33,960 research outputs found
Static potential in scalar QED with non-minimal coupling
Here we compute the static potential in scalar at leading order in
. We show that the addition of a non-minimal coupling of Pauli-type
(\eps j^{\mu}\partial^{\nu}A^{\alpha}), although it breaks parity, it does
not change the analytic structure of the photon propagator and consequently the
static potential remains logarithmic (confining) at large distances. The
non-minimal coupling modifies the potential, however, at small charge
separations giving rise to a repulsive force of short range between opposite
sign charges, which is relevant for the existence of bound states. This effect
is in agreement with a previous calculation based on Mller
scattering, but differently from such calculation we show here that the
repulsion appears independently of the presence of a tree level Chern-Simons
term which rather affects the large distance behavior of the potential turning
it into constant.Comment: 13 pages, 3 figure
Discrete optimization problems with random cost elements
In a general class of discrete optimization problems, some of the elements mayhave random costs associated with them. In such a situation, the notion of optimalityneeds to be suitably modified. In this work we define an optimal solutionto be a feasible solution with the minimum risk. We focus on the minsumobjective function, for which we prove that knowledge of the mean values ofthese random costs is enough to reduce the problem into one with fixed costs.We discuss the implications of using sample means when the true means ofthe costs of the random elements are not known, and explore the relation betweenour results and those from post-optimality analysis. We also show thatdiscrete optimization problems with min-max objective functions depend moreintricately on the distributions of the random costs.
Planar Two-particle Coulomb Interaction: Classical and Quantum Aspects
The classical and quantum aspects of planar Coulomb interactions have been
studied in detail. In the classical scenario, Action Angle Variables are
introduced to handle relativistic corrections, in the scheme of
time-independent perturbation theory. Complications arising due to the
logarithmic nature of the potential are pointed out. In the quantum case,
harmonic oscillator approximations are considered and effects of the
perturbations on the excited (oscillator) states have been analysed. In both
the above cases, the known 3+1-dimensional analysis is carried through side by
side, for a comparison with the 2+1-dimensional (planar) results.Comment: LaTex, Figures on request, e-mail:<[email protected]
On solving discrete optimization problems with one random element under general regret functions
In this paper we consider the class of stochastic discrete optimization problems in which the feasibility of a solution does not depend on the particular values the random elements in the problem take. Given a regret function, we introduce the concept of the risk associated with a solution, and define an optimal solution as one having the least possible risk. We show that for discrete optimization problems with one random element and with min-sum objective functions a least risk solution for the stochastic problem can be obtained by solving a non-stochastic counterpart where the latter is constructed by replacing the random element of the former with a suitable parameter. We show that the above surrogate is the mean if the stochastic problem has only one symmetrically distributed random element. We obtain bounds for this parameter for certain classes of asymmetric distributions and study the limiting behavior of this parameter in details under two asymptotic frameworks. \u
On solving discrete optimization problems with multiple random elements under general regret functions
In this paper we attempt to find least risk solutions for stochastic discrete optimization problems (SDOP) with multiple random elements, where the feasibility of a solution does not depend on the particular values the random elements in the problem take. While the optimal solution, for a linear regret function, can be obtained by solving an auxiliary (non-stochastic) discrete optimization problem (DOP), the situation is complex under general regret. We characterize a finite number of solutions which will include the optimal solution. We establish through various examples that the results from Ghosh, Mandal and Das (2005) can be extended only partially for SDOPs with additional characteristics. We present a result where in selected cases, a complex SDOP may be decomposed into simpler ones facilitating the job of finding an optimal solution to the complex problem. We also propose numerical local search algorithms for obtaining an optimal solution. \u
Infrared emission from interstellar dust cloud with two embedded sources: IRAS 19181+1349
Mid and far infrared maps of many Galactic star forming regions show multiple
peaks in close proximity, implying more than one embedded energy sources. With
the aim of understanding such interstellar clouds better, the present study
models the case of two embedded sources. A radiative transfer scheme has been
developed to deal with an uniform density dust cloud in a cylindrical geometry,
which includes isotropic scattering in addition to the emission and absorption
processes. This scheme has been applied to the Galactic star forming region
associated with IRAS 19181+1349, which shows observational evidence for two
embedded energy sources. Two independent modelling approaches have been
adopted, viz., to fit the observed spectral energy distribution (SED) best; or
to fit the various radial profiles best, as a function of wavelength. Both the
models imply remarkably similar physical parameters.Comment: 17 pages, 6 Figures, uses epsf.sty. To appear in Journal of
Astronophysics & Astronom
Response of strongly-interacting matter to magnetic field: some exact results
We derive some exact results concerning the response of strongly-interacting
matter to external magnetic fields. Our results come from consideration of
triangle anomalies in medium. First, we define an "axial magnetic
susceptibility," then we examine its beahvior in two flavor QCD via response
theory. In the chirally restored phase, this quantity is proportional to the
fermion chemical potential, while in the phase of broken chiral symmetry it can
be related, through triangle anomalies, to an in-medium amplitude for the
neutral pion to decay to two photons. We confirm the latter result by
calculation in a linear sigma model, where this amplitude is already known in
the literature.Comment: 13 pages, no figures, To be submitted to Physical Review D, fixed an
omitted referenc
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