Bayesian Generalized Probability Calculus for Density Matrices

One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be diagonal. We develop a probability calculus based on these more general distributions that includes definitions of joints, conditionals and formulas that relate these, including analogs of the Theorem of Total Probability and various Bayes rules for the calculation of posterior density matrices. The resulting calculus parallels the familiar "conventional" probability calculus and always retains the latter as a special case when all matrices are diagonal. We motivate both the conventional and the generalized Bayes rule with a minimum relative entropy principle, where the Kullbach-Leibler version gives the conventional Bayes rule and Umegaki's quantum relative entropy the new Bayes rule for density matrices. Whereas the conventional Bayesian methods maintain uncertainty about which model has the highest data likelihood, the generalization maintains uncertainty about which unit direction has the largest variance. Surprisingly the bounds also generalize: as in the conventional setting we upper bound the negative log likelihood of the data by the negative log likelihood of the MAP estimator

Coronal Shock Waves, EUV Waves, and Their Relation to CMEs. III. Shock-Associated CME/EUV Wave in an Event with a Two-Component EUV Transient

On 17 January 2010, STEREO-B observed in extreme ultraviolet (EUV) and white light a large-scale dome-shaped expanding coronal transient with perfectly connected off-limb and on-disk signatures. Veronig et al. (2010, ApJL 716, 57) concluded that the dome was formed by a weak shock wave. We have revealed two EUV components, one of which corresponded to this transient. All of its properties found from EUV, white light, and a metric type II burst match expectations for a freely expanding coronal shock wave including correspondence to the fast-mode speed distribution, while the transient sweeping over the solar surface had a speed typical of EUV waves. The shock wave was presumably excited by an abrupt filament eruption. Both a weak shock approximation and a power-law fit match kinematics of the transient near the Sun. Moreover, the power-law fit matches expansion of the CME leading edge up to 24 solar radii. The second, quasi-stationary EUV component near the dimming was presumably associated with a stretched CME structure; no indications of opening magnetic fields have been detected far from the eruption region.Comment: 18 pages, 10 figures. Solar Physics, published online. The final publication is available at http://www.springerlink.co

Coronal Shock Waves, EUV waves, and Their Relation to CMEs. I. Reconciliation of "EIT waves", Type II Radio Bursts, and Leading Edges of CMEs

We show examples of excitation of coronal waves by flare-related abrupt eruptions of magnetic rope structures. The waves presumably rapidly steepened into shocks and freely propagated afterwards like decelerating blast waves that showed up as Moreton waves and EUV waves. We propose a simple quantitative description for such shock waves to reconcile their observed propagation with drift rates of metric type II bursts and kinematics of leading edges of coronal mass ejections (CMEs). Taking account of different plasma density falloffs for propagation of a wave up and along the solar surface, we demonstrate a close correspondence between drift rates of type II bursts and speeds of EUV waves, Moreton waves, and CMEs observed in a few known events.Comment: 30 pages, 15 figures. Solar Physics, published online. The final publication is available at http://www.springerlink.co

Large-scale Bright Fronts in the Solar Corona: A Review of "EIT waves"

``EIT waves" are large-scale coronal bright fronts (CBFs) that were first observed in 195 \AA\ images obtained using the Extreme-ultraviolet Imaging Telescope (EIT) onboard the \emph{Solar and Heliospheric Observatory (SOHO)}. Commonly called ``EIT waves", CBFs typically appear as diffuse fronts that propagate pseudo-radially across the solar disk at velocities of 100--700 km s$^{-1}$ with front widths of 50-100 Mm. As their speed is greater than the quiet coronal sound speed ($c_s\leq$200 km s$^{-1}$) and comparable to the local Alfv\'{e}n speed ($v_A\leq$1000 km s$^{-1}$), they were initially interpreted as fast-mode magnetoacoustic waves ($v_{f}=(c_s^2 + v_A^2)^{1/2}$). Their propagation is now known to be modified by regions where the magnetosonic sound speed varies, such as active regions and coronal holes, but there is also evidence for stationary CBFs at coronal hole boundaries. The latter has led to the suggestion that they may be a manifestation of a processes such as Joule heating or magnetic reconnection, rather than a wave-related phenomena. While the general morphological and kinematic properties of CBFs and their association with coronal mass ejections have now been well described, there are many questions regarding their excitation and propagation. In particular, the theoretical interpretation of these enigmatic events as magnetohydrodynamic waves or due to changes in magnetic topology remains the topic of much debate.Comment: 34 pages, 19 figure

Decoherence of molecular wave packets in an anharmonic potential

The time evolution of anharmonic molecular wave packets is investigated under the influence of the environment consisting of harmonic oscillators. These oscillators represent photon or phonon modes and assumed to be in thermal equilibrium. Our model explicitly incorporates the fact that in the case of a nonequidistant spectrum the rates of the environment induced transitions are different for each transition. The nonunitary time evolution is visualized by the aid of the Wigner function related to the vibrational state of the molecule. The time scale of decoherence is much shorter than that of dissipation, and gives rise to states which are mixtures of localized states along the phase space orbit of the corresponding classical particle. This behavior is to a large extent independent of the coupling strength, the temperature of the environment and also of the initial state.Comment: 7 pages, 4 figure

What is the Nature of EUV Waves? First STEREO 3D Observations and Comparison with Theoretical Models

One of the major discoveries of the Extreme ultraviolet Imaging Telescope (EIT) on SOHO were intensity enhancements propagating over a large fraction of the solar surface. The physical origin(s) of the so-called `EIT' waves is still strongly debated. They are considered to be either wave (primarily fast-mode MHD waves) or non-wave (pseudo-wave) interpretations. The difficulty in understanding the nature of EUV waves lies with the limitations of the EIT observations which have been used almost exclusively for their study. Their limitations are largely overcome by the SECCHI/EUVI observations on-board the STEREO mission. The EUVI telescopes provide high cadence, simultaneous multi-temperature coverage, and two well-separated viewpoints. We present here the first detailed analysis of an EUV wave observed by the EUVI disk imagers on December 07, 2007 when the STEREO spacecraft separation was $\approx 45^\circ$. Both a small flare and a CME were associated with the wave cadence, and single temperature and viewpoint coverage. These limitations are largely overcome by the SECCHI/EUVI observations on-board the STEREO mission. The EUVI telescopes provide high cadence, simultaneous multi-temperature coverage, and two well-separated viewpoints. Our findings give significant support for a fast-mode interpretation of EUV waves and indicate that they are probably triggered by the rapid expansion of the loops associated with the CME.Comment: Solar Physics, 2009, Special STEREO Issue, in pres