113,903 research outputs found
Hamilton-Jacobi Approach for Power-Law Potentials
The classical and relativistic Hamilton-Jacobi approach is applied to the
one-dimensional homogeneous potential, , where and
are continuously varying parameters. In the non-relativistic case, the
exact analytical solution is determined in terms of , and the total
energy . It is also shown that the non-linear equation of motion can be
linearized by constructing a hypergeometric differential equation for the
inverse problem . A variable transformation reducing the general problem
to that one of a particle subjected to a linear force is also established. For
any value of , it leads to a simple harmonic oscillator if , an
"anti-oscillator" if , or a free particle if E=0. However, such a
reduction is not possible in the relativistic case. For a bounded relativistic
motion, the first order correction to the period is determined for any value of
. For , it is found that the correction is just twice that one
deduced for the simple harmonic oscillator (), and does not depend on the
specific value of .Comment: 12 pages, Late
Energy Conditions and Segre Classification of Phantom Fields
Recent discoveries in the field of observational cosmology have provided
increasing evidence that the Universe is undergoing a late time acceleration,
which has also stimulated speculations on the nature of the dark component
responsible for such a phenomenon. Among several candidates discussed in the
current literature, phantom fields, an exotic scalar field with a negative
kinetic term and that violates most of the classical energy conditions, appear
as a real possibility according to recent observational analysis. In this paper
we examine the invariant characterization for the energy-momentum tensor of
phantom fields through the Segre algebraic classification in the framework of
general relativity. We also discuss some constraints which are imposed on the
values of from the classical energy conditions.Comment: 4 pages, 1 figure, to appear in Phys. Lett.
Anomalous exchange interaction between intrinsic spins in conducting graphene systems
We address the nature and possible observable consequences of singular
one-electron states that appear when strong defects are introduced in the
metallic family of graphene, namely, metallic carbon nanotubes and nanotori. In
its simplest form, after creating two defects on the same sublattice, a state
may emerge at the Fermi energy presenting very unusual properties: It is
unique, normalizable, and features a wave function equally distributed around
both defects. As a result, the exchange coupling between the magnetic moments
generated by the two defects is anomalous. The intrinsic spins couple
ferromagnetically, as expected, but do not present an antiferromagnetic excited
state at any distance. We propose the use of metallic carbon nanotubes as a
novel electronic device based on this anomalous coupling between spins which
can be useful for the robust transmission of magnetic information at large
distances.Comment: 5 pages 5 fugure
Social Entrepreneurship That Truly Benefits the Poor: An Integrative Justice Approach
The phenomenal growth of social entrepreneurship over thelast decade has ably demonstrated how technology, innovation, and anentrepreneurial spirit can afford better solutions to the vexing social andenvironmental problems of our time than can traditional aid and charitybasedefforts. In most cases, but not always, the poor and disadvantagedhave benefited from the growth of social entrepreneurship. In order toensure that social entrepreneurship does indeed benefit the poor, it isimperative that there be normative guidelines for fair and just engagementwith impoverished populations. A model that has been presented in themarketing and public policy literature is the integrative justice model (IJM)for impoverished populations. While the IJM was developed primarily in thecontext of multinational corporations (MNCs) operating in emerging markets,its applicability extends beyond MNCs. This article attempts to apply theIJM principles in the context of social entrepreneurship in order to providesocial entrepreneurial organizations (SEOs) with a normative frameworkaimed at ensuring that the poor truly benefit from their activities. Basedon this framework, the article suggests certain areas to which SEOs oughtto be particularly attentive in their practice. The article also makes somesuggestions for further research
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