1,149 research outputs found
Quantum models of classical mechanics: maximum entropy packets
In a previous paper, a project of constructing quantum models of classical
properties has been started. The present paper concludes the project by turning
to classical mechanics. The quantum states that maximize entropy for given
averages and variances of coordinates and momenta are called ME packets. They
generalize the Gaussian wave packets. A non-trivial extension of the
partition-function method of probability calculus to quantum mechanics is
given. Non-commutativity of quantum variables limits its usefulness. Still, the
general form of the state operators of ME packets is obtained with its help.
The diagonal representation of the operators is found. A general way of
calculating averages that can replace the partition function method is
described. Classical mechanics is reinterpreted as a statistical theory.
Classical trajectories are replaced by classical ME packets. Quantum states
approximate classical ones if the product of the coordinate and momentum
variances is much larger than Planck constant. Thus, ME packets with large
variances follow their classical counterparts better than Gaussian wave
packets.Comment: 26 pages, no figure. Introduction and the section on classical limit
are extended, new references added. Definitive version accepted by Found.
Phy
Do solar neutrinos decay?
Despite the fact that the solar neutrino flux is now well-understood in the
context of matter-affected neutrino mixing, we find that it is not yet possible
to set a strong and model-independent bound on solar neutrino decays. If
neutrinos decay into truly invisible particles, the Earth-Sun baseline defines
a lifetime limit of \tau/m \agt 10^{-4} s/eV. However, there are many
possibilities which must be excluded before such a bound can be established.
There is an obvious degeneracy between the neutrino lifetime and the mixing
parameters. More generally, one must also allow the possibility of active
daughter neutrinos and/or antineutrinos, which may partially conceal the
characteristic features of decay. Many of the most exotic possibilities that
presently complicate the extraction of a decay bound will be removed if the
KamLAND reactor antineutrino experiment confirms the large-mixing angle
solution to the solar neutrino problem and measures the mixing parameters
precisely. Better experimental and theoretical constraints on the B
neutrino flux will also play a key role, as will tighter bounds on absolute
neutrino masses. Though the lifetime limit set by the solar flux is weak, it is
still the strongest direct limit on non-radiative neutrino decay. Even so,
there is no guarantee (by about eight orders of magnitude) that neutrinos from
astrophysical sources such as a Galactic supernova or distant Active Galactic
Nuclei will not decay.Comment: Very minor corrections, corresponds to published versio
Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions
We address the thermodynamics (equilibrium density profiles, phase diagram,
instability analysis...) and the collapse of a self-gravitating gas of Brownian
particles in D dimensions, in both canonical and microcanonical ensembles. In
the canonical ensemble, we derive the analytic form of the density scaling
profile which decays as f(x)=x^{-\alpha}, with alpha=2. In the microcanonical
ensemble, we show that f decays as f(x)=x^{-\alpha_{max}}, where \alpha_{max}
is a non-trivial exponent. We derive exact expansions for alpha_{max} and f in
the limit of large D. Finally, we solve the problem in D=2, which displays
rather rich and peculiar features
Cosmic-ray acceleration in supernova remnants: non-linear theory revised
A rapidly growing amount of evidences, mostly coming from the recent
gamma-ray observations of Galactic supernova remnants (SNRs), is seriously
challenging our understanding of how particles are accelerated at fast shocks.
The cosmic-ray (CR) spectra required to account for the observed phenomenology
are in fact as steep as , i.e., steeper than the
test-particle prediction of first-order Fermi acceleration, and significantly
steeper than what expected in a more refined non-linear theory of diffusive
shock acceleration. By accounting for the dynamical back-reaction of the
non-thermal particles, such a theory in fact predicts that the more efficient
the particle acceleration, the flatter the CR spectrum. In this work we put
forward a self-consistent scenario in which the account for the magnetic field
amplification induced by CR streaming produces the conditions for reversing
such a trend, allowing --- at the same time --- for rather steep spectra and CR
acceleration efficiencies (about 20%) consistent with the hypothesis that SNRs
are the sources of Galactic CRs. In particular, we quantitatively work out the
details of instantaneous and cumulative CR spectra during the evolution of a
typical SNR, also stressing the implications of the observed levels of
magnetization on both the expected maximum energy and the predicted CR
acceleration efficiency. The latter naturally turns out to saturate around
10-30%, almost independently of the fraction of particles injected into the
acceleration process as long as this fraction is larger than about .Comment: 24 pages, 5 figures, accepted for publication in JCA
The effect of spontaneous collapses on neutrino oscillations
We compute the effect of collapse models on neutrino oscillations. The effect
of the collapse is to modify the evolution of the `spatial' part of the wave
function, which indirectly amounts to a change on the flavor components. In
many respects, this phenomenon is similar to neutrino propagation through
matter. For the analysis we use the mass proportional CSL model, and perform
the calculation to second order perturbation theory. As we will show, the CSL
prediction is very small - mainly due to the very small mass of neutrinos - and
practically undetectable.Comment: 24 pages, RevTeX. Updated versio
A novel determination of the local dark matter density
We present a novel study on the problem of constructing mass models for the
Milky Way, concentrating on features regarding the dark matter halo component.
