53,445 research outputs found
Lorentz contraction, geometry and range in antiproton-proton annihilation into two pions
We present a geometric interpretation of the so-called annihilation range in
reactions of the type {\em two light mesons} based upon Lorentz
effects in the highly relativistic final states
(). Lorentz-boosted meson wave
functions, within the framework of the constituent quark model, result in a
richer angular dependence of the annihilation amplitudes and thus in higher
partial wave contributions () than usually obtained. This approach sheds
some light on what could be a "{\em short}" annihilation range and how it is
influenced by the angular distribution of the final states.Comment: LEAP05 (Bonn/Juelich) proceedings, 5 page
Relativistic effects and angular dependence in the reaction antiproton-proton -> pi^- pi^+
We present a new fit to the LEAR data on antiproton-proton -> pi^- pi^+
differential cross sections and analyzing powers motivated by relativistic
considerations. Within a quark model describing this annihilation we argue,
since the pions are highly energetic, that relativistic effects cannot be
neglected. The intrinsic pion wave functions are Lorentz transformed to the
center of mass frame. This change in quark geometry gives rise to additional
angular dependence in the transition operators and results in a relative
enhancement of higher J \ge 2 partial wave amplitudes. The fit to the data is
improved significantly.Comment: Revtex 4, 7 pages, 5 figures. Continuation and results of a previous
paper: nucl-th/040305
A relativistic treatment of pion wave functions in the annihilation antiproton-proton -> pi^-pi^+
Quark model intrinsic wave functions of highly energetic pions in the
reaction \bar pp->\pi^-\pi^+ are subjected to a relativistic treatment. The
annihilation is described in a constituent quark model with A2 and R2
flavor-flux topology and the annihilated quark-antiquark pairs are in 3P_0 and
3S_1 states. We study the effects of pure Lorentz transformations on the
antiquark and quark spatial wave functions and their respective spinors in the
pion. The modified quark geometry of the pion has considerable impact on the
angular dependence of the annihilation mechanisms.Comment: 10 pages in revtex format, 3 figure
Trilinear Higgs couplings in the two Higgs doublet model with CP violation
We carry out a detailed analysis of the general two Higgs doublet model with
CP violation. We describe two different parametrizations of this model, and
then study the Higgs boson masses and the trilinear Higgs couplings for these
two parametrizations. Within a rather general model, we find that the trilinear
Higgs couplings have a significant dependence on the details of the model, even
when the lightest Higgs boson mass is taken to be a fixed parameter. We include
radiative corrections in the one-loop effective potential approximation in our
analysis of the Higgs boson masses and the Higgs trilinear couplings. The
one-loop corrections to the trilinear couplings of the two Higgs doublet model
also depend significantly on the details of the model, and can be rather large.
We study quantitatively the trilinear Higgs couplings, and show that these
couplings are typically several times larger than the corresponding Standard
Model trilinear Higgs coupling in some regions of the parameter space. We also
briefly discuss the decoupling limit of the two Higgs doublet model.Comment: 23 pages, 15 figures. v2: References added, version to appear in PR
Intraspecific variability modulates interspecific variability in animal organismal stoichiometry.
