Effective action and the quantum equation of motion

We carefully analyse the use of the effective action in dynamical problems, in particular the conditions under which the equation \frac{\delta \Ga} {\delta \phi}=0 can be used as a quantum equation of motion, and the relation between the asymptotic states involved in the definition of \Ga and the initial state of the system. By considering the quantum mechanical example of a double-well potential, where we can get exact results for the time evolution of the system, we show that an approximation to the effective potential in the quantum equation of motion that correctly describes the dynamical evolution of the system is obtained with the help of the wilsonian RG equation (already at the lowest order of the derivative expansion), while the commonly used one-loop effective potential fails to reproduce the exact results.Comment: 28 pages, 13 figures. Revised version to appear in The European Physical Journal

Estimation of ageing of proper elements from the observed structures of asteroid families

The possible presence of noise affecting the proper elements of asteroid families (due to several dynamical and also physical effects) influences the reconstruction of the original velocity fields. A noise on eccentricities alone is not sufficient to explain the observed features, and a noise on semimajor axes must also be taken into account. A preliminary quantitative evaluation of these noises on both elements is attempted

Fitting the mass distributions of Koronis family: new ideas and related physical constraints

It is well known that collisions progressively modify the observable properties of asteroids. Unfortunately several uncertainties affect the physics of energetic collisions involving asteroids - and, more in general, massive bodies. The main open question is the value of their impact strength, i.e. the specific energy required for fragmentation. It depends on - not completely known - properties of scaling from the sizes typical of laboratory experiments to astronomical sizes and also on the - even more uncertain - effect of previous collisions, