132 research outputs found
The robustness of equilibria on convex solids
We examine the minimal magnitude of perturbations necessary to change the
number of static equilibrium points of a convex solid . We call the
normalized volume of the minimally necessary truncation robustness and we seek
shapes with maximal robustness for fixed values of . While the upward
robustness (referring to the increase of ) of smooth, homogeneous convex
solids is known to be zero, little is known about their downward robustness.
The difficulty of the latter problem is related to the coupling (via integrals)
between the geometry of the hull \bd K and the location of the center of
gravity . Here we first investigate two simpler, decoupled problems by
examining truncations of \bd K with fixed, and displacements of with
\bd K fixed, leading to the concept of external \rm and internal \rm
robustness, respectively. In dimension 2, we find that for any fixed number
, the convex solids with both maximal external and maximal internal
robustness are regular -gons. Based on this result we conjecture that
regular polygons have maximal downward robustness also in the original, coupled
problem. We also show that in the decoupled problems, 3-dimensional regular
polyhedra have maximal internal robustness, however, only under additional
constraints. Finally, we prove results for the full problem in case of 3
dimensional solids. These results appear to explain why monostatic pebbles
(with either one stable, or one unstable point of equilibrium) are found so
rarely in Nature.Comment: 20 pages, 6 figure
Magnetic noise spectrum measurement by an atom laser in gravity
Bose-Einstein condensates of ultracold atoms can be used to sense
fluctuations of the magnetic field by means of transitions into untrapped
hyperfine states. It has been shown recently that counting the outcoupled atoms
can yield the power spectrum of the magnetic noise. We calculate the spectral
resolution function which characterizes the condensate as a noise measurement
device in this scheme. We use the description of the radio-frequency
outcoupling scheme of an atom laser which takes into account the gravitational
acceleration. Employing both an intuitive and the exact three-dimensional and
fully quantum mechanical approach we derive the position-dependent spectral
resolution function for condensates of different size and shape
Parametric amplification of the mechanical vibrations of a suspended nanowire by magnetic coupling to a Bose-Einstein condensate
We consider the possibility of parametric amplification of a mechanical
vibration mode of a nanowire due to its interaction with a Bose-Einstein
condensate (BEC) of ultracold atoms. The magneto-mechanical coupling is
mediated by the vibrationally modulated magnetic field around the
current-carrying nanowire, which can induce atomic transitions between
different hyperfine sublevels. We theoretically analyze the limitations arising
from the fact that the spin inverted atomic medium which feeds the mechanical
oscillation has a finite bandwidth in the range of the chemical potential of
the condensate
Electroweak instantons as a solution to the ultrahigh energy cosmic ray puzzle
We propose a scenario in which a simple power-like primary spectrum for
protons with sources at cosmological distances leads to a quantitative
description of all the details of the observed cosmic ray spectrum for energies
from 10^{17} eV to 10^{21} eV. As usual, the ultrahigh energy protons with
energies above E_{GZK} ~ 4 x 10^{19} eV loose a large fraction of their
energies by the photoproduction of pions on the cosmic microwave background,
which finally decay mainly into neutrinos. In our scenario, these so-called
cosmogenic neutrinos interact with nucleons in the atmosphere through Standard
Model electroweak instanton-induced processes and produce air showers which are
hardly distinguishable from ordinary hadron-initiated air showers. In this way,
they give rise to a second contribution to the observed cosmic ray spectrum --
in addition to the one from above mentioned protons -- which reaches beyond
E_{GZK}. Since the whole observed spectrum is uniquely determined by a single
primary injection spectrum, no fine tuning is needed to fix the ratio of the
spectra below and above E_{GZK}. The statistical analysis shows an excellent
goodness of this scenario. Possible tests of it range from observations at
cosmic ray facilities and neutrino telescopes to searches for QCD
instanton-induced processes at HERA.Comment: 14 pages, 7 figure
Dynamical Chiral Symmetry Breaking on the Light Front.II. The Nambu--Jona-Lasinio Model
An investigation of dynamical chiral symmetry breaking on the light front is
made in the Nambu--Jona-Lasinio model with one flavor and N colors. Analysis of
the model suffers from extraordinary complexity due to the existence of a
"fermionic constraint," i.e., a constraint equation for the bad spinor
component. However, to solve this constraint is of special importance. In
classical theory, we can exactly solve it and then explicitly check the
property of ``light-front chiral transformation.'' In quantum theory, we
introduce a bilocal formulation to solve the fermionic constraint by the 1/N
expansion. Systematic 1/N expansion of the fermion bilocal operator is realized
by the boson expansion method. The leading (bilocal) fermionic constraint
becomes a gap equation for a chiral condensate and thus if we choose a
nontrivial solution of the gap equation, we are in the broken phase. As a
result of the nonzero chiral condensate, we find unusual chiral transformation
of fields and nonvanishing of the light-front chiral charge. A leading order
eigenvalue equation for a single bosonic state is equivalent to a leading order
fermion-antifermion bound-state equation. We analytically solve it for scalar
and pseudoscalar mesons and obtain their light-cone wavefunctions and masses.
All of the results are entirely consistent with those of our previous analysis
on the chiral Yukawa model.Comment: 23 pages, REVTEX, the version to be published in Phys.Rev.D; Some
clarifications in discussion of the LC wavefunctions adde
Grand Unification Signal from Ultra High Energy Cosmic Rays?
The spectrum of ultrahigh energy (above \approx 10^{9} GeV) cosmic rays is
consistent with the decay of GUT scale particles. The predicted mass is
m_X=10^b GeV, where b=14.6_{-1.7}^{+1.6}.Comment: 4 pages, 3 figures one figure removed, one table added, conclusions
essentially remained the same within errorbar
Determinisitic Optical Fock State Generation
We present a scheme for the deterministic generation of N-photon Fock states
from N three-level atoms in a high-finesse optical cavity. The method applies
an external laser pulsethat generates an -photon output state while
adiabatically keeping the atom-cavity system within a subspace of optically
dark states. We present analytical estimates of the error due to amplitude
leakage from these dark states for general N, and compare it with explicit
results of numerical simulations for N \leq 5. The method is shown to provide a
robust source of N-photon states under a variety of experimental conditions and
is suitable for experimental implementation using a cloud of cold atoms
magnetically trapped in a cavity. The resulting N-photon states have potential
applications in fundamental studies of non-classical states and in quantum
information processing.Comment: 25 pages, 9 figure
Clustering in Highest Energy Cosmic Rays: Physics or Statistics?
Directional clustering can be expected in cosmic ray observations due to
purely statistical fluctuations for sources distributed randomly in the sky. We
develop an analytic approach to estimate the probability of random cluster
configurations, and use these results to study the strong potential of the
HiRes, Auger, Telescope Array and EUSO/OWL/AirWatch facilities for deciding
whether any observed clustering is most likely due to non-random sources.Comment: 19 pages, LaTeX, 3 figure
Extensive air showers with TeV-scale quantum gravity
One of the possible consequences of the existence of extra degrees of freedom
beyond the electroweak scale is the increase of neutrino-nucleon cross sections
() beyond Standard Model predictions. At ultra-high energies
this may allow the existence of neutrino-initiated extensive air showers. In
this paper, we examine the most relevant observables of such showers. Our
analysis indicates that the future Pierre Auger Observatory could be
potentially powerful in probing models with large compact dimensions.Comment: 7 pages revtex, 5 eps fig
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