Interspecific differences in organismal stoichiometry (OS) have been documented in a wide range of animal taxa and are of significant interest for understanding evolutionary patterns in OS. In contrast, intraspecific variation in animal OS has generally been treated as analytical noise or random variation, even though available data suggest intraspecific variability in OS is widespread. Here, we assess how intraspecific variation in OS affects inferences about interspecific OS differences using two co-occurring Neotropical fishes: Poecilia reticulata and Rivulus hartii. A wide range of OS has been observed within both species and has been attributed to environmental differences among stream systems. We assess the contributions of species identity, stream system, and the interactions between stream and species to variability in N:P, C:P, and C:N. Because predation pressure can impact the foraging ecology and life-history traits of fishes, we compare predictors of OS between communities that include predators, and communities where predators are absent. We find that species identity is the strongest predictor of N:P, while stream or the interaction of stream and species contribute more to the overall variation in C:P and C:N. Interspecific differences in N:P, C:P, and C:N are therefore not consistent among streams. The relative contribution of stream or species to OS qualitatively changes between the two predation communities, but these differences do not have appreciable effects in interspecific patterns. We conclude that although species identity is a significant predictor of OS, intraspecific OS is sometimes sufficient to overwhelm or obfuscate interspecific differences in OS
Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic Field
In this paper we consider the minimum time population transfer problem for
the -component of the spin of a (spin 1/2) particle driven by a magnetic
field, controlled along the x axis, with bounded amplitude. On the Bloch sphere
(i.e. after a suitable Hopf projection), this problem can be attacked with
techniques of optimal syntheses on 2-D manifolds. Let be the two
energy levels, and the bound on the field amplitude. For
each couple of values and , we determine the time optimal synthesis
starting from the level and we provide the explicit expression of the time
optimal trajectories steering the state one to the state two, in terms of a
parameter that can be computed solving numerically a suitable equation. For
, every time optimal trajectory is bang-bang and in particular the
corresponding control is periodic with frequency of the order of the resonance
frequency . On the other side, for , the time optimal
trajectory steering the state one to the state two is bang-bang with exactly
one switching. Fixed we also prove that for the time needed to
reach the state two tends to zero. In the case there are time optimal
trajectories containing a singular arc. Finally we compare these results with
some known results of Khaneja, Brockett and Glaser and with those obtained by
controlling the magnetic field both on the and directions (or with one
external field, but in the rotating wave approximation). As byproduct we prove
that the qualitative shape of the time optimal synthesis presents different
patterns, that cyclically alternate as , giving a partial proof of a
conjecture formulated in a previous paper.Comment: 31 pages, 10 figures, typos correcte
Colloidal ionic complexes on periodic substrates: ground state configurations and pattern switching
We theoretically and numerically studied ordering of "colloidal ionic
clusters" on periodic substrate potentials as those generated by optical
trapping. Each cluster consists of three charged spherical colloids: two
negatively and one positively charged. The substrate is a square or rectangular
array of traps, each confining one such cluster. By varying the lattice
constant from large to small, the observed clusters are first rod-like and form
ferro- and antiferro-like phases, then they bend into a banana-like shape and
finally condense into a percolated structure. Remarkably, in a broad parameter
range between single-cluster and percolated structures, we have found stable
supercomplexes composed of six colloids forming grape-like or rocket-like
structures. We investigated the possibility of macroscopic pattern switching by
applying external electrical fields.Comment: 14 pages, 13 figure
Time Resolved Correlation measurements of temporally heterogeneous dynamics
Time Resolved Correlation (TRC) is a recently introduced light scattering
technique that allows to detect and quantify dynamic heterogeneities. The
technique is based on the analysis of the temporal evolution of the speckle
pattern generated by the light scattered by a sample, which is quantified by
, the degree of correlation between speckle images recorded at
time and . Heterogeneous dynamics results in significant
fluctuations of with time . We describe how to optimize TRC
measurements and how to detect and avoid possible artifacts. The statistical
properties of the fluctuations of are analyzed by studying their
variance, probability distribution function, and time autocorrelation function.
We show that these quantities are affected by a noise contribution due to the
finite number of detected speckles. We propose and demonstrate a method to
correct for the noise contribution, based on a extrapolation
scheme. Examples from both homogeneous and heterogeneous dynamics are provided.
Connections with recent numerical and analytical works on heterogeneous glassy
dynamics are briefly discussed.Comment: 19 pages, 15 figures. Submitted to PR
Transformations of Heun's equation and its integral relations
We find transformations of variables which preserve the form of the equation
for the kernels of integral relations among solutions of the Heun equation.
These transformations lead to new kernels for the Heun equation, given by
single hypergeometric functions (Lambe-Ward-type kernels) and by products of
two hypergeometric functions (Erd\'elyi-type). Such kernels, by a limiting
process, also afford new kernels for the confluent Heun equation.Comment: This version was published in J. Phys. A: Math. Theor. 44 (2011)
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