Entanglement is not very useful for estimating multiple phases

The problem of the estimation of multiple phases (or of commuting unitaries) is considered. This is a sub-model of the estimation of a completely unknown unitary operation where it has been shown in recent works that there are considerable improvements by using entangled input states and entangled measurements. Here it is shown that when estimating commuting unitaries, there is practically no advantage in using entangled input states or entangled measurements.Comment: v2. New title, improved Fig.3, other minor changes, Accepted in PR

Prominence seismology using the period ratio of transverse thread oscillations

The ratio of the period of the fundamental mode to that of the first overtone of kink oscillations, from here on the "period ratio", is a seismology tool that can be used to infer information about the spatial variation of density along solar magnetic flux tubes. The period ratio is 2 in longitudinally homogeneous thin tubes, but it differs from 2 due to longitudinal inhomogeneity. In this paper we investigate the period ratio in longitudinally inhomogeneous prominence threads and explore its implications for prominence seismology. We numerically solve the two-dimensional eigenvalue problem of kink oscillations in a model of a prominence thread. We take into account three nonuniform density profiles along the thread. In agreement with previous works that used simple piecewise constant density profiles, we find that the period ratio is larger than 2 in prominence threads. When the ratio of the central density to that at the footpoints is fixed, the period ratio depends strongly on the form of the density profile along the thread. The more concentrated the dense prominence plasma near the center of the tube, the larger the period ratio. However, the period ratio is found to be independent of the specific density profile when the spatially averaged density in the thread is the same for all the profiles. An empirical fit of the dependence of the period ratio on the average density is given and its use for prominence seismology is discussed.Comment: Accepted for publication in A&

The spatial damping of magnetohydrodynamic waves in a flowing partially ionised prominence plasma

Solar prominences are partially ionised plasmas displaying flows and oscillations. These oscillations show time and spatial damping and, commonly, have been explained in terms of magnetohydrodynamic (MHD) waves. We study the spatial damping of linear non-adiabatic MHD waves in a flowing partially ionised plasma, having prominence-like physical properties. We consider single fluid equations for a partially ionised hydrogen plasma including in the energy equation optically thin radiation, thermal conduction by electrons and neutrals, and heating. Keeping the frequency real and fixed, we have solved the obtained dispersion relations for the complex wavenumber, k, and have analysed the behaviour of the damping length, wavelength and the ratio of the damping length to the wavelength, versus period, for Alfven, fast, slow and thermal waves.Comment: 28 pages, 9 figure

The statistical significance of the N-S asymmetry of solar activity revisited

The main aim of this study is to point out the difficulties found when trying to assess the statistical significance of the North-South asymmetry (hereafter SSNSA) of the most usually considered time series of solar activity. First of all, we distinguish between solar activity time series composed by integer or non-integer and dimensionless data, or composed by non-integer and dimensional data. For each of these cases, we discuss the most suitable statistical tests which can be applied and highlight the difficulties to obtain valid information about the statistical significance of solar activity time series. Our results suggest that, apart from the need to apply the suitable statistical tests, other effects such as the data binning, the considered units and the need, in some tests, to consider groups of data, affect substantially the determination of the statistical significance of the asymmetry. Our main conclusion is that the assessment of the statistical significance of the N-S asymmetry of solar activity is a difficult matter and that an absolute answer cannot be given, since many different effects influence the results given by the statistical tests. In summary, the quantitative results about the statistical significance of the N-S asymmetry of solar activity provided by different authors, as well as the studies about its behaviour, must be considered with care because they depend from the chosen values of different parameters or from the considered units.Comment: Astronomy and Astrophysics Latex, 9 pages, 4 figure

Effect of partial ionization on wave propagation in solar magnetic flux tubes

Observations show that waves are ubiquitous in the solar atmosphere and may play an important role for plasma heating. The study of waves in the solar corona is usually based on linear ideal magnetohydrodynamics (MHD) for a fully ionized plasma. However, the plasma in the photosphere and the chromosphere is only partially ionized. Here we investigate theoretically the impact of partial ionization on MHD wave propagation in cylindrical flux tubes in the two-fluid model. We derive the general dispersion relation that takes into account the effects of neutral-ion collisions and the neutral gas pressure. We take the neutral-ion collision frequency as an arbitrary parameter. Particular results for transverse kink modes and slow magnetoacoustic modes are shown. We find that the wave frequencies only depend on the properties of the ionized fluid when the neutral-ion collision frequency is much lower that the wave frequency. For high collision frequencies realistic of the solar atmosphere ions and neutrals behave as a single fluid with an effective density corresponding to the sum of densities of both fluids and an effective sound velocity computed as the average of the sound velocities of ions and neutrals. The MHD wave frequencies are modified accordingly. The neutral gas pressure can be neglected when studying transverse kink waves but it has to be taken into account for a consistent description of slow magnetoacoustic waves. The MHD waves are damped due to neutral-ion collisions. The damping is most efficient when the wave frequency and the collision frequency are of the same order of magnitude. For high collision frequencies slow magnetoacoustic waves are more efficiently damped than transverse kink waves. In addition, we find the presence of cut-offs for certain combinations of parameters that cause the waves to become non-propagating.Comment: Accepted for publication in A&

On the scaling of the damping time for resonantly damped oscillations in coronal loops

There is not as yet full agreement on the mechanism that causes the rapid damping of the oscillations observed by TRACE in coronal loops. It has been suggested that the variation of the observed values of the damping time as function of the corresponding observed values of the period contains information on the possible damping mechanism. The aim of this Letter is to show that, for resonant absorption, this is definitely not the case unless detailed a priori information on the individual loops is available

Slow surface wave damping in plasmas with anisotropic viscosity and thermal conductivity

This paper studies the damping of slow surface MHD waves propagating along the equilibrium magnetic field on a finite-thickness magnetic interface. The plasma is assumed to be strongly magnetised, and the full Braginskii's expressions for viscosity and the heat flux are used. The primary focus of the paper is on the competition between resonant absorption in the thin dissipative layer embracing the ideal resonant position and the bulk wave damping due to viscosity and thermal conductivity as damping mechanisms for surface MHD waves. The dependence of the wave damping decrement on the wave length and the dissipative coefficients is studied. Application of the obtained results to the surface MHD wave damping in the solar chromosphere is discussed

Transverse oscillations of two coronal loops

We study transverse fast magnetohydrodynamic waves in a system of two coronal loops modeled as smoothed, dense plasma cylinders in a uniform magnetic field. The collective oscillatory properties of the system due to the interaction between the individual loops are investigated from two points of view. Firstly, the frequency and spatial structure of the normal modes are studied. The system supports four trapped normal modes in which the loops move rigidly in the transverse direction. The direction of the motions is either parallel or perpendicular to the plane containing the axes of the loops. Two of these modes correspond to oscillations of the loops in phase, while in the other two they move in antiphase. Thus, these solutions are the generalization of the kink mode of a single cylinder to the double cylinder case. Secondly, we analyze the time-dependent problem of the excitation of the pair of tubes. We find that depending on the shape and location of the initial disturbance, different normal modes can be excited. The frequencies of normal modes are accurately recovered from the numerical simulations. In some cases, because of the simultaneous excitation of several eigenmodes, the system shows beating and the phase lag between the loops is $\pi/2$.Comment: Accepted for publication in The Astrophysical Journa