700 research outputs found
Exact gravitational lensing and rotation curve
Based on the geodesic equation in a static spherically symmetric metric we
discuss the rotation curve and gravitational lensing. The rotation curve
determines one function in the metric without assuming Einstein's equations.
Then lensing is considered in the weak field approximation of general
relativity. From the null geodesics we derive the lensing equation and
corrections to it.Comment: 12 pages, 1 figur
New solutions of Heun general equation
We show that in four particular cases the derivative of the solution of Heun
general equation can be expressed in terms of a solution to another Heun
equation. Starting from this property, we use the Gauss hypergeometric
functions to construct series solutions to Heun equation for the mentioned
cases. Each of the hypergeometric functions involved has correct singular
behavior at only one of the singular points of the equation; the sum, however,
has correct behavior
Complementarity in generic open quantum systems
We develop a unified, information theoretic interpretation of the
number-phase complementarity that is applicable both to finite-dimensional
(atomic) and infinite-dimensional (oscillator) systems, with number treated as
a discrete Hermitian observable and phase as a continuous positive operator
valued measure (POVM). The relevant uncertainty principle is obtained as a
lower bound on {\it entropy excess}, , the difference between the entropy of
one variable, typically the number, and the knowledge of its complementary
variable, typically the phase, where knowledge of a variable is defined as its
relative entropy with respect to the uniform distribution. In the case of
finite dimensional systems, a weighting of phase knowledge by a factor
() is necessary in order to make the bound tight, essentially on account
of the POVM nature of phase as defined here. Numerical and analytical evidence
suggests that tends to 1 as system dimension becomes infinite. We study
the effect of non-dissipative and dissipative noise on these complementary
variables for oscillator as well as atomic systems.Comment: 18 pages, 15 figures; accepted for publication in Modern Physics
Letters
Meta-stable Vacuum in Spontaneously Broken N=2 Supersymmetric Gauge Theory
We consider an N=2 supersymmetric SU(2) \times U(1) gauge theory with N_f=2
massless flavors and a Fayet-Iliopoulos (FI) term. In the presence of the FI
term, supersymmetry is spontaneously broken at tree level (on the Coulomb
branch), leaving a pseudo-flat direction in the classical potential. This
vacuum degeneracy is removed once quantum corrections are taken into account.
Due to the SU(2) gauge dynamics, the effective potential exhibits a local
minimum at the dyon point, where not only supersymmetry but also U(1)_R
symmetry is broken, while a supersymmetric vacuum would be realized toward
infinity with the runaway behavior of the potential. This local minimum is
found to be parametrically long-lived. Interestingly, from a phenomenological
point of view, in this meta-stable vacuum the massive hypermultiplets inherent
in the theory play the role of the messenger fields in the gauge mediation
scenario, when the Standard Model gauge group is embedded into their flavor
symmetry.Comment: 27 pages, 11 figures, journal reference added, minor modifications in
the tex
The Meson Production in Proton-Proton Collisions in Next-To-Leading Order and Infrared Renormalons
In this article, we investigate the next-to-leading order contribution of the
higher-twist Feynman diagrams to the large- inclusive pion production
cross section in proton-proton collisions and present the general formulae for
the higher-twist differential cross sections in the case of the running
coupling and frozen coupling approaches. We compared the resummed
next-to-leading order higher-twist cross sections with the ones obtained in the
framework of the frozen coupling approach and leading-twist cross section. The
structure of infrared renormalon singularities of the higher twist subprocess
cross section and it's resummed expression (the Borel sum) are found. It is
shown that the resummed result depends on the choice of the meson wave
functions used in the calculations. We discuss the phenomenological
consequences of possible higher-twist contributions to the meson production in
proton-proton collisions in next-to-leading order at RHIC.Comment: 33 pages, 15 figures, 4 table
Brownian Motion and Polymer Statistics on Certain Curved Manifolds
We have calculated the probability distribution function G(R,L|R',0) of the
end-to-end vector R-R' and the mean-square end-to-end distance (R-R')^2 of a
Gaussian polymer chain embedded on a sphere S^(D-1) in D dimensions and on a
cylinder, a cone and a curved torus in 3-D.
We showed that: surface curvature induces a geometrical localization area; at
short length the polymer is locally "flat" and (R-R')^2 = L l in all cases; at
large scales, (R-R')^2 is constant for the sphere, it is linear in L for the
cylinder and reaches different constant values for the torus. The cone vertex
induces (function of opening angle and R') contraction of the chain for all
lengths. Explicit crossover formulas are derived.Comment: 9 pages, 4 figures, RevTex, uses amssymb.sty and multicol.sty, to
appear in Phys. Rev
The Weibull-Geometric distribution
In this paper we introduce, for the first time, the Weibull-Geometric
distribution which generalizes the exponential-geometric distribution proposed
by Adamidis and Loukas (1998). The hazard function of the last distribution is
monotone decreasing but the hazard function of the new distribution can take
more general forms. Unlike the Weibull distribution, the proposed distribution
is useful for modeling unimodal failure rates. We derive the cumulative
distribution and hazard functions, the density of the order statistics and
calculate expressions for its moments and for the moments of the order
statistics. We give expressions for the R\'enyi and Shannon entropies. The
maximum likelihood estimation procedure is discussed and an algorithm EM
(Dempster et al., 1977; McLachlan and Krishnan, 1997) is provided for
estimating the parameters. We obtain the information matrix and discuss
inference. Applications to real data sets are given to show the flexibility and
potentiality of the proposed distribution
Mean-Field Treatment of the Many-Body Fokker-Planck Equation
We review some properties of the stationary states of the Fokker - Planck
equation for N interacting particles within a mean field approximation, which
yields a non-linear integrodifferential equation for the particle density.
Analytical results show that for attractive long range potentials the steady
state is always a precipitate containing one cluster of small size. For
arbitrary potential, linear stability analysis allows to state the conditions
under which the uniform equilibrium state is unstable against small
perturbations and, via the Einstein relation, to define a critical temperature
Tc separating two phases, uniform and precipitate. The corresponding phase
diagram turns out to be strongly dependent on the pair-potential. In addition,
numerical calculations reveal that the transition is hysteretic. We finally
discuss the dynamics of relaxation for the uniform state suddenly cooled below
Tc.Comment: 13 pages, 8 figure
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