Average output entropy for quantum channels

We study the regularized average Renyi output entropy \bar{S}_{r}^{\reg} of quantum channels. This quantity gives information about the average noisiness of the channel output arising from a typical, highly entangled input state in the limit of infinite dimensions. We find a closed expression for \beta_{r}^{\reg}, a quantity which we conjecture to be equal to \Srreg. We find an explicit form for \beta_{r}^{\reg} for some entanglement-breaking channels, and also for the qubit depolarizing channel $\Delta_{\lambda}$ as a function of the parameter $\lambda$. We prove equality of the two quantities in some cases, in particular we conclude that for $\Delta_{\lambda}$ both are non-analytic functions of the variable $\lambda$.Comment: 32 pages, several plots and figures; positivity condition added for Theorem on entanglement breaking channels; new result for entrywise positive channel

Laboratory simulations of astrophysical jets and solar coronal loops: new results

An experimental program underway at Caltech has produced plasmas where the shape is neither fixed by the vacuum chamber nor fixed by an external coil set, but instead is determined by self-organization. The plasma dynamics is highly reproducible and so can be studied in considerable detail even though the morphology of the plasma is both complex and time-dependent. A surprising result has been the observation that self-collimating MHD-driven plasma jets are ubiquitous and play a fundamental role in the self-organization. The jets can be considered lab-scale simulations of astrophysical jets and in addition are intimately related to solar coronal loops. The jets are driven by the combination of the axial component of the J×B force and the axial pressure gradient resulting from the non-uniform pinch force associated with the flared axial current density. Behavior is consistent with a model showing that collimation results from axial non-uniformity of the jet velocity. In particular, flow stagnation in the jet frame compresses frozen-in azimuthal magnetic flux, squeezes together toroidal magnetic field lines, thereby amplifying the embedded toroidal magnetic field, enhancing the pinch force, and hence causing collimation of the jet

Aluminum arsenide cleaved-edge overgrown quantum wires

We report conductance measurements in quantum wires made of aluminum arsenide, a heavy-mass, multi-valley one-dimensional (1D) system. Zero-bias conductance steps are observed as the electron density in the wire is lowered, with additional steps observable upon applying a finite dc bias. We attribute these steps to depopulation of successive 1D subbands. The quantum conductance is substantially reduced with respect to the anticipated value for a spin- and valley-degenerate 1D system. This reduction is consistent with disorder-induced, intra-wire backscattering which suppresses the transmission of 1D modes. Calculations are presented to demonstrate the role of strain in the 1D states of this cleaved-edge structure.Comment: Submitted to Applied Physics Letter

Critical dynamics of diluted relaxational models coupled to a conserved density (diluted model C)

We consider the influence of quenched disorder on the relaxational critical dynamics of a system characterized by a non-conserved order parameter coupled to the diffusive dynamics of a conserved scalar density (model C). Disorder leads to model A critical dynamics in the asymptotics, however it is the effective critical behavior which is often observed in experiments and in computer simulations and this is described by the full set of dynamical equations of diluted model C. Indeed different scenarios of effective critical behavior are predicted.Comment: 4 pages, 5 figure

On the spectrum of S=1/2 XXX Heisenberg chain with elliptic exchange

It is found that the Hamiltonian of S=1/2 isotropic Heisenberg chain with $N$ sites and elliptic non-nearest-neighbor exchange is diagonalized in each sector of the Hilbert space with magnetization $N/2-M$, $1<M\leq[N/2]$, by means of double quasiperiodic meromorphic solutions to the $M$-particle quantum Calogero-Moser problem on a line. The spectrum and highest-weight states are determined by the solutions of the systems of transcendental equations of the Bethe-ansatz type which arise as restrictions to particle pseudomomenta.Comment: 9 pages, Late

Integrability and Ergodicity of Classical Billiards in a Magnetic Field

We consider classical billiards in plane, connected, but not necessarily bounded domains. The charged billiard ball is immersed in a homogeneous, stationary magnetic field perpendicular to the plane. The part of dynamics which is not trivially integrable can be described by a "bouncing map". We compute a general expression for the Jacobian matrix of this map, which allows to determine stability and bifurcation values of specific periodic orbits. In some cases, the bouncing map is a twist map and admits a generating function which is useful to do perturbative calculations and to classify periodic orbits. We prove that billiards in convex domains with sufficiently smooth boundaries possess invariant tori corresponding to skipping trajectories. Moreover, in strong field we construct adiabatic invariants over exponentially large times. On the other hand, we present evidence that the billiard in a square is ergodic for some large enough values of the magnetic field. A numerical study reveals that the scattering on two circles is essentially chaotic.Comment: Explanations added in Section 5, Section 6 enlarged, small errors corrected; Large figures have been bitmapped; 40 pages LaTeX, 15 figures, uuencoded tar.gz. file. To appear in J. Stat. Phys. 8

