9,739 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
The Impact of Leadership on Innovation Management
The study sought to evaluate the influence of leadership on innovation management taking into consideration the predominant leadership styles, the leadership effectiveness, and the relationship between leadership effectiveness and innovation management of a group of executives of several organizations in a BRIC country (Brazil). To identify the predominant leadership styles, as well as the leadership effectiveness of the 400 involved executives, it has been used an instrument available in the market. To compute the innovation management performance, an existing model, the Value InnovationModel, has been applied leading to the value innovation index for each one of the 48 involved organizations. To investigate the relationship between leadership effectiveness, taken the average value per organization, and the value innovation index, it has been used the linear regression statistics computing the linear correlation coefficient between the before mentioned variables. The study has uncovered lack of flexibility regarding the leadership styles, presenting styles of selling and sharing ideas as dominants. The study also showed that the leadership effectiveness of the involved executives was at a moderate level. Finally, the research pointed out a high positive relationship between leadership effectiveness and innovation management success, measured by the value innovation index
Potential Scattering in Dirac Field Theory
We develop the potential scattering of a spinor within the context of
perturbation field theory. As an application, we reproduce, up to second order
in the potential, the diffusion results for a potential barrier of quantum
mechanics. An immediate consequence is a simple generalization to arbitrary
potential forms, a feature not possible in quantum mechanics.Comment: 7 page
Quaternionic potentials in non-relativistic quantum mechanics
We discuss the Schrodinger equation in presence of quaternionic potentials.
The study is performed analytically as long as it proves possible, when not, we
resort to numerical calculations. The results obtained could be useful to
investigate an underlying quaternionic quantum dynamics in particle physics.
Experimental tests and proposals to observe quaternionic quantum effects by
neutron interferometry are briefly reviewed.Comment: 21 pages, 16 figures (ps), AMS-Te
Thermostatistics in the neighborhood of the -mode solution for the Fermi-Pasta-Ulam system: from weak to strong chaos
We consider a -mode solution of the Fermi-Pasta-Ulam system. By
perturbing it, we study the system as a function of the energy density from a
regime where the solution is stable to a regime, where is unstable, first
weakly and then strongly chaotic. We introduce, as indicator of stochasticity,
the ratio (when is defined) between the second and the first moment of a
given probability distribution. We will show numerically that the transition
between weak and strong chaos can be interpreted as the symmetry breaking of a
set of suitable dynamical variables. Moreover, we show that in the region of
weak chaos there is numerical evidence that the thermostatistic is governed by
the Tsallis distribution.Comment: 15 pages, 5 figure
Quaternionic Electroweak Theory and CKM Matrix
We find in our quaternionic version of the electroweak theory an apparently
hopeless problem: In going from complex to quaternions, the calculation of the
real-valued parameters of the CKM matrix drastically changes. We aim to explain
this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published
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
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
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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