Zero energy resonance and the logarithmically slow decay of unstable multilevel systems

The long time behavior of the reduced time evolution operator for unstable multilevel systems is studied based on the N-level Friedrichs model in the presence of a zero energy resonance.The latter means the divergence of the resolvent at zero energy. Resorting to the technique developed by Jensen and Kato [Duke Math. J. 46, 583 (1979)], the zero energy resonance of this model is characterized by the zero energy eigenstate that does not belong to the Hilbert space. It is then shown that for some kinds of the rational form factors the logarithmically slow decay of the reduced time evolution operator can be realized.Comment: 31 pages, no figure

Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems

The long-time behavior of the survival probability for unstable multilevel systems that follows the power-decay law is studied based on the N-level Friedrichs model, and is shown to depend on the initial population in unstable states. A special initial state maximizing the asymptote of the survival probability at long times is found and examined by considering the spontaneous emission process for the hydrogen atom interacting with the electromagnetic field.Comment: 5 pages, 1 table. Accepted for publication in Phys. Rev.

Theoretical Study of One-dimensional Chains of Metal Atoms in Nanotubes

Using first-principles total-energy pseudopotential calculations, we have studied the properties of chains of potassium and aluminum in nanotubes. For BN tubes, there is little interaction between the metal chains and the tubes, and the conductivity of these tubes is through carriers located at the inner part of the tube. In contrast, for small radius carbon nanotubes, there are two types of interactions: charge-transfer (dominant for alkali atoms) leading to strong ionic cohesion, and hybridization (for multivalent metal atoms) resulting in a smaller cohesion. For Al-atomic chains in carbon tubes, we show that both effects contribute. New electronic properties related to these confined atomic chains of metal are analyzed.Comment: 12 pages + 3 figure

Instabilities and stickiness in a 3D rotating galactic potential

We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color and rotation. We investigate the structure of the invariant manifolds that we found in the neighborhood of simple and double unstable periodic orbits in the 4D spaces of section. We consider orbits in the neighborhood of the families x1v2, belonging to the x1 tree, and the z-axis (the rotational axis of our system). Close to the transition points from stability to simple instability, in the neighborhood of the bifurcated simple unstable x1v2 periodic orbits we encounter the phenomenon of stickiness as the asymptotic curves of the unstable manifold surround regions of the phase space occupied by rotational tori existing in the region. For larger energies, away from the bifurcating point, the consequents of the chaotic orbits form clouds of points with mixing of color in their 4D representations. In the case of double instability, close to x1v2 orbits, we find clouds of points in the four dimensional spaces of section. However, in some cases of double unstable periodic orbits belonging to the z-axis family we can visualize the associated unstable eigensurface. Chaotic orbits close to the periodic orbit remain sticky to this surface for long times (of the order of a Hubble time or more). Among the orbits we studied we found those close to the double unstable orbits of the x1v2 family having the largest diffusion speed.Comment: 29pages, 25 figures, accepted for publication in the International Journal of Bifurcation and Chao

Decoupled and inhomogeneous gas flows in S0 galaxies

A recent analysis of the "Einstein" sample of early-type galaxies has revealed that at any fixed optical luminosity Lb S0 galaxies have lower mean X-ray luminosity Lx per unit Lb than ellipticals. Following a previous analytical investigation of this problem (Ciotti & Pellegrini 1996), we have performed 2D numerical simulations of the gas flows inside S0 galaxies in order to ascertain the effectiveness of rotation and/or galaxy flattening in reducing the Lx/Lb ratio. The flow in models without SNIa heating is considerably ordered, and essentially all the gas lost by the stars is cooled and accumulated in the galaxy center. If rotation is present, the cold material settles in a disk on the galactic equatorial plane. Models with a time decreasing SNIa heating host gas flows that can be much more complex. After an initial wind phase, gas flows in energetically strongly bound galaxies tend to reverse to inflows. This occurs in the polar regions, while the disk is still in the outflow phase. In this phase of strong decoupling, cold filaments are created at the interface between inflowing and outflowing gas. Models with more realistic values of the dynamical quantities are preferentially found in the wind phase with respect to their spherical counterparts of equal Lb. The resulting Lx of this class of models is lower than in spherical models with the same Lb and SNIa heating. At variance with cooling flow models, rotation is shown to have only a marginal effect in this reduction, while the flattening is one of the driving parameters for such underluminosity, in accordance with the analytical investigation.Comment: 32 pages LaTex file, plus 5 .ps figures and macro aasms4.sty -- Accepted on Ap

Initial wave packets and the various power-law decreases of scattered wave packets at long times

The long time behavior of scattered wave packets $\psi (x,t)$ from a finite-range potential is investigated, by assuming $\psi (x,t)$ to be initially located outside the potential. It is then shown that $\psi (x,t)$ can asymptotically decrease in the various power laws at long time, according to its initial characteristics at small momentum. As an application, we consider the square-barrier potential system and demonstrate that $\psi (x,t)$ exhibits the asymptotic behavior $t^{-3/2}$, while another behavior like $t^{-5/2}$ can also appear for another $\psi (x,t)$.Comment: 5 pages, 1 figur