Thermal fluctuations and longitudinal relaxation of single-domain magnetic particles at elevated temperatures

We present numerical and analytical results for the swiching times of magnetic nanoparticles with uniaxial anisotropy at elevated temperatures, including the vicinity of T_c. The consideration is based in the Landau-Lifshitz-Bloch equation that includes the relaxation of the magnetization magnitude M. The resulting switching times are shorter than those following from the naive Landau-Lifshitz equation due to (i) additional barrier lowering because of the reduction of M at the barrier and (ii) critical divergence of the damping parameters.Comment: 4 PR pages, 1 figur

Contact complete integrability

Complete integrability in a symplectic setting means the existence of a Lagrangian foliation leaf-wise preserved by the dynamics. In the paper we describe complete integrability in a contact set-up as a more subtle structure: a flag of two foliations, Legendrian and co-Legendrian, and a holonomy-invariant transverse measure of the former in the latter. This turns out to be equivalent to the existence of a canonical $\R\ltimes \R^{n-1}$ structure on the leaves of the co-Legendrian foliation. Further, the above structure implies the existence of $n$ contact fields preserving a special contact 1-form, thus providing the geometric framework and establishing equivalence with previously known definitions of contact integrability. We also show that contact completely integrable systems are solvable in quadratures. We present an example of contact complete integrability: the billiard system inside an ellipsoid in pseudo-Euclidean space, restricted to the space of oriented null geodesics. We describe a surprising acceleration mechanism for closed light-like billiard trajectories

Meteoroid Bulk Density and Ceplecha Types

Determination of asteroid bulk density is an important aspect of NEO characterization, yet difficult to measure. As a fraction of meteoroids originate from asteroids (including some NEOs), a study of meteoroid bulk densities can potentially provide useful insights into the densities of NEOs and PHOs in lieu of mutual perturbations, satellite, or expensive spacecraft missions. NASA's Meteoroid Environment Office characterizes the meteoroid environment for the purpose of spacecraft risk and operations. To accurately determine the risk, a distribution of meteoroid bulk densities are needed. This is not trivial to determine. If the particle survives to the ground the bulk density can be directly measured, however only the most dense particles land on the Earth. The next best approach is to model the meteor's ablation, which is not straightforward. Clear deceleration is necessary to do this and there are discrepancies in results between models. One approach to a distribution of bulk density is to use a measured proxy for the densities, then calibrate the proxy with known densities from meteorite falls, ablation modelling, and other sources. An obvious proxy choice is the Ceplecha type, K(sub B), thought to indicate the strength of a meteoroid. KB is frequented cited as a good proxy for meteoroid densities, but we find it is poorly correlated with density. However, a distinct split by dynamical type was seen with Jovian Tisserand parameter, T(sub J), with meteoroids from Halley Type comets (T(sub J less than 2 ) exhibiting much lower densities than those originating from Jupiter and asteroids (T(sub J greater than 2)

Spacecraft Risk Posed by the 2016 Perseid Outburst

The Perseids are one of the more prolific annual showers, known for high rates and for producing bright meteors. Outbursts of this shower have been noted in the 1860s, the early 1990s, 2004, and 2009, with the 1993 outburst being especially active (peak ZHR above 300). The 1993 Perseids also affected the space-faring nations, as the launch of the STS-51 mission was delayed by NASA until after the shower maximum due to an inability to predict the shower intensity, and the ESA telecommunications satellite Olympus suffered a mission-ending anomaly attributed to a static discharge caused by a Perseid impact [1]. Rates were again high (peak ZHR around 200) in 2009, when the NASA/USGS imaging satellite Landsat-5 experienced a gyro anomaly just before the shower peak; however in this case, the satellite was recovered and normal operations resumed one week later [2]. It is interesting to note that both spacecraft anomalies were not what is typically expected from meteoroid strikes, i.e., physical damage or an attitude displacement due to transfer of momentum. It would appear that the very fast Perseids (59 km s(sup -1) have a marked ability to produce plasma upon impact, which can then serve as a conductive path for discharge currents. The shower is expected to outburst again in 2016, and we present the results from the MSFC Meteoroid Stream Model [4], which predicts enhanced activity on a level similar to that of 2009 as the Earth passes through several debris trails on the night of August 11-12 (UT). We then compare our results to those of other modelers