We have considered a variegated sample of dynamical observables for the Galaxy,
including several results which have appeared recently, and studied a 7- or
8-dimensional parameter space - defining the Galaxy model - by implementing a
Bayesian approach to the parameter estimation based on a Markov Chain Monte
Carlo method. The main result of this analysis is a novel determination of the
local dark matter halo density which, assuming spherical symmetry and either an
Einasto or an NFW density profile is found to be around 0.39 GeV cm with
a 1- error bar of about 7%; more precisely we find a for the Einasto profile and for the NFW. This is in contrast to the
standard assumption that is about 0.3 GeV cm with an
uncertainty of a factor of 2 to 3. A very precise determination of the local
halo density is very important for interpreting direct dark matter detection
experiments. Indeed the results we produced, together with the recent accurate
determination of the local circular velocity, should be very useful to
considerably narrow astrophysical uncertainties on direct dark matter
detection.Comment: 31 pages,11 figures; minor changes in the text; two figures adde
Reaction and Axial Vector Coupling
The reaction is studied in the region of low
to investigate the effect of deuteron structure and width of the
resonance on the differential cross section. The results are used to extract
the axial vector coupling from the experimental data on
this reaction. The possibility to determine this coupling from electroweak
interaction experiments with high intensity electron accelerators is discussed.Comment: 14 pages, REVTEX, 5 figure
Physics and the measurement of continuous variables
Wigner had expressed the opinion that the impossibility of exact measurements
of single operators like position operators rendered the notion of geometrical
points somewhat dubious in physics. Using Sewell's recent resolution of the
measurement problem (collapse of the wave packet) in quantum mechanics and
extending it to the measurement of operators with continuous spectra, we are
able to compare the situation in quantum mechanics with that in quantum
mechanics. Our conclusion is that the notion of a geometrical point is as
meaningful in quantum mechanics as it is in classical mechanics.Comment: 20 page
Anisotropic distribution functions for spherical galaxies
A method is presented for finding anisotropic distribution functions for
stellar systems with known, spherically symmetric, densities, which depends
only on the two classical integrals of the energy and the magnitude of the
angular momentum. It requires the density to be expressed as a sum of products
of functions of the potential and of the radial coordinate. The solution
corresponding to this type of density is in turn a sum of products of functions
of the energy and of the magnitude of the angular momentum. The products of the
density and its radial and transverse velocity dispersions can be also
expressed as a sum of products of functions of the potential and of the radial
coordinate. Several examples are given, including some of new anisotropic
distribution functions. This device can be extended further to the related
problem of finding two-integral distribution functions for axisymmetric
galaxies.Comment: 5 figure
"Dark energy" in the Local Void
The unexpected discovery of the accelerated cosmic expansion in 1998 has
filled the Universe with the embarrassing presence of an unidentified "dark
energy", or cosmological constant, devoid of any physical meaning. While this
standard cosmology seems to work well at the global level, improved knowledge
of the kinematics and other properties of our extragalactic neighborhood
indicates the need for a better theory. We investigate whether the recently
suggested repulsive-gravity scenario can account for some of the features that
are unexplained by the standard model. Through simple dynamical considerations,
we find that the Local Void could host an amount of antimatter
() roughly equivalent to the mass of a typical
supercluster, thus restoring the matter-antimatter symmetry. The antigravity
field produced by this "dark repulsor" can explain the anomalous motion of the
Local Sheet away from the Local Void, as well as several other properties of
nearby galaxies that seem to require void evacuation and structure formation
much faster than expected from the standard model. At the global cosmological
level, gravitational repulsion from antimatter hidden in voids can provide more
than enough potential energy to drive both the cosmic expansion and its
acceleration, with no need for an initial "explosion" and dark energy.
Moreover, the discrete distribution of these dark repulsors, in contrast to the
uniformly permeating dark energy, can also explain dark flows and other
recently observed excessive inhomogeneities and anisotropies of the Universe.Comment: 6 pages, accepted as a Letter to the Editor by Astrophysics and Space
Scienc
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