A remark on zeta functions of finite graphs via quantum walks

From the viewpoint of quantum walks, the Ihara zeta function of a finite graph can be said to be closely related to its evolution matrix. In this note we introduce another kind of zeta function of a graph, which is closely related to, as to say, the square of the evolution matrix of a quantum walk. Then we give to such a function two types of determinant expressions and derive from it some geometric properties of a finite graph. As an application, we illustrate the distribution of poles of this function comparing with those of the usual Ihara zeta function.Comment: 14 pages, 1 figur

Spectrophotometric observations of comet P/Giacobini-Zinner

Spectroscopic observations of the Giacobini-Zinner comet were performed on March 20, June 20 and 21, September 11, and October 19, 1985. The September observations were performed at perihelion, exactly at the time of the International Cometary Explorer (ICE) encounter with the comet. The March and June observations were obtained with an intensified image dissector scanner (IIDS) on the 2.1-meter Kitt Peak telescope and the September and the October observations were obtained with a charge-coupled device (CCD) on the 4-meter Kitt Peak telescope. The nucleus spectra from these observations are presented

Modeling the coma of 2060 Chiron

Observations of comet-like activity and a resolved coma have established that 2060 Chiron is a comet. Determinations of its radius range from 65 to 200 km. This unusually large size for a comet suggests that the atmosphere of Chiron is intermediate to the tightly bound, thin atmospheres typical of planets and satellite and the greatly extended atmospheres in free expansion typical of cometary comae. Under certain conditions it may gravitationally bind an atmosphere that is thick compared to its size, while a significant amount of gas escapes to an extensive exosphere. These attributes coupled with reports of sporadic outbursts at large heliocentric distances and the identification of CN in the coma make Chiron a challenging object to model. Simple models of gas production and the dusty coma were recently presented but a general concensus on many basic features has not emerged. Development was begun on a more complete coma model of Chiron. The objectives are to report progress on this model and give the preliminary results for understanding Chiron

A preliminary model of the coma of 2060 Chiron

We have included gravity in our fluid dynamic model with chemical kinetics of dusty comet comae and applied it with two dust sizes to 2060 Chiron. A progress report on the model and preliminary results concerning gas/dust dynamics and chemistry is given

Disturbances of both cometary and Earth's magnetospheres excited by single solar flares

In the solar wind a comet plays the role of a windvane that moves three-dimensionally in the heliomagnetosphere. Among the solar systems bodies, only comets have a wide range of inclination angles of their orbital planes to the ecliptic plane ranging from 0 to 90 deg. Therefore, observations of cometary plasma tails are useful in probing the heliomagnetospheric conditions in the high heliolatitudinal region. A comet can be compared to a polar-orbiting probe encircling the Sun. We will introduce two rare cases in which the magnetospheres of both the comet and the Earth are disturbed by a single solar flare

Continuous deformations of the Grover walk preserving localization

The three-state Grover walk on a line exhibits the localization effect characterized by a non-vanishing probability of the particle to stay at the origin. We present two continuous deformations of the Grover walk which preserve its localization nature. The resulting quantum walks differ in the rate at which they spread through the lattice. The velocities of the left and right-traveling probability peaks are given by the maximum of the group velocity. We find the explicit form of peak velocities in dependence on the coin parameter. Our results show that localization of the quantum walk is not a singular property of an isolated coin operator but can be found for entire families of coins

Stability conditions and positivity of invariants of fibrations

We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a natural connection between them, related to a yet another stability condition, the linear stability. Finally we make some speculations and prove new results in higher dimension.Comment: Final version, to appear in the Springer volume dedicated to Klaus Hulek on the occasion of his 60-th birthda

Truncated Levy Random Walks and Generalized Cauchy Processes

A continuous Markovian model for truncated Levy random walks is proposed. It generalizes the approach developed previously by Lubashevsky et al. Phys. Rev. E 79, 011110 (2009); 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010) allowing for nonlinear friction in wondering particle motion and saturation of the noise intensity depending on the particle velocity. Both the effects have own reason to be considered and individually give rise to truncated Levy random walks as shown in the paper. The nonlinear Langevin equation governing the particle motion was solved numerically using an order 1.5 strong stochastic Runge-Kutta method and the obtained numerical data were employed to calculate the geometric mean of the particle displacement during a certain time interval and to construct its distribution function. It is demonstrated that the time dependence of the geometric mean comprises three fragments following one another as the time scale increases that can be categorized as the ballistic regime, the Levy type regime (superballistic, quasiballistic, or superdiffusive one), and the standard motion of Brownian particles. For the intermediate Levy type part the distribution of the particle displacement is found to be of the generalized Cauchy form with cutoff. Besides, the properties of the random walks at hand are shown to be determined mainly by a certain ratio of the friction coefficient and the noise intensity rather then their characteristics individually.Comment: 7 pages, 3 figure

Mosaic CCD method: A new technique for observing dynamics of cometary magnetospheres

On April 29, 1990, the plasma tail of Comet Austin was observed with a CCD camera on the 105-cm Schmidt telescope at the Kiso Observatory of the University of Tokyo. The area of the CCD used in this observation is only about 1 sq cm. When this CCD is used on the 105-cm Schmidt telescope at the Kiso Observatory, the area corresponds to a narrow square view of 12 ft x 12 ft. By comparison with the photograph of Comet Austin taken by Numazawa (personal communication) on the same night, we see that only a small part of the plasma tail can be photographed at one time with the CCD. However, by shifting the view on the CCD after each exposure, we succeeded in imaging the entire length of the cometary magnetosphere of 1.6 x 10(exp 6) km. This new technique is called 'the mosaic CCD method'. In order to study the dynamics of cometary plasma tails, seven frames of the comet from the head to the tail region were twice imaged with the mosaic CCD method and two sets of images were obtained. Six microstructures, including arcade structures, were identified in both the images. Sketches of the plasma tail including microstructures are included