On the Relation of Hard X-ray Peak Flux and Outburst Waiting Time in the Black Hole Transient GX 339-4

Aims. In this work we re-investigated the empirical relation between the hard X-ray peak flux and the outburst waiting time found previously in the black hole transient GX 339-4. We tested the relation using the observed hard X-ray peak flux of the 2007 outburst of GX 339-4, clarified issues about faint flares, and estimated the lower limit of hard X-ray peak flux for the next outburst. Methods. We included Swift/BAT data obtained in the past four years. Together with the CGRO/BATSE and RXTE/HEXTE light curves, the observations used in this work cover a period of 18 years. Results. The observation of the 2007 outburst confirms the empirical relation discovered before. This strengthens the apparent link between the mass in the accretion disk and the peak luminosity of the brightest hard state that the black hole transient can reach. We also show that faint flares with peak fluxes smaller than about 0.12 crab do not affect the empirical relation. We predict that the hard X-ray peak flux of the next outburst should be larger than 0.65 crab, which will make it at least the second brightest in the hard X-ray since 1991.Comment: 4 pages, 3 figures, accepted by A&

Calibration of the EU Oxybarometer for Nakhlites

Martian meteorites have various characteristics, which are direct clues to understanding the petrogenesis of Mars rocks. The variation in oxidation state among the Martian meteorites must have important implications for redox conditions of the Martian crust/mantle and overall differentiation on Mars. Wadhwa [1] and Herd et al. [2] reported that Martian basalts were formed under a range of oxidation states, suggesting complex petrogenesis processes. The nakhlites, which have rather different characteristics from basaltic shergottites, may give us additional clues to Martian petrogenesis. The oxidation states of meteorites are usually described by the oxygen fugacity (fO2) under which the meteorites crystallized. One of the methods to estimate the oxygen fugacity is the depth of Eu anomaly. Eu(2+)/Eu(3+) is determined by the oxygen fugacity and partitioning is different for Eu(2+) and Eu(3+). Therefore, the depth of Eu anomaly in a mineral is a function of the oxygen fugacity and the Eu2+/Eu3+ in the melt from which the mineral crystallized. This method has some advantages over another major method, the two-oxide oxybarometer [3], which can more easily be affected by subsolidus processes. The Eu oxybarometer can analyze the cores of the earliest formed crystals in Martian meteorites, which means it can give us a better indication of the oxygen fugacity of the parent melt. The calibration of the Eu oxybarometer has been done with the basaltic shergottites before [4]. However, it has never been applied to nakhlites (Oe et al. [5] measured the depth of Eu anomaly in the synthetic pyroxene only at QFM). Partition coefficients are strongly affected by phase compositions, especially pyroxene Ca content and melt Al content [e.g., 5,6]. The composition of nakhlite pyroxene is rather different from basaltic shergottite pyroxene. Thus, there may be problems in applying the Eu oxybarometer calibration for the basaltic shergottites [7] to nakhlites. Thus, we report in this abstract preliminary results of our experimental calibration of the depth of Eu anomaly in pyroxene vs. oxygen fugacity for nakhlites

Stellar Bar Evolution in Cuspy and Flat-Cored Triaxial CDM Halos

We analyze the evolution of stellar bars in galactic disks in mildly triaxial flat-core and cuspy CDM halos. We use tailored simulations of rigid and live halos which include the feedback from disk/bar onto the halo in order to test the work by El-Zant & Shlosman (2002). The latter used the Liapunov exponents to analyze the fate of bars in analytical asymmetric halos. We find: (1) The bar growth is similar in all rigid axisymmetric and triaxial halos. (2) Bars in live models vertically buckle and form a pseudobulge with a boxy/peanut shape. (3) In live axisymmetric halos, the bar strength varies little during the secular evolution. The bar pattern speed anticorrelates with the halo core size. The bar strength is larger for smaller disk-to-halo mass ratios within disk radii, the bar size correlates with the halo core sizes, and the bar pattern speeds -- with the halo central mass concentration. Bars embedded in live triaxial halos have a starkly different fate: they dissolve on ~1.5-5 Gyr due to the onset of chaos over continuous zones, leaving behind a weak oval distortion. The onset of chaos is related to the halo triaxiality, the fast rotating bar and the halo cuspiness. Before the bar dissolves, the region outside it develops strong spiral structures, especially in the live triaxial halos. (4) More angular momentum is absorbed by the triaxial halos as compared to the axisymmetric models and its exchange is mediated by resonances. (5) Cuspy halos are more susceptible than flat-core halos to having their prolateness washed out by the bar. We analyze these results in terms of the stability of trajectories and development of chaos. We set constraints on the triaxiality of DM halos by comparing our predictions to recent observations of bars out to z~1.Comment: 17 pages, 14 figures, Astrophysical Journal, in press, Vol. 637. Updated version (text, references