38,319 research outputs found
Unstable particles in non-relativistic quantum mechanics?
The Schroedinger equation is up-to-a-phase invariant under the Galilei group.
This phase leads to the Bargmann's superselection rule, which forbids the
existence of the superposition of states with different masses and implies that
unstable particles cannot be described consistently in non-relativistic quantum
mechanics. In this paper we claim that Bargmann's rule neglects physical
effects and that a proper description of non-relativistic quantum mechanics
requires to take into account this phase through the Extended Galilei group and
the definition of its action on spacetime coordinates.Comment: Prepared for the proceedings of VIII DGFM-SMF Worksho
Langlands duality for finite-dimensional representations of quantum affine algebras
We describe a correspondence (or duality) between the q-characters of
finite-dimensional representations of a quantum affine algebra and its
Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this
duality for the Kirillov-Reshetikhin modules and their irreducible tensor
products. In the course of the proof we introduce and construct "interpolating
(q,t)-characters" depending on two parameters which interpolate between the
q-characters of a quantum affine algebra and its Langlands dual.Comment: 40 pages; several results and comments added. Accepted for
publication in Letters in Mathematical Physic
Concentration dependence of the up- and down-conversion emission colours of Er3+-doped Y2O3: a time-resolved spectroscopy analysis
Er3+ energy transfer mechanisms and their influence on the dynamics and emission colours are considered for upconversion and downconversion regimes.</jats:p
Robust forward simulations of recurrent hitchhiking
Evolutionary forces shape patterns of genetic diversity within populations
and contribute to phenotypic variation. In particular, recurrent positive
selection has attracted significant interest in both theoretical and empirical
studies. However, most existing theoretical models of recurrent positive
selection cannot easily incorporate realistic confounding effects such as
interference between selected sites, arbitrary selection schemes, and
complicated demographic processes. It is possible to quantify the effects of
arbitrarily complex evolutionary models by performing forward population
genetic simulations, but forward simulations can be computationally prohibitive
for large population sizes (). A common approach for overcoming these
computational limitations is rescaling of the most computationally expensive
parameters, especially population size. Here, we show that ad hoc approaches to
parameter rescaling under the recurrent hitchhiking model do not always provide
sufficiently accurate dynamics, potentially skewing patterns of diversity in
simulated DNA sequences. We derive an extension of the recurrent hitchhiking
model that is appropriate for strong selection in small population sizes, and
use it to develop a method for parameter rescaling that provides the best
possible computational performance for a given error tolerance. We perform a
detailed theoretical analysis of the robustness of rescaling across the
parameter space. Finally, we apply our rescaling algorithms to parameters that
were previously inferred for Drosophila, and discuss practical considerations
such as interference between selected sites
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