2,665 research outputs found
Feller Processes: The Next Generation in Modeling. Brownian Motion, L\'evy Processes and Beyond
We present a simple construction method for Feller processes and a framework
for the generation of sample paths of Feller processes. The construction is
based on state space dependent mixing of L\'evy processes.
Brownian Motion is one of the most frequently used continuous time Markov
processes in applications. In recent years also L\'evy processes, of which
Brownian Motion is a special case, have become increasingly popular.
L\'evy processes are spatially homogeneous, but empirical data often suggest
the use of spatially inhomogeneous processes. Thus it seems necessary to go to
the next level of generalization: Feller processes. These include L\'evy
processes and in particular Brownian motion as special cases but allow spatial
inhomogeneities.
Many properties of Feller processes are known, but proving the very existence
is, in general, very technical. Moreover, an applicable framework for the
generation of sample paths of a Feller process was missing. We explain, with
practitioners in mind, how to overcome both of these obstacles. In particular
our simulation technique allows to apply Monte Carlo methods to Feller
processes.Comment: 22 pages, including 4 figures and 8 pages of source code for the
generation of sample paths of Feller processe
Boundary correlation function of fixed-to-free bcc operators in square-lattice Ising model
We calculate the boundary correlation function of fixed-to-free boundary
condition changing operators in the square-lattice Ising model. The correlation
function is expressed in four different ways using block Toeplitz
determinants. We show that these can be transformed into a scalar Toeplitz
determinant when the size of the matrix is even. To know the asymptotic
behavior of the correlation function at large distance we calculate the
asymptotic behavior of this scalar Toeplitz determinant using the Szeg\"o's
theorem and the Fisher-Hartwig theorem. At the critical temperature we confirm
the power-law behavior of the correlation function predicted by conformal field
theory
Metastable precursors during the oxidation of the Ru(0001) surface
Using density-functional theory, we predict that the oxidation of the
Ru(0001) surface proceeds via the accumulation of sub-surface oxygen in
two-dimensional islands between the first and second substrate layer. This
leads locally to a decoupling of an O-Ru-O trilayer from the underlying metal.
Continued oxidation results in the formation and stacking of more of these
trilayers, which unfold into the RuO_2(110) rutile structure once a critical
film thickness is exceeded. Along this oxidation pathway, we identify various
metastable configurations. These are found to be rather close in energy,
indicating a likely lively dynamics between them at elevated temperatures,
which will affect the surface chemical and mechanical properties of the
material.Comment: 11 pages including 9 figures. Submitted to Phys. Rev. B. Related
publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm
Opacity in compact extragalactic radio sources and its effect on radio-optical reference frame alignment
Accurate alignment of the radio and optical celestial reference frames
requires detailed understanding of physical factors that may cause offsets
between the positions of the same object measured in different spectral bands.
Opacity in compact extragalactic jets (due to synchrotron self-absorption and
external free-free absorption) is one of the key physical phenomena producing
such an offset, and this effect is well-known in radio astronomy ("core
shift"). We have measured the core shifts in a sample of 29 bright compact
extragalactic radio sources observed using very long baseline interferometry
(VLBI) at 2.3 and 8.6 GHz. We report the results of these measurements and
estimate that the average shift between radio and optical positions of distant
quasars would be of the order of 0.1-0.2 mas. This shift exceeds positional
accuracy of GAIA and SIM. We suggest two possible approaches to carefully
investigate and correct for this effect in order to align accurately the radio
and optical positions. Both approaches involve determining a Primary Reference
Sample of objects to be used for tying the radio and optical reference frames
together.Comment: 4 pages, 1 figure; to appear in IAU Symposium 248 Proceedings, "A
Giant Step: from Milli- to Micro-arcsecond Astrometry", eds. W.-J. Jin, I.
Platais, M. Perryma
Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle
We prove that for any matrix, , and with ,
we have that \|(z-A)^{-1}\|\leq\cot (\frac{\pi}{4n}) \dist (z,
\spec(A))^{-1}. We apply this result to the study of random orthogonal
polynomials on the unit circle.Comment: 27 page
Out of equilibrium correlations in the XY chain
We study the transversal XY spin-spin correlations in the non-equilibrium
steady state constructed in \cite{AP03} and prove their spatial exponential
decay close to equilibrium
Interpretation of increased energetic particle flux measurements by SEPT aboard the STEREO spacecraft and contamination
Context. Interplanetary (IP) shocks are known to be accelerators of energetic
charged particles observed in-situ in the heliosphere. However, the
acceleration of near-relativistic electrons by shocks in the interplanetary
medium is often questioned. On 9 August 2011 a Corotating Interaction Region
(CIR) passed STEREO B (STB) that resulted in a flux increase in the electron
and ion channels of the Solar Electron and Proton Telescope (SEPT). Because
electron measurements in the few keV to several 100 keV range rely on the
so-called magnet foil technique, which is utilized by SEPT, ions can contribute
to the electron channels. Aims. We aim to investigate whether the flux increase
in the electron channels of SEPT during the CIR event on 9 August 2011 is
caused by ion contamination only. Methods. We compute the SEPT response
functions for protons and helium utilizing an updated GEANT4 model of SEPT. The
CIR energetic particle ion spectra for protons and helium are assumed to follow
a Band function in energy per nucleon with a constant helium to proton ratio.
