37 research outputs found
A note on Duffin-Kemmer-Petiau equation in (1+1) space-time dimensions
In the last years several papers addressed the supposed spin-1 sector of the
massive Duffin-Kemmer-Petiau (DKP) equation restricted to (1+1) space-time
dimensions. In this note we show explicitly that this is a misleading approach,
since the DKP algebra in (1+1) dimensions admits only a spin-0 representation.
Our result also is useful to understand why several recent papers found
coincident results for both spin-0 and spin-1 sectors of the DKP theory in
(3+1) dimensions when the dynamics is restricted to one space dimension.Comment: 3 pages, no figure
Distributional approach to point interactions in one-dimensional quantum mechanics
We consider the one-dimensional quantum mechanical problem of defining
interactions concentrated at a single point in the framework of the theory of
distributions. The often ill-defined product which describes the interaction
term in the Schr\"odinger and Dirac equations is replaced by a well-defined
distribution satisfying some simple mathematical conditions and, in addition,
the physical requirement of probability current conservation is imposed. A
four-parameter family of interactions thus emerges as the most general point
interaction both in the non-relativistic and in the relativistic theories (in
agreement with results obtained by self-adjoint extensions). Since the
interaction is given explicitly, the distributional method allows one to carry
out symmetry investigations in a simple way, and it proves to be useful to
clarify some ambiguities related to the so-called interaction.Comment: Open Access link:
http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00023/abstrac
Relativistic Tunneling Through Two Successive Barriers
We study the relativistic quantum mechanical problem of a Dirac particle
tunneling through two successive electrostatic barriers. Our aim is to study
the emergence of the so-called \emph{Generalized Hartman Effect}, an effect
observed in the context of nonrelativistic tunneling as well as in its
electromagnetic counterparts, and which is often associated with the
possibility of superluminal velocities in the tunneling process. We discuss the
behavior of both the phase (or group) tunneling time and the dwell time, and
show that in the limit of opaque barriers the relativistic theory also allows
the emergence of the Generalized Hartman Effect. We compare our results with
the nonrelativistic ones and discuss their interpretation.Comment: 7 pages, 3 figures. Revised version, with a new appendix added.
Slightly changes in the styles and captions of Figures 1 and 2. To appear in
Physical Review
Some aspects of the synchronization in coupled maps
Through numerical simulations we analyze the synchronization time and the
Lyapunov dimension of a coupled map lattice consisting of a chain of chaotic
logistic maps exhibiting power law interactions. From the observed behaviors we
find a lower bound for the size of the lattice, independent of the range
and strength of the interaction, which imposes a practical lower bound in
numerical simulations for the system to be considered in the thermodynamic
limit. We also observe the existence of a strong correlation between the
averaged synchronization time and the Lyapunov dimension. This is an
interesting result because it allows an analytical estimation of the
synchronization time, which otherwise requires numerical simulations.Comment: 4 pages, 6 figure
Do firms share the same functional form of their growth rate distribution? A new statistical test
We introduce a new statistical test of the hypothesis that a balanced panel
of firms have the same growth rate distribution or, more generally, that they
share the same functional form of growth rate distribution. We applied the test
to European Union and US publicly quoted manufacturing firms data, considering
functional forms belonging to the Subbotin family of distributions. While our
hypotheses are rejected for the vast majority of sets at the sector level, we
cannot rejected them at the subsector level, indicating that homogenous panels
of firms could be described by a common functional form of growth rate
distribution.Comment: 17 pages, 3 figures, 2 table
Salecker-Wigner-Peres clock and average tunneling times
The quantum clock of Salecker-Wigner-Peres is used, by performing a
post-selection of the final state, to obtain average transmission and
reflection times associated to the scattering of localized wave packets by
static potentials in one dimension. The behavior of these average times is
studied for a gaussian wave packet, centered around a tunneling wave number,
incident on a rectangular barrier and, in particular, on a double delta barrier
potential. The regime of opaque barriers is investigated and the results show
that the average transmission time does not saturate, showing no evidence of
the Hartman effect (or its generalized version).Comment: 9 pages, 4 figure
HodgeRank as a new tool to explore the structure of a social representation
Social representation theory is a branch of social psychology that aims to identify the framework of concepts, ideas, opinions, beliefs, or feelings shared by the individuals within a social group, regarding a social object. Two main problems arise in this theory. The first concerns the identification of the content of the representation, which is the set of cognitive elements shared by the group; the second concerns its structure, which is the way these elements are organized and related among themselves. It is desirable that the methods to address these problems be simple, in regards to the feasibility of the data collection, and reliable, in the sense that they should provide a clear picture of the content and the structure of the representation. No single method proposed in the literature until now fully satisfies these features at the same time. Here we propose the use of HodgeRank, a global ranking method based on the Hodge combinatorial theory, as a new tool to explore the structure of a social representation. In this proposal, the input data is the same as those required for the hierarchical word associations, which is the main method in the field of social representations. However, the HodgeRank provides richer results when compared to the usual approach to analysing this kind of data, based on the VergĂ©sâ double-entry table. The main outcome of the HodgeRank is a graph, analogous to an electric circuit, from which some structural elements of the representation can already be identified. Moreover, the HodgeRank technique identifies the sources of inconsistencies between the global ranking and the aggregated answers within the social group. We interpret such inconsistencies in terms of the stability of the representation and use them to raise conjectures about the potential dynamics of the representation. We illustrate the application of this method in the study of a social representation of COVID-19 within a group of students and also within a group of faculty members from higher education institutions in Brazil
On the Salecker-Wigner-Peres clock and double barrier tunneling
In this work we revisit the Salecker-Wigner-Peres clock formalism and show
that it can be directly applied to the phenomenon of tunneling. Then we apply
this formalism to the determination of the tunneling time of a non relativistic
wavepacket, sharply concentrated around a tunneling energy, incident on a
symmetric double barrier potential. In order to deepen the discussion about the
generalized Hartmann effect, we consider the case in which the clock runs only
when the particle can be found inside the region \emph{between} the barriers
and show that, whenever the probability to find the particle in this region is
non negligible, the corresponding time (which in this case turns out to be a
dwell time) increases with the barrier spacing.Comment: To appear in Phys. Rev.