445 research outputs found
Scattering in one dimension: The coupled Schroedinger equation, threshold behaviour and Levinson's theorem
We formulate scattering in one dimension due to the coupled Schr\"{o}dinger
equation in terms of the matrix, the unitarity of which leads to
constraints on the scattering amplitudes. Levinson's theorem is seen to have
the form , where is the phase of
the matrix at zero energy, the number of bound states with nonzero
binding energy, the number of half-bound states, and the number of
coupled equations. In view of the effects due to the half-bound states, the
threshold behaviour of the scattering amplitudes is investigated in general,
and is also illustrated by means of particular potential models.Comment: to appear in Journal of Mathematic Physics, RevTex, 16 pages, 3
figures (PostScript
Factor PD-Clustering
Factorial clustering methods have been developed in recent years thanks to
the improving of computational power. These methods perform a linear
transformation of data and a clustering on transformed data optimizing a common
criterion. Factorial PD-clustering is based on Probabilistic Distance
clustering (PD-clustering). PD-clustering is an iterative, distribution free,
probabilistic, clustering method. Factor PD-clustering make a linear
transformation of original variables into a reduced number of orthogonal ones
using a common criterion with PD-Clustering. It is demonstrated that Tucker 3
decomposition allows to obtain this transformation. Factor PD-clustering makes
alternatively a Tucker 3 decomposition and a PD-clustering on transformed data
until convergence. This method could significantly improve the algorithm
performance and allows to work with large dataset, to improve the stability and
the robustness of the method
Coherence of neutrino flavor mixing in quantum field theory
In the simplistic quantum mechanical picture of flavor mixing, conditions on
the maximum size and minimum coherence time of the source and detector regions
for the observation of interference---as well as the very viability of the
approach---can only be argued in an ad hoc way from principles external to the
formalism itself. To examine these conditions in a more fundamental way, the
quantum field theoretical -matrix approach is employed in this paper,
without the unrealistic assumption of microscopic stationarity. The fully
normalized, time-dependent neutrino flavor mixing event rates presented here
automatically reveal the coherence conditions in a natural, self-contained, and
physically unambiguous way, while quantitatively describing the transition to
their failure.Comment: 12 pages, submitted to Phys. Rev.
Tipping in a Low-Dimensional Model of a Tropical Cyclone
A presumed impact of global climate change is the increase in frequency and
intensity of tropical cyclones. Due to the possible destruction that occurs
when tropical cyclones make landfall, understanding their formation should be
of mass interest. In 2017, Kerry Emanuel modeled tropical cyclone formation by
developing a low-dimensional dynamical system which couples tangential wind
speed of the eye-wall with the inner-core moisture. For physically relevant
parameters, this dynamical system always contains three fixed points: a stable
fixed point at the origin corresponding to a non-storm state, an additional
asymptotically stable fixed point corresponding to a stable storm state, and a
saddle corresponding to an unstable storm state. The goal of this work is to
provide insight into the underlying mechanisms that govern the formation and
suppression of tropical cyclones through both analytical arguments and
numerical experiments. We present a case study of both rate and noise-induced
tipping between the stable states, relating to the destabilization or formation
of a tropical cyclone. While the stochastic system exhibits transitions both to
and from the non-storm state, noise-induced tipping is more likely to form a
storm, whereas rate-induced tipping is more likely to be the way a storm is
destabilized, and in fact, rate-induced tipping can never lead to the formation
of a storm when acting alone. For rate-induced tipping acting as a destabilizer
of the storm, a striking result is that both wind shear and maximal potential
velocity have to increase, at a substantial rate, in order to effect tipping
away from the active hurricane state. For storm formation through noise-induced
tipping, we identify a specific direction along which the non-storm state is
most likely to get activated
Addendum to Finite-size effects on multibody neutrino exchange
The interaction energy of the neutrons due to massless neutrino exchange in a
neutron star has recently been proved, using an effective theory, to be
extremely small and infrared-safe. Our comment here is of conceptual order: two
approaches to compute the total interaction energy density have recently been
proposed. Here, we study the connection between these two approaches. From CP
invariance, we argue that the resulting interaction energy has to be even in
the parameter , which expresses the static neutrino
potential created by a neutron medium of density .Comment: Latex file (Revtex), 9 pages, 1 figure, one reference change
Three heavy jet events at hadron colliders as a sensitive probe of the Higgs sector
Assuming that a non-standard neutral Higgs with an enhanced Yukawa coupling
to a bottom quark is observed at future hadron experiments, we propose a method
for a better understanding of the Higgs sector. Our procedure is based on
"counting" the number of events with heavy jets (where "heavy" stands for a c
or b jet) versus b jets, in the final state of processes in which the Higgs is
produced in association with a single high p_T c or b jet. We show that an
observed signal of the type proposed, at either the Tevatron or the LHC, will
rule out the popular two Higgs doublet model of type II as well as its
supersymmetric version - the Minimal Supersymmetric Standard Model (MSSM), and
may provide new evidence in favor of some more exotic multi Higgs scenarios. As
an example, we show that in a version of a two Higgs doublet model which
naturally accounts for the large mass of the top quark, our signal can be
easily detected at the LHC within that framework. We also find that such a
signal may be observable at the upgraded Tevatron RunIII, if the neutral Higgs
in this model has a mass around 100 GeV and \tan\beta > 50 and if the
efficiency for distinguishing a c jet from a light jet will reach the level of
50%.Comment: Revtex, 11 pages, 4 figures embedded in the text. Main changes with
respect to Version 1: Numerical results re-calculated using the CTEQ5L pdf,
improved discussion on the experimental consequences, new references added.
Conclusions remain unchanged. As will appear in Phys. Rev.
Heterofusion:Fusing genomics data of different measurement scales
In systems biology, it is becoming increasingly common to measure biochemical entities at different levels of the same biological system. Hence, data fusion problems are abundant in the life sciences. With the availability of a multitude of measuring techniques, one of the central problems is the heterogeneity of the data. In this paper, we discuss a specific form of heterogeneity, namely, that of measurements obtained at different measurement scales, such as binary, ordinal, interval, and ratioâscaled variables. Three generic fusion approaches are presented of which two are new to the systems biology community. The methods are presented, put in context, and illustrated with a realâlife genomics example
Towards a unique formula for neutrino oscillations in vacuum
We show that all correct results obtained by applying quantum field theory to
neutrino oscillations can be understood in terms of a single oscillation
formula. In particular, the model proposed by Grimus and Stockinger is shown to
be a subcase of the model proposed by Giunti, Kim and Lee, while the new
oscillation formulas proposed by Ioannisian and Pilaftsis and by Shtanov are
disproved. We derive an oscillation formula without making any relativistic
assumption and taking into account the dispersion, so that the result is valid
for both neutrinos and mesons. This unification gives a stronger
phenomenological basis to the neutrino oscillation formula. We also prove that
the coherence length can be increased without bound by more accurate energy
measurements. Finally, we insist on the wave packet interpretation of the
quantum field treatments of oscillations.Comment: 30 pages, 1 figure; the proof that plane wave oscillations do no
exist is extended to stationary models; the influence of dispersion is
explained in more detail
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