60 research outputs found
A five-dimensional perspective on the Klein-Gordon equation
We discuss the Klein-Gordon (KG) equation using a 5D space-time approach. We
explicitly show that the KG equation in flat space-time admits a consistent
probabilistic interpretation with positively defined probability density.
However, the probabilistic interpretation is not covariant. In the
non-relativistic limit, the formalism reduces naturally to that of the
Schr\"odinger equation. We further discuss other interpretations of the KG
equation (and their non-relativistic limits) resulting from the 5D space-time
picture. Finally, we apply our results to the problem of hydrogenic spectra and
calculate the canonical sum of the hydrogenic atom.Comment: 13 pages, 1 figur
On spinless null propagation in five dimensional space-times with approximate space-like Killing symmetry
Five-dimensional (5D) space-time symmetry greatly facilitates how a 4D
observer perceives the propagation of a single spinless particle in a 5D
space-time. In particular, if the 5D geometry is independent of the fifth
coordinate then the 5D physics may be interpreted as 4D quantum mechanics. In
this work we address the case where symmetry is approximate, focusing on the
case where the 5D geometry depends weakly on the fifth coordinate. We show that
concepts developed for the case of exact symmetry approximately hold when other
concepts such as decaying quantum states, resonant quantum scattering and
Stokes drag are adopted, as well. We briefly comment on the optical model of
the nuclear interactions and Millikan's oil drop experiment.Comment: 6 pages, Typos correcte
The diffusion dynamics of choice: From durable goods markets to fashion first names
Goods, styles, ideologies are adopted by society through various mechanisms.
In particular, adoption driven by innovation is extensively studied by
marketing economics. Mathematical models are currently used to forecast the
sales of innovative goods. Inspired by the theory of diffusion processes
developed for marketing economics, we propose, for the first time, a predictive
framework for the mechanism of fashion, which we apply to first names. Analyses
of French, Dutch and US national databases validate our modelling approach for
thousands of first names, covering, on average, more than 50% of the yearly
incidence in each database. In these cases, it is thus possible to forecast how
popular the first names will become and when they will run out of fashion.
Furthermore, we uncover a clear distinction between popularity and fashion:
less popular names, typically not included in studies of fashion, may be driven
by fashion, as well.Comment: 11 pages, 1 table, 2 figures, 4 pages of supporting informatio
Role of word-of-mouth for programs of voluntary vaccination: A game-theoretic approach
We propose a model describing the synergetic feedback between word-of-mouth
(WoM) and epidemic dynamics controlled by voluntary vaccination. We combine a
game-theoretic model for the spread of WoM and a compartmental model describing
disease dynamics in the presence of a program of voluntary vaccination.
We evaluate and compare two scenarios, depending on what WoM disseminates: (1)
vaccine advertising, which may occur whether or not an epidemic is ongoing and
(2) epidemic status, notably disease prevalence. Understanding the synergy
between the two strategies could be particularly important for organizing
voluntary vaccination campaigns. We find that, in the initial phase of an
epidemic, vaccination uptake is determined more by vaccine advertising than the
epidemic status. As the epidemic progresses, epidemic status become
increasingly important for vaccination uptake, considerably accelerating
vaccination uptake toward a stable vaccination coverage.Comment: 10 pages, 2 figure
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