38,046 research outputs found
A Modified Version of the Waxman Algorithm
The iterative algorithm recently proposed by Waxman for solving eigenvalue
problems, which relies on the method of moments, has been modified to improve
its convergence considerably without sacrificing its benefits or elegance. The
suggested modification is based on methods to calculate low-lying eigenpairs of
large bounded hermitian operators or matrices
Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies
Heuristic arguments and numerical simulations support the Belinskii et al
(BKL) claim that the approach to the singularity in generic gravitational
collapse is characterized by local Mixmaster dynamics (LMD). Here, one way to
identify LMD in collapsing spatially inhomogeneous cosmologies is explored. By
writing the metric of one spacetime in the standard variables of another,
signatures for LMD may be found. Such signatures for the dynamics of spatially
homogeneous Mixmaster models in the variables of U(1)-symmetric cosmologies are
reviewed. Similar constructions for U(1)-symmetric spacetimes in terms of the
dynamics of generic -symmetric spacetime are presented.Comment: 17 pages, 5 figures. Contribution to CQG Special Issue "A Spacetime
Safari: Essays in Honour of Vincent Moncrief
CP Violation and Arrows of Time Evolution of a Neutral or Meson from an Incoherent to a Coherent State
We study the evolution of a neutral meson prepared as an incoherent equal
mixture of and . Denoting the density matrix by \rho(t) =
{1/2} N(t) [\1 + \vec{\zeta}(t) \cdot \vec{\sigma} ] , the norm of the state
is found to decrease monotonically from one to zero, while the magnitude
of the Stokes vector increases monotonically from zero to
one. This property qualifies these observables as arrows of time. Requiring
monotonic behaviour of for arbitrary values of and
yields a bound on the CP-violating overlap , which is similar to, but weaker than, the known unitarity
bound. A similar requirement on yields a new bound,
which is particularly effective in limiting
the CP-violating overlap in the - system. We obtain the Stokes
parameter which shows how the average strangeness of the beam
evolves from zero to . The evolution of the Stokes vector from
to has a resemblance to an order
parameter of a system undergoing spontaneous symmetry breaking.Comment: 13 pages, 6 figures. Inserted conon "." in title; minor change in
text. To appear in Physical review
Simultaneous Multiwavelength Observations of Magnetic Activity in Ultracool Dwarfs. IV. The Active, Young Binary NLTT 33370 AB (=2MASS J13142039+1320011)
We present multi-epoch simultaneous radio, optical, H{\alpha}, UV, and X-ray
observations of the active, young, low-mass binary NLTT 33370 AB (blended
spectral type M7e). This system is remarkable for its extreme levels of
magnetic activity: it is the most radio-luminous ultracool dwarf (UCD) known,
and here we show that it is also one of the most X-ray luminous UCDs known. We
detect the system in all bands and find a complex phenomenology of both flaring
and periodic variability. Analysis of the optical light curve reveals the
simultaneous presence of two periodicities, 3.7859 0.0001 and 3.7130
0.0002 hr. While these differ by only ~2%, studies of differential
rotation in the UCD regime suggest that it cannot be responsible for the two
signals. The system's radio emission consists of at least three components:
rapid 100% polarized flares, bright emission modulating periodically in phase
with the optical emission, and an additional periodic component that appears
only in the 2013 observational campaign. We interpret the last of these as a
gyrosynchrotron feature associated with large-scale magnetic fields and a cool,
equatorial plasma torus. However, the persistent rapid flares at all rotational
phases imply that small-scale magnetic loops are also present and reconnect
nearly continuously. We present an SED of the blended system spanning more than
9 orders of magnitude in wavelength. The significant magnetism present in NLTT
33370 AB will affect its fundamental parameters, with the components' radii and
temperatures potentially altered by ~+20% and ~-10%, respectively. Finally, we
suggest spatially resolved observations that could clarify many aspects of this
system's nature.Comment: emulateapj, 22 pages, 15 figures, ApJ in press; v2: fixes low-impact
error in Figure 15; v3: now in-pres
On the push&pull protocol for rumour spreading
The asynchronous push&pull protocol, a randomized distributed algorithm for
spreading a rumour in a graph , works as follows. Independent Poisson clocks
of rate 1 are associated with the vertices of . Initially, one vertex of
knows the rumour. Whenever the clock of a vertex rings, it calls a random
neighbour : if knows the rumour and does not, then tells the
rumour (a push operation), and if does not know the rumour and knows
it, tells the rumour (a pull operation). The average spread time of
is the expected time it takes for all vertices to know the rumour, and the
guaranteed spread time of is the smallest time such that with
probability at least , after time all vertices know the rumour. The
synchronous variant of this protocol, in which each clock rings precisely at
times , has been studied extensively. We prove the following results
for any -vertex graph: In either version, the average spread time is at most
linear even if only the pull operation is used, and the guaranteed spread time
is within a logarithmic factor of the average spread time, so it is . In the asynchronous version, both the average and guaranteed spread times
are . We give examples of graphs illustrating that these bounds
are best possible up to constant factors. We also prove theoretical
relationships between the guaranteed spread times in the two versions. Firstly,
in all graphs the guaranteed spread time in the asynchronous version is within
an factor of that in the synchronous version, and this is tight.
Next, we find examples of graphs whose asynchronous spread times are
logarithmic, but the synchronous versions are polynomially large. Finally, we
show for any graph that the ratio of the synchronous spread time to the
asynchronous spread time is .Comment: 25 page
Minisuperspace Model for Revised Canonical Quantum Gravity
We present a reformulation of the canonical quantization of gravity, as
referred to the minisuperspace; the new approach is based on fixing a Gaussian
(or synchronous) reference frame and then quantizing the system via the
reconstruction of a suitable constraint; then the quantum dynamics is re-stated
in a generic coordinates system and it becomes dependent on the lapse function.
The analysis follows a parallelism with the case of the non-relativistic
particle and leads to the minisuperspace implementation of the so-called {\em
kinematical action} as proposed in \cite{M02} (here almost coinciding also with
the approach presented in \cite{KT91}). The new constraint leads to a
Schr\"odinger equation for the system. i.e. to non-vanishing eigenvalues for
the super-Hamiltonian operator; the physical interpretation of this feature
relies on the appearance of a ``dust fluid'' (non-positive definite) energy
density, i.e. a kind of ``materialization'' of the reference frame. As an
example of minisuperspace model, we consider a Bianchi type IX Universe, for
which some dynamical implications of the revised canonical quantum gravity are
discussed. We also show how, on the classical limit, the presence of the dust
fluid can have relevant cosmological issues. Finally we upgrade our analysis by
its extension to the generic cosmological solution, which is performed in the
so-called long-wavelength approximation. In fact, near the Big-Bang, we can
neglect the spatial gradients of the dynamical variables and arrive to
implement, in each space point, the same minisuperspace paradigm valid for the
Bianchi IX model.Comment: 16 pages, no figures, to appear on International Journal of Modern
Physics
- …