8,023 research outputs found
The quantum Gaussian well
Different features of a potential in the form of a Gaussian well have been
discussed extensively. Although the details of the calculation are involved,
the general approach uses a variational method and WKB approximation,
techniques which should be familiar to advanced undergraduates. A numerical
solution of the Schr\"odinger equation through diagonalization has been
developed in a self-contained way, and physical applications of the potential
are mentioned.Comment: 11 pages, 4 figures, To be published in American Journal of Physic
Stability of Circular Orbits in General Relativity: A Phase Space Analysis
Phase space method provides a novel way for deducing qualitative features of
nonlinear differential equations without actually solving them. The method is
applied here for analyzing stability of circular orbits of test particles in
various physically interesting environments. The approach is shown to work in a
revealing way in Schwarzschild spacetime. All relevant conclusions about
circular orbits in the Schwarzschild-de Sitter spacetime are shown to be
remarkably encoded in a single parameter. The analysis in the rotating Kerr
black hole readily exposes information as to how stability depends on the ratio
of source rotation to particle angular momentum. As a wider application, it is
exemplified how the analysis reveals useful information when applied to motion
in a refractive medium, for instance, that of optical black holes.Comment: 20 pages. Accepted for publication in Int. J. theor. Phy
Quantum Hall Effect and Semimetallic Behavior of Dual-Gated ABA-Stacked Trilayer Graphene
The electronic structure of multilayer graphenes depends strongly on the
number of layers as well as the stacking order. Here we explore the electronic
transport of purely ABA-stacked trilayer graphenes in a dual-gated field-effect
device configuration. We find that both the zero-magnetic-field transport and
the quantum Hall effect at high magnetic fields are distinctly different from
the monolayer and bilayer graphenes, and that they show electron-hole
asymmetries that are strongly suggestive of a semimetallic band overlap. When
the ABA trilayers are subjected to an electric field perpendicular to the
sheet, Landau level splittings due to a lifting of the valley degeneracy are
clearly observed.Comment: 5 figure
Matter waves in a gravitational field: An index of refraction for massive particles in general relativity
We consider the propagation of massive-particle de Broglie waves in a static,
isotropic metric in general relativity. We demonstrate the existence of an
index of refraction that governs the waves and that has all the properties of a
classical index of refraction. We confirm our interpretation with a WKB
solution of the general-relativistic Klein-Gordon equation. Finally, we make
some observations on the significance of the optical action.Comment: 20 pages, latex, ps and pdf. To appear in Am.J.Phys September, 200
The Dynamics of Radio Galaxies and Double-Double Radio Galaxies
Relativistic and magnetised plasma ejected by radio loud AGNs through jets
form the diffuse lobes of radio galaxies. The radiating particles
(electron/electron-positron) in lobes emit in radio via the synchrotron process
and X-ray via inverse-Compton scattering of cosmic microwave background
photons. The thermal environment around radio galaxies emits X-rays via the
thermal bremsstrahlung process. By combining information from these processes
we can measure physical conditions in and around the radio lobes and thus study
the dynamics of radio galaxies, including double-double radio galaxies.Comment: 11 pages, 4 figures, Diffuse Radio Plasma Conference proceedings
(held in Raman Research Institute, Bangalore, India
Coupling Unifications in Gauge-Higgs Unified Orbifold Models
Supersymmetric gauge theories, in higher dimensions compactified in an
orbifold, give a natural framework to unify the gauge bosons, Higgs fields and
even the matter fields in a single multiplet of the unifying gauge symmetry.
The extra dimensions and the supersymmetry are the two key ingredients for such
an unification. In this work, we investigate various scenarios for the
unification of the three gauge couplings, and the Yukawa couplings in the
Minimal Supersymmetric Standard Model (MSSM), as well as the trilinear Higgs
couplings \lambda and \kappa of the Non-Minimal Supersymmetric Standard Model
(NMSSM). We present an SU(8) model in six dimensions with N=2 supersymmetry,
compactified in a T^2/Z_6 orbifold which unifies the three gauge couplings with
\lambda and \kappa of NMSSM. Then, we present an SU(9) model in 6D, which, in
addition, includes partial unification of Yukawa couplings, either for the
up-type (top quark and Dirac tau-neutrino) or down-type (bottom quark and tau
lepton). We also study the phenomenological implications of these various
unification scenarios using the appropriate renormalization group equations,
and show that such unification works very well with the measured low energy
values of the couplings. The predicted upper bounds for the lightest neutral
Higgs boson mass in our model is higher than those in MSSM, but lower that
those in the general NMSSM (where the couplings \lambda and \kappa are
arbitrary). Some of the predictions of our models can be tested in the upcoming
Large Hadron Collider.Comment: 29 pages, 4 figure
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