8,032 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
Globalization and the definition of the relevant geographic market in antitrust practices.
This paper starts from the antitrust practices in the European Community and the US with respect to the delineation of the relevant geographic market in dealing with concentrations and shows that relugations and guidelines at this moment focus almost exclusively on demand substitution. However, the process of globalization involves essentially global supply conditions and competition. A methodology is presented for delineating the relevant geographic market, that better takes this globalization trend into account and brings both demand and supply substitution better in balance. The practical use of the methodology is illustrated for the Volvo-Scandia merger case that was blocked by the European Commission in 1999.Antitrust; Globalization; Demand; Substitution; Processes; Competition; Working;
Study to determine suitable high temperature, high altitude, total temperature sensors Final report
High temperature, high altitude total temperature sensor development - thermocouple devic
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
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
Weak measurement og the composite Goo-Haenchen shift in the critical region
By using a weak measurement technique, we investigated the interplay between
the angular and lateral Goos-Haenchen shift of a focused He-Ne laser beam for
incidence near the critical angle. We verified that this interplay dramatically
affects the composite Goos-Haenchen shift of the propagated beam. The
experimental results confirm theoretical predictions that recently appeared in
the literature.Comment: 10 pages, 3 figure
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 Spinors and Flavor Oscillations
In the standard treatment of particle oscillations the mass eigenstates are
implicitly assumed to be scalars and, consequently, the spinorial form of
neutrino wave functions is not included in the calculations. To analyze this
additional effect, we discuss the oscillation probability formula obtained by
using the Dirac equation as evolution equation for the neutrino mass
eigenstates. The initial localization of the spinor state also implies an
interference between positive and negative energy components of mass eigenstate
wave packets which modifies the standard oscillation probability.Comment: 14 pages, 1 figure, AMS-Te
An Analytic Approach to the Wave Packet Formalism in Oscillation Phenomena
We introduce an approximation scheme to perform an analytic study of the
oscillation phenomena in a pedagogical and comprehensive way. By using Gaussian
wave packets, we show that the oscillation is bounded by a time-dependent
vanishing function which characterizes the slippage between the mass-eigenstate
wave packets. We also demonstrate that the wave packet spreading represents a
secondary effect which plays a significant role only in the non-relativistic
limit. In our analysis, we note the presence of a new time-dependent phase and
calculate how this additional term modifies the oscillating character of the
flavor conversion formula. Finally, by considering Box and Sine wave packets we
study how the choice of different functions to describe the particle
localization changes the oscillation probability.Comment: 16 pages, 7 figures, AMS-Te
Quantum coherent transport in a three-arm beam splitter and a Braess paradox
The Braess paradox encountered in classical networks is a counterintuitive
phenomenon when the flow in a road network can be impeded by adding a new road
or, more generally, the overall net performance can degrade after addition of
an extra available choice. In this work, we discuss the possibility of a
similar effect in a phase-coherent quantum transport and demonstrate it by
example of a simple Y-shaped metallic fork. To reveal the Braess-like partial
suppression of the charge flow in such device, it is proposed to transfer two
outgoing arms into a superconducting state. We show that the differential
conductance-vs-voltage spectrum of the hybrid fork structure varies
considerably when the extra link between the two superconducting leads is added
and it can serve as an indicator of quantum correlations which manifest
themselves in the quantum Braess paradox.Comment: 9 pages, 3 figures, the author version presented at the Quantum 2017
Workshop (Torino, Italy, 7-13 May 2017) and submitted to the International
Journal of Quantum Information; v2: reference 9 added and the introduction
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