1,540 research outputs found
Current moments of 1D ASEP by duality
We consider the exponential moments of integrated currents of 1D asymmetric
simple exclusion process using the duality found by Sch\"utz. For the ASEP on
the infinite lattice we show that the th moment is reduced to the problem of
the ASEP with less than or equal to particles.Comment: 13 pages, no figur
The determinant representation for quantum correlation functions of the sinh-Gordon model
We consider the quantum sinh-Gordon model in this paper. Using known formulae
for form factors we sum up all their contributions and obtain a closed
expression for a correlation function. This expression is a determinant of an
integral operator. Similar determinant representations were proven to be useful
not only in the theory of correlation functions, but also in the matrix models.Comment: 21 pages, Latex, no figure
The Determinant Representation for a Correlation Function in Scaling Lee-Yang Model
We consider the scaling Lee-Yang model. It corresponds to the unique
perturbation of the minimal CFT model M(2,5). This is not a unitary model. We
used known expression for form factors in order to obtain a closed expression
for a correlation function of a trace of energy-momentum tensor. This
expression is a determinant of an integral operator. Similar determinant
representation were proven to be useful not only for quantum correlation
functions but also in matrix models.Comment: 14 pages, LaTeX, no figure
The Isotropic Radio Background and Annihilating Dark Matter
Observations by ARCADE-2 and other telescopes sensitive to low frequency
radiation have revealed the presence of an isotropic radio background with a
hard spectral index. The intensity of this observed background is found to
exceed the flux predicted from astrophysical sources by a factor of
approximately 5-6. In this article, we consider the possibility that
annihilating dark matter particles provide the primary contribution to the
observed isotropic radio background through the emission of synchrotron
radiation from electron and positron annihilation products. For reasonable
estimates of the magnetic fields present in clusters and galaxies, we find that
dark matter could potentially account for the observed radio excess, but only
if it annihilates mostly to electrons and/or muons, and only if it possesses a
mass in the range of approximately 5-50 GeV. For such models, the annihilation
cross section required to normalize the synchrotron signal to the observed
excess is sigma v ~ (0.4-30) x 10^-26 cm^3/s, similar to the value predicted
for a simple thermal relic (sigma v ~ 3 x 10^-26 cm^3/s). We find that in any
scenario in which dark matter annihilations are responsible for the observed
excess radio emission, a significant fraction of the isotropic gamma ray
background observed by Fermi must result from dark matter as well.Comment: 11 pages, 6 figure
Eigenvalue correlations in non-Hermitean symplectic random matrices
Correlation function of complex eigenvalues of N by N random matrices drawn
from non-Hermitean random matrix ensemble of symplectic symmetry is given in
terms of a quaternion determinant. Spectral properties of Gaussian ensembles
are studied in detail in the regimes of weak and strong non-Hermiticity.Comment: 14 page
The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results
The mathematically correct computation of the spin glasses free energy in the
infinite range limit crowns 25 years of mathematic efforts in solving this
model. The exact solution of the model was found many years ago by using a
heuristic approach; the results coming from the heuristic approach were crucial
in deriving the mathematical results. The mathematical tools used in the
rigorous approach are quite different from those of the heuristic approach. In
this note we will review the heuristic approach to spin glasses in the light of
the rigorous results; we will also discuss some conjectures that may be useful
to derive the solution of the model in an alternative way.Comment: 12 pages, 1 figure; lecture at the Flato Colloquia Day, Thursday 27
November, 200
On the Riemann-Hilbert approach to the asymptotic analysis of the correlation functions of the Quantum Nonlinear Schrodinger equation. Non-free fermionic case
We consider the local field dynamical temperature correlation function of the
Quantum Nonlinear Schrodinger equation with the finite coupling constant. This
correlation function admits a Fredholm determinant representation. The related
operator-valued Riemann--Hilbert problem is used for analysing the leading term
of the large time and long distance asymptotics of the correlation function.Comment: 70 pages, Latex, 4 figure
Equation of state and high-pressure phase transitions in Mg2GeO4 olivine
Germanates are often used as structural analogs of planetary silicates. We
have explored the high-pressure phase relations in Mg2GeO4 using diamond anvil
cell experiments combined with synchrotron x-ray diffraction and computations
based on density functional theory. Upon room temperature compression,
forsterite remains stable up to 30 GPa. At higher pressures, a phase transition
to a CmC21 structure was observed, which remained stable to the peak pressure
of 105 GPa. Using a 3rd order Birch Murnaghan fit to the experimental data, we
obtained V0 = 305.1 (3) A3, K0 = 124.6 (14) GPa and K' = 3.86 (fixed) for
forsterite and V0 = 263.5 (15) A3, K0 = 175 (7) GPa and K' = 4.2 (fixed) for
the CmC21 phase. In three separate runs, the forsterite sample was compressed
to 26 GPa, 54 GPa and 105 GPa respectively and then laser-heated to ~2500 K. On
laser heating, a mixture of perovskite MgGeO3 + MgO was found to be stable at
the lower pressure conditions, whereas post-perovskite + MgO was observed at
the highest pressure
Parametric level statistics in random matrix theory: Exact solution
An exact solution to the problem of parametric level statistics in
non-Gaussian ensembles of N by N Hermitian random matrices with either soft or
strong level confinement is formulated within the framework of the orthogonal
polynomial technique. Being applied to random matrices with strong level
confinement, the solution obtained leads to emergence of a new connection
relation that makes a link between the parametric level statistics and the
scalar two-point kernel in the thermodynamic limit.Comment: 4 pages (revtex
Guest charges in an electrolyte: renormalized charge, long- and short-distance behavior of the electric potential and density profile
We complement a recent exact study by L. Samaj on the properties of a guest
charge immersed in a two-dimensional electrolyte with charges . In
particular, we are interested in the behavior of the density profiles and
electric potential created by the charge and the electrolyte, and in the
determination of the renormalized charge which is obtained from the
long-distance asymptotics of the electric potential. In Samaj's previous work,
exact results for arbitrary coulombic coupling were obtained for a
system where all the charges are points, provided and .
Here, we first focus on the mean field situation which we believe describes
correctly the limit but large. In this limit we can
study the case when the guest charge is a hard disk and its charge is above the
collapse value . We compare our results for the renormalized charge
with the exact predictions and we test on a solid ground some conjectures of
the previous study. Our study shows that the exact formulas obtained by Samaj
for the renormalized charge are not valid for , contrary to a
hypothesis put forward by Samaj. We also determine the short-distance
asymptotics of the density profiles of the coions and counterions near the
guest charge, for arbitrary coulombic coupling. We show that the coion density
profile exhibit a change of behavior if the guest charge becomes large enough
(). This is interpreted as a first step of the counterion
condensation (for large coulombic coupling), the second step taking place at
the usual Manning--Oosawa threshold
- …