14,593 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
Energy and centrality dependence of particle multiplicity in heavy ion collisions from = 20 to 2760 GeV
The centrality dependence of midrapidity charged-particle multiplicities at a
nucleon-nucleon center-of-mass energy of 2.76 TeV from CMS are compared to
PHOBOS data at 200 and 19.6 GeV. The results are first fitted with a
two-component model which parameterizes the separate contributions of nucleon
participants and nucleon-nucleon collisions. A more direct comparison involves
ratios of multiplicity densities per participant pair between the different
collision energies. The results support and extend earlier indications that the
influences of centrality and collision energy on midrapidity charged-particle
multiplicities are to a large degree independent.Comment: 5 pages, 2 figures, 1 table, Replaced with published version, v3 has
fixed typ
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
Relativistic tunneling through opaque barriers
We propose an analytical study of relativistic tunneling through opaque
barriers. We obtain a closed formula for the phase time. This formula is in
excellent agreement with the numerical simulations and corrects the standard
formula obtained by the stationary phase method. An important result is found
when the upper limit of the incoming energy distribution coincides with the
upper limit of the tunneling zone. In this case, the phase time is proportional
to the barrier width.Comment: 11 pages, 3 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
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
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
A Sagittarius-Induced Origin for the Monoceros Ring
The Monoceros ring is a collection of stars in nearly-circular orbits at
roughly 18 kpc from the Galactic center. It may have originated (i) as the
response of the disc to perturbations excited by satellite companions or (ii)
from the tidal debris of a disrupted dwarf galaxy. The metallicity of Monoceros
stars differs from that of disc stars at comparable Galactocentric distances,
an observation that disfavours the first scenario. On the other hand, circular
orbits are difficult to accommodate in the tidal-disruption scenario, since it
requires a satellite which at the time of disruption was itself in a nearly
circular orbit. Such satellite could not have formed at the location of the
ring and, given its low mass, dynamical friction is unlikely to have played a
major role in its orbital evolution. We search cosmological simulations for
low-mass satellites in nearly-circular orbits and find that they result, almost
invariably, from orbital changes induced by collisions with more massive
satellites: the radius of the circular orbit thus traces the galactocentric
distance of the collision. Interestingly, the Sagittarius dwarf, one of the
most luminous satellites of the Milky Way, is in a polar orbit that crosses the
Galactic plane at roughly the same Galactocentric distance as Monoceros. We use
idealized simulations to demonstrate that an encounter with Sagittarius might
well have led to the circularization and subsequent tidal demise of the
progenitor of the Monoceros ring.Comment: 6 pages, 4 figures, to match version published in MNRAS Letters
(http://onlinelibrary.wiley.com/doi/10.1111/j.1745-3933.2011.01035.x/abstract
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