14,674 research outputs found
Solving simple quaternionic differential equations
The renewed interest in investigating quaternionic quantum mechanics, in
particular tunneling effects, and the recent results on quaternionic
differential operators motivate the study of resolution methods for
quaternionic differential equations. In this paper, by using the real matrix
representation of left/right acting quaternionic operators, we prove existence
and uniqueness for quaternionic initial value problems, discuss the reduction
of order for quaternionic homogeneous differential equations and extend to the
non-commutative case the method of variation of parameters. We also show that
the standard Wronskian cannot uniquely be extended to the quaternionic case.
Nevertheless, the absolute value of the complex Wronskian admits a
non-commutative extension for quaternionic functions of one real variable.
Linear dependence and independence of solutions of homogeneous (right) H-linear
differential equations is then related to this new functional. Our discussion
is, for simplicity, presented for quaternionic second order differential
equations. This involves no loss of generality. Definitions and results can be
readily extended to the n-order case.Comment: 9 pages, AMS-Te
A Semiotic Analysis on the Perceived Meanings of Coca Cola “Anthem” Video Commercial
This study observes the perceived meanings produced by young adult (18 to 30 years old) and older (50 to 65 years old) respondents as respondents from different age group can produce different perceived meanings from each other. The writer's finding is that in perceiving, young adult respondents tend to emphasize on Coca Cola's emotional roles. On the other hand, the older respondents emphasize on Coca Cola's physical roles
Right eigenvalue equation in quaternionic quantum mechanics
We study the right eigenvalue equation for quaternionic and complex linear
matrix operators defined in n-dimensional quaternionic vector spaces. For
quaternionic linear operators the eigenvalue spectrum consists of n complex
values. For these operators we give a necessary and sufficient condition for
the diagonalization of their quaternionic matrix representations. Our
discussion is also extended to complex linear operators, whose spectrum is
characterized by 2n complex eigenvalues. We show that a consistent analysis of
the eigenvalue problem for complex linear operators requires the choice of a
complex geometry in defining inner products. Finally, we introduce some
examples of the left eigenvalue equations and highlight the main difficulties
in their solution.Comment: 24 pages, AMS-Te
Graphene tests of Klein phenomena
Graphene is characterized by chiral electronic excitations. As such it
provides a perfect testing ground for the production of Klein pairs
(electron/holes). If confirmed, the standard results for barrier phenomena must
be reconsidered with, as a byproduct, the accumulation within the barrier of
holes.Comment: 8 page
Quaternionic eigenvalue problem
We discuss the (right) eigenvalue equation for , and
linear quaternionic operators. The possibility to introduce an
isomorphism between these operators and real/complex matrices allows to
translate the quaternionic problem into an {\em equivalent} real or complex
counterpart. Interesting applications are found in solving differential
equations within quaternionic formulations of quantum mechanics.Comment: 13 pages, AMS-Te
Dense Gas in the Milky Way
We present a study of dense gas emission in the Milky Way in order to serve
as a basis for comparison with extragalactic results. This study combines new
observations of HCN, CS, and CO in individual GMCs and in the Milky Way plane
with published studies of emission from these molecules in the inner 500 pc of
the Milky Way. We find a strong trend in the fraction of emission from dense
gas tracers as a function of location in the Milky Way: in the bulge,
I_{HCN}/I_{CO} = 0.081 \pm 0.004, in the plane, I_{HCN}/I_{CO} = 0.026 \pm
0.008 on average, and over the full extent of nearby GMCs, I_{HCN}/I_{CO} =
0.014 \pm 0.020. Similar trends are seen in I_{CS}/I_{CO}. The low intensities
of the HCN and CS emission in the plane suggests that these lines are produced
by gas at moderate densities; they are thus not like the emission produced by
the dense, pc-scale star forming cores in nearby GMCs. The contrast between the
bulge and disk ratios in the Milky Way is likely to be caused by a combination
of higher kinetic temperatures as well as a higher dense gas fraction in the
bulge of the Milky Way.Comment: 34 pages LaTeX, AASTEX macros, includes 11 postscript figures. To
appear in ApJ 478, March 199
A New Phase Time Formula for Opaque Barrier Tunneling
After a brief review of the derivation of the standard phase time formula,
based on the use of the stationary phase method, we propose, in the opaque
limit, an alternative method to calculate the phase time. The new formula for
the phase time is in excellent agreement with the numerical simulations and
shows that for wave packets whose upper limit of the momentum distribution is
very close to the barrier height, the transit time is proportional to the
barrier width.Comment: 9 pages, 2 figure
Dirac Equation Studies in the Tunnelling Energy Zone
We investigate the tunnelling zone V0 < E < V0+m for a one-dimensional
potential within the Dirac equation. We find the appearance of superluminal
transit times akin to the Hartman effect.Comment: 12 pages, 4 figure
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