376,918 research outputs found

### Generalization of correlated electron-ion dynamics from nonequilibrium Green's functions

We present a new formulation of the correlated electron-ion dynamics (CEID)
by using equations of motion for nonequilibrium Green's functions, which
generalizes CEID to a general nonequilibrium statistical ensemble that allows
for a variable total number of electrons. We make a rigorous connection between
CEID and diagrammatic perturbation theory, which furthermore allows the key
approximations in CEID to be quantified in diagrammatic terms, and, in
principle, improved. We compare analytically the limiting behavior of CEID and
the self-consistent Born approximation (SCBA) for a general dynamical
nonequilibrium state. This comparison shows that CEID and SCBA coincide in the
weak electron-phonon coupling limit, while they differ in the large ionic mass
limit where we can readily quantify their difference. In particular, we
illustrate the relation between CEID and SCBA by perturbation theory at the
fourth-order in the coupling strength.Comment: 21 pages, 2 figure

### Harnack Inequalities for Stochastic Equations Driven by L\'evy Noise

By using coupling argument and regularization approximations of the
underlying subordinator, dimension-free Harnack inequalities are established
for a class of stochastic equations driven by a L\'evy noise containing a
subordinate Brownian motion. The Harnack inequalities are new even for linear
equations driven by L\'evy noise, and the gradient estimate implied by our
log-Harnack inequality considerably generalizes some recent results on gradient
estimates and coupling properties derived for L\'evy processes or linear
equations driven by L\'evy noise. The main results are also extended to
semi-linear stochastic equations in Hilbert spaces.Comment: 15 page

### Diffuse PeV neutrinos from gamma-ray bursts

The IceCube collaboration recently reported the potential detection of two
cascade neutrino events in the energy range 1-10 PeV. We study the possibility
that these PeV neutrinos are produced by gamma-ray bursts (GRBs), paying
special attention to the contribution by untriggered GRBs that elude detection
due to their low photon flux. Based on the luminosity function, rate
distribution with redshift and spectral properties of GRBs, we generate, using
Monte-Carlo simulation, a GRB sample that reproduce the observed fluence
distribution of Fermi/GBM GRBs and an accompanying sample of untriggered GRBs
simultaneously. The neutrino flux of every individual GRBs is calculated in the
standard internal shock scenario, so that the accumulative flux of the whole
samples can be obtained. We find that the neutrino flux in PeV energies
produced by untriggered GRBs is about 2 times higher than that produced by the
triggered ones. Considering the existing IceCube limit on the neutrino flux of
triggered GRBs, we find that the total flux of triggered and untriggered GRBs
can reach at most a level of ~10^-9 GeV cm^-2 s^-1 sr^-1, which is insufficient
to account for the reported two PeV neutrinos. Possible contributions to
diffuse neutrinos by low-luminosity GRBs and the earliest population of GRBs
are also discussed.Comment: Accepted by ApJ, one more figure added to show the contribution to
the diffuse neutrino flux by untriggered GRBs with different luminosity,
results and conclusions unchange

### Gradient Estimates and Applications for SDEs in Hilbert Space with Multiplicative Noise and Dini Continuous Drift

Consider the stochastic evolution equation in a separable Hilbert space with
a nice multiplicative noise and a locally Dini continuous drift. We prove that
for any initial data the equation has a unique (possibly explosive) mild
solution. Under a reasonable condition ensuring the non-explosion of the
solution, the strong Feller property of the associated Markov semigroup is
proved. Gradient estimates and log-Harnack inequalities are derived for the
associated semigroup under certain global conditions, which are new even in
finite-dimensions.Comment: 36 page

### Log-Sobolev inequalities: Different roles of Ric and Hess

Let $P_t$ be the diffusion semigroup generated by $L:=\Delta +\nabla V$ on a
complete connected Riemannian manifold with $\operatorname {Ric}\ge-(\sigma
^2\rho_o^2+c)$ for some constants $\sigma, c>0$ and $\rho_o$ the Riemannian
distance to a fixed point. It is shown that $P_t$ is hypercontractive, or the
log-Sobolev inequality holds for the associated Dirichlet form, provided
$-\operatorname {Hess}_V\ge\delta$ holds outside of a compact set for some
constant $\delta >(1+\sqrt{2})\sigma \sqrt{d-1}.$ This indicates, at least in
finite dimensions, that $\operatorname {Ric}$ and $-\operatorname {Hess}_V$
play quite different roles for the log-Sobolev inequality to hold. The
supercontractivity and the ultracontractivity are also studied.Comment: Published in at http://dx.doi.org/10.1214/08-AOP444 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org

### Non-dipolar gauge links for transverse-momentum-dependent pion wave functions

I discuss the factorization-compatible definitions of
transverse-momentum-dependent (TMD) pion wave functions which are fundamental
theory inputs entering QCD factorization formulae for many hard exclusive
processes. I will first demonstrate that the soft subtraction factor introduced
to remove both rapidity and pinch singularities can be greatly reduced by
making the maximal use of the freedom to construct the Wilson-line paths when
defining the TMD wave functions. I will then turn to show that the newly
proposed TMD definition with non-dipolar Wilson lines is equivalent to the one
with dipolar gauge links and with a complicated soft function, to all orders of
the perturbative expansion in the strong coupling, as far as the infrared
behavior is concerned.Comment: 7 pages, 3 figure

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