6,577 research outputs found
Unlocking Undergraduate Problem Solving
It is difficult to find good problems for undergraduates. In this article, we explore an interesting problem that can be used in virtually any mathematics course. We then offer natural generalizations, state and prove some related results, and ultimately end with several open problems suitable for undergraduate research. Finally, we attempt to shed some light on what makes a problem interesting
Supersymmetric Electroweak Baryogenesis in the WKB approximation
We calculate the baryon asymmetry generated at the electroweak phase
transition in the minimal supersymmetric standard model, treating the particles
in a WKB approximation in the bubble wall background. A set of diffusion
equations for the particle species relevant to baryon generation, including
source terms arising from the CP violation associated with the complex phase
of the parameter, are derived from Boltzmann equations, and
solved. The conclusion is that must be \gsim 0.1 to generate a
baryon asymmetry consistent with nucleosynthesis. We compare our results to
several other recent computations of the effect, arguing that some are
overestimates.Comment: 12 pages, 1 figure, corrected some criticisms of hep-ph/9702409; to
appear in Phys. Lett.
No new limit on the size distribution of gamma-ray bursts
The results of a study (Carter et. al.) of gamma ray bursts using long duration balloon exposure are analyzed. Arguments are presented against the conclusion that the size spectrum extrapolates to a power law with index from -1.0 to -0.5, and that therefore the gamma ray bursts are of galactic origin. It is claimed that the data are consistent with an upper limit over 100 times that proposed, and that therefore no conclusion can be drawn from the measurements regarding the nature or origin of gamma ray bursts. The resulting upper limit to the rate of occurrence of small bursts lies above the -1.5 index power law extrapolation of the size spectrum of known events, i.e., greater than the rate expected from an infinitely extended source region
Testing for Features in the Primordial Power Spectrum
Well-known causality arguments show that events occurring during or at the
end of inflation, associated with reheating or preheating, could contribute a
blue component to the spectrum of primordial curvature perturbations, with the
dependence k^3. We explore the possibility that they could be observably large
in CMB, LSS, and Lyman-alpha data. We find that a k^3 component with a cutoff
at some maximum k can modestly improve the fits (Delta chi^2=2.0, 5.4) of the
low multipoles (l ~ 10 - 50) or the second peak (l ~ 540) of the CMB angular
spectrum when the three-year WMAP data are used. Moreover, the results from
WMAP are consistent with the CBI, ACBAR, 2dFGRS, and SDSS data when they are
included in the analysis. Including the SDSS galaxy clustering power spectrum,
we find weak positive evidence for the k^3 component at the level of Delta chi'
= 2.4, with the caveat that the nonlinear evolution of the power spectrum may
not be properly treated in the presence of the k^3 distortion. To investigate
the high-k regime, we use the Lyman-alpha forest data (LUQAS, Croft et al., and
SDSS Lyman-alpha); here we find evidence at the level Delta chi^2' = 3.8.
Considering that there are two additional free parameters in the model, the
above results do not give a strong evidence for features; however, they show
that surprisingly large bumps are not ruled out. We give constraints on the
ratio between the k^3 component and the nearly scale-invariant component, r_3 <
1.5, over the range of wave numbers 0.0023/Mpc < k < 8.2/Mpc. We also discuss
theoretical models which could lead to the k^3 effect, including ordinary
hybrid inflation and double D-term inflation models. We show that the
well-motivated k^3 component is also a good representative of the generic
spikelike feature in the primordial perturbation power spectrum.Comment: 23 pages, 6 figures; added new section on theoretical motivation for
k^3 term, and discussion of double D-term hybrid inflation models; title
changed, added a new section discussing the generic spikelike features,
published in IJMP
Narrow-line Laser Cooling by Adiabatic Transfer
We propose and demonstrate a novel laser cooling mechanism applicable to
particles with narrow-linewidth optical transitions. By sweeping the frequency
of counter-propagating laser beams in a sawtooth manner, we cause adiabatic
transfer back and forth between the ground state and a long-lived optically
excited state. The time-ordering of these adiabatic transfers is determined by
Doppler shifts, which ensures that the associated photon recoils are in the
opposite direction to the particle's motion. This ultimately leads to a robust
cooling mechanism capable of exerting large forces via a weak transition and
with reduced reliance on spontaneous emission. We present a simple intuitive
model for the resulting frictional force, and directly demonstrate its efficacy
for increasing the total phase-space density of an atomic ensemble. We rely on
both simulation and experimental studies using the 7.5~kHz linewidth S
to P transition in Sr. The reduced reliance on spontaneous
emission may allow this adiabatic sweep method to be a useful tool for cooling
particles that lack closed cycling transitions, such as molecules.Comment: 5 pages, 4 figure
Supersymmetric electroweak phase transition: beyond perturbation theory
We compute the three-dimensional effective action for the minimal supersymmetric standard model, which describes the light modes of the theory near the finite-temperature electroweak phase transition, keeping the one-loop corrections from the third generation quarks and squarks. Using the lattice results of Kajantie et al. for the phase transition in the same class of 3-D models, we find that the strength of the phase transition is sufficient for electroweak baryogenesis, in much broader regions of parameter space than have been indicated by purely perturbative analyses. In particular we find that, while small values of \tan\beta are favored, positive results persist even for arbitrarily large values of \tan\beta if the mass of the A^0 boson is between 40 and 100 GeV, a region of parameters which has not been previously identified as being favorable for electroweak baryogenesis
- …