Results. Our analysis leads to a helium to proton ratio of 16.9% and a proton
flux following a Band function with the parameters /
(cm2 s sr MeV/nuc.), keV/nuc. and spectral indices of and which are in good agreement with measurements by
the Suprathermal Ion Telescope (SIT) aboard STB. Conclusions. Since our results
explain the SEPT measurements, we conclude that no significant amount of
electrons were accelerated between keV and keV by the CIR
Composition, structure and stability of RuO_2(110) as a function of oxygen pressure
Using density-functional theory (DFT) we calculate the Gibbs free energy to
determine the lowest-energy structure of a RuO_2(110) surface in thermodynamic
equilibrium with an oxygen-rich environment. The traditionally assumed
stoichiometric termination is only found to be favorable at low oxygen chemical
potentials, i.e. low pressures and/or high temperatures. At realistic O
pressure, the surface is predicted to contain additional terminal O atoms.
Although this O excess defines a so-called polar surface, we show that the
prevalent ionic model, that dismisses such terminations on electrostatic
grounds, is of little validity for RuO_2(110). Together with analogous results
obtained previously at the (0001) surface of corundum-structured oxides, these
findings on (110) rutile indicate that the stability of non-stoichiometric
terminations is a more general phenomenon on transition metal oxide surfaces.Comment: 12 pages including 5 figures. Submitted to Phys. Rev. B. Related
publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm
One-dimensional pair cascade emission in gamma-ray binaries
In gamma-ray binaries such as LS 5039 a large number of electron-positron
pairs are created by the annihilation of primary very high energy (VHE)
gamma-rays with photons from the massive star. The radiation from these
particles contributes to the total high energy gamma-ray flux and can initiate
a cascade, decreasing the effective gamma-ray opacity in the system. The aim of
this paper is to model the cascade emission and investigate if it can account
for the VHE gamma-ray flux detected by HESS from LS 5039 at superior
conjunction, where the primary gamma-rays are expected to be fully absorbed. A
one-dimensional cascade develops along the line-of-sight if the deflections of
pairs induced by the surrounding magnetic field can be neglected. A
semi-analytical approach can then be adopted, including the effects of the
anisotropic seed radiation field from the companion star. Cascade equations are
numerically solved, yielding the density of pairs and photons. In LS 5039, the
cascade contribution to the total flux is large and anti-correlated with the
orbital modulation of the primary VHE gamma-rays. The cascade emission
dominates close to superior conjunction but is too strong to be compatible with
HESS measurements. Positron annihilation does not produce detectable 511 keV
emission. This study provides an upper limit to cascade emission in gamma-ray
binaries at orbital phases where absorption is strong. The pairs are likely to
be deflected or isotropized by the ambient magnetic field, which will reduce
the resulting emission seen by the observer. Cascade emission remains a viable
explanation for the detected gamma-rays at superior conjunction in LS 5039.Comment: 8 pages, 7 figures, 1 table, accepted for publication in Astronomy
and Astrophysic
Area laws for the entanglement entropy - a review
Physical interactions in quantum many-body systems are typically local:
Individual constituents interact mainly with their few nearest neighbors. This
locality of interactions is inherited by a decay of correlation functions, but
also reflected by scaling laws of a quite profound quantity: The entanglement
entropy of ground states. This entropy of the reduced state of a subregion
often merely grows like the boundary area of the subregion, and not like its
volume, in sharp contrast with an expected extensive behavior. Such "area laws"
for the entanglement entropy and related quantities have received considerable
attention in recent years. They emerge in several seemingly unrelated fields,
in the context of black hole physics, quantum information science, and quantum
many-body physics where they have important implications on the numerical
simulation of lattice models. In this Colloquium we review the current status
of area laws in these fields. Center stage is taken by rigorous results on
lattice models in one and higher spatial dimensions. The differences and
similarities between bosonic and fermionic models are stressed, area laws are
related to the velocity of information propagation, and disordered systems,
non-equilibrium situations, classical correlation concepts, and topological
entanglement entropies are discussed. A significant proportion of the article
is devoted to the quantitative connection between the entanglement content of
states and the possibility of their efficient numerical simulation. We discuss
matrix-product states, higher-dimensional analogues, and states from
entanglement renormalization and conclude by highlighting the implications of
area laws on quantifying the effective degrees of freedom that need to be
considered in simulations.Comment: 28 pages, 2 figures, final versio
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