformation raises an interesting new
question for a generic finite sized spin glass model: at a given temperature,
what is the distribution (over disorder) of the thermally averaged number of
spins that are aligned to their local fields? We show that this distribution
remains nontrivial even at infinite temperature and can be computed explicitly
in few cases such as in the Sherrington-Kirkpatrick model with Gaussian
disorder.Comment: 10 pages Revtex (two-column), 1 eps figure (included
Collapse dynamics of trapped Bose-Einstein condensates
We analyze the implosion and subsequent explosion of a trapped condensate
after the scattering length is switched to a negative value. Our results
compare very well qualitatively and fairly well quantitatively with the results
of recent experiments at JILA.Comment: 4 pages, 3 figure
Second harmonic generation and birefringence of some ternary pnictide semiconductors
A first-principles study of the birefringence and the frequency dependent
second harmonic generation (SHG) coefficients of the ternary pnictide
semiconductors with formula ABC (A = Zn, Cd; B = Si, Ge; C = As, P) with
the chalcopyrite structures was carried out. We show that a simple empirical
observation that a smaller value of the gap is correlated with larger value of
SHG is qualitatively true. However, simple inverse power scaling laws between
gaps and SHG were not found. Instead, the real value of the nonlinear response
is a result of a very delicate balance between different intraband and
interband terms.Comment: 13 pages, 12 figure
Billiards in a general domain with random reflections
We study stochastic billiards on general tables: a particle moves according
to its constant velocity inside some domain until it hits the boundary and bounces randomly inside according to some
reflection law. We assume that the boundary of the domain is locally Lipschitz
and almost everywhere continuously differentiable. The angle of the outgoing
velocity with the inner normal vector has a specified, absolutely continuous
density. We construct the discrete time and the continuous time processes
recording the sequence of hitting points on the boundary and the pair
location/velocity. We mainly focus on the case of bounded domains. Then, we
prove exponential ergodicity of these two Markov processes, we study their
invariant distribution and their normal (Gaussian) fluctuations. Of particular
interest is the case of the cosine reflection law: the stationary distributions
for the two processes are uniform in this case, the discrete time chain is
reversible though the continuous time process is quasi-reversible. Also in this
case, we give a natural construction of a chord "picked at random" in
, and we study the angle of intersection of the process with a
-dimensional manifold contained in .Comment: 50 pages, 10 figures; To appear in: Archive for Rational Mechanics
and Analysis; corrected Theorem 2.8 (induced chords in nonconvex subdomains
Correlated N-boson systems for arbitrary scattering length
We investigate systems of identical bosons with the focus on two-body
correlations and attractive finite-range potentials. We use a hyperspherical
adiabatic method and apply a Faddeev type of decomposition of the wave
function. We discuss the structure of a condensate as function of particle
number and scattering length. We establish universal scaling relations for the
critical effective radial potentials for distances where the average distance
between particle pairs is larger than the interaction range. The correlations
in the wave function restore the large distance mean-field behaviour with the
correct two-body interaction. We discuss various processes limiting the
stability of condensates. With correlations we confirm that macroscopic
tunneling dominates when the trap length is about half of the particle number
times the scattering length.Comment: 15 pages (RevTeX4), 11 figures (LaTeX), submitted to Phys. Rev. A.
Second version includes an explicit comparison to N=3, a restructured
manuscript, and updated figure
Region of Excessive Flux of PeV Cosmic Rays in the Direction Toward Pulsars PSR J1840+5640 and LAT PSR J1836+5925
An analysis of arrival directions of extensive air showers (EAS) registered
with the EAS MSU and EAS-1000 prototype arrays has revealed a region of
excessive flux of PeV cosmic rays in the direction toward pulsars PSR
J1840+5640 and LAT PSR J1836+5925 at significance level up to 4.5sigma. The
first of the pulsars was discovered almost 30 years ago and is a well-studied
old radio pulsar located at the distance of 1.7pc from the Solar system. The
second pulsar belongs to a new type of pulsars, discovered by the space
gamma-ray observatory Fermi, pulsations of which are not observed in optical
and radio wavelengths but only in the gamma-ray range of energies
(gamma-ray-only pulsars). In our opinion, the existence of the region of
excessive flux of cosmic rays registered with two different arrays provides a
strong evidence that isolated pulsars can give a noticeable contribution to the
flux of Galactic cosmic rays in the PeV energy range.Comment: 14 pages; v.2: a few remarks to match a version accepted for
Astronomy Letters added. They can be found by redefining the \NEW command in
the preamble of the LaTeX fil
RQM description of the charge form factor of the pion and its asymptotic behavior
The pion charge and scalar form factors, and , are first
calculated in different forms of relativistic quantum mechanics. This is done
using the solution of a mass operator that contains both confinement and
one-gluon-exchange interactions. Results of calculations, based on a one-body
current, are compared to experiment for the first one. As it could be expected,
those point-form, and instant and front-form ones in a parallel momentum
configuration fail to reproduce experiment. The other results corresponding to
a perpendicular momentum configuration (instant form in the Breit frame and
front form with ) do much better. The comparison of charge and scalar
form factors shows that the spin-1/2 nature of the constituents plays an
important role. Taking into account that only the last set of results
represents a reasonable basis for improving the description of the charge form
factor, this one is then discussed with regard to the asymptotic QCD-power-law
behavior . The contribution of two-body currents in achieving the right
power law is considered while the scalar form factor, , is shown to
have the right power-law behavior in any case. The low- behavior of the
charge form factor and the pion-decay constant are also discussed.}Comment: 30 pages, 10 figure
Self-optimization, community stability, and fluctuations in two individual-based models of biological coevolution
We compare and contrast the long-time dynamical properties of two
individual-based models of biological coevolution. Selection occurs via
multispecies, stochastic population dynamics with reproduction probabilities
that depend nonlinearly on the population densities of all species resident in
the community. New species are introduced through mutation. Both models are
amenable to exact linear stability analysis, and we compare the analytic
results with large-scale kinetic Monte Carlo simulations, obtaining the
population size as a function of an average interspecies interaction strength.
Over time, the models self-optimize through mutation and selection to
approximately maximize a community fitness function, subject only to
constraints internal to the particular model. If the interspecies interactions
are randomly distributed on an interval including positive values, the system
evolves toward self-sustaining, mutualistic communities. In contrast, for the
predator-prey case the matrix of interactions is antisymmetric, and a nonzero
population size must be sustained by an external resource. Time series of the
diversity and population size for both models show approximate 1/f noise and
power-law distributions for the lifetimes of communities and species. For the
mutualistic model, these two lifetime distributions have the same exponent,
while their exponents are different for the predator-prey model. The difference
is probably due to greater resilience toward mass extinctions in the food-web
like communities produced by the predator-prey model.Comment: 26 pages, 12 figures. Discussion of early-time dynamics added. J.
Math. Biol., in pres
Mean first-passage time for random walks on undirected networks
In this paper, by using two different techniques we derive an explicit
formula for the mean first-passage time (MFPT) between any pair of nodes on a
general undirected network, which is expressed in terms of eigenvalues and
eigenvectors of an associated matrix similar to the transition matrix. We then
apply the formula to derive a lower bound for the MFPT to arrive at a given
node with the starting point chosen from the stationary distribution over the
set of nodes. We show that for a correlated scale-free network of size with
a degree distribution , the scaling of the lower bound is
. Also, we provide a simple derivation for an eigentime
identity. Our work leads to a comprehensive understanding of recent results
about random walks on complex networks, especially on scale-free networks.Comment: 7 pages, no figures; definitive version published in European
Physical Journal
Origins of the Ambient Solar Wind: Implications for Space Weather
The Sun's outer atmosphere is heated to temperatures of millions of degrees,
and solar plasma flows out into interplanetary space at supersonic speeds. This
paper reviews our current understanding of these interrelated problems: coronal
heating and the acceleration of the ambient solar wind. We also discuss where
the community stands in its ability to forecast how variations in the solar
wind (i.e., fast and slow wind streams) impact the Earth. Although the last few
decades have seen significant progress in observations and modeling, we still
do not have a complete understanding of the relevant physical processes, nor do
we have a quantitatively precise census of which coronal structures contribute
to specific types of solar wind. Fast streams are known to be connected to the
central regions of large coronal holes. Slow streams, however, appear to come
from a wide range of sources, including streamers, pseudostreamers, coronal
loops, active regions, and coronal hole boundaries. Complicating our
understanding even more is the fact that processes such as turbulence,
stream-stream interactions, and Coulomb collisions can make it difficult to
unambiguously map a parcel measured at 1 AU back down to its coronal source. We
also review recent progress -- in theoretical modeling, observational data
analysis, and forecasting techniques that sit at the interface between data and
theory -- that gives us hope that the above problems are indeed solvable.Comment: Accepted for publication in Space Science Reviews. Special issue
connected with a 2016 ISSI workshop on "The Scientific Foundations of Space
Weather." 44 pages, 9 figure
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