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 $T^2$-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 KK or BB Meson from an Incoherent to a Coherent State

We study the evolution of a neutral $K$ meson prepared as an incoherent equal mixture of $K^0$ and $\bar{K^0}$. Denoting the density matrix by \rho(t) = {1/2} N(t) [\1 + \vec{\zeta}(t) \cdot \vec{\sigma} ] , the norm of the state $N(t)$ is found to decrease monotonically from one to zero, while the magnitude of the Stokes vector $|\vec{\zeta}(t)|$ increases monotonically from zero to one. This property qualifies these observables as arrows of time. Requiring monotonic behaviour of $N(t)$ for arbitrary values of $\gamma_L, \gamma_S$ and $\Delta m$ yields a bound on the CP-violating overlap $\delta = \braket{K_L}{K_S}$, which is similar to, but weaker than, the known unitarity bound. A similar requirement on $|\vec{\zeta}(t)|$ yields a new bound, $\delta^2 < {1/2} (\frac{\Delta \gamma}{\Delta m}) \sinh (\frac{3\pi}{4} \frac{\Delta \gamma}{\Delta m})$ which is particularly effective in limiting the CP-violating overlap in the $B^0$-$\bar{B^0}$ system. We obtain the Stokes parameter $\zeta_3(t)$ which shows how the average strangeness of the beam evolves from zero to $\delta$. The evolution of the Stokes vector from $|\vec{\zeta}| = 0$ to $|\vec{\zeta}| = 1$ 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 $\pm$ 0.0001 and 3.7130 $\pm$ 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 $G$, works as follows. Independent Poisson clocks of rate 1 are associated with the vertices of $G$. Initially, one vertex of $G$ knows the rumour. Whenever the clock of a vertex $x$ rings, it calls a random neighbour $y$: if $x$ knows the rumour and $y$ does not, then $x$ tells $y$ the rumour (a push operation), and if $x$ does not know the rumour and $y$ knows it, $y$ tells $x$ the rumour (a pull operation). The average spread time of $G$ is the expected time it takes for all vertices to know the rumour, and the guaranteed spread time of $G$ is the smallest time $t$ such that with probability at least $1-1/n$, after time $t$ all vertices know the rumour. The synchronous variant of this protocol, in which each clock rings precisely at times $1,2,\dots$, has been studied extensively. We prove the following results for any $n$-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 $O(n\log n)$. In the asynchronous version, both the average and guaranteed spread times are $\Omega(\log n)$. 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 $O(\log n)$ 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 $O(n^{2/3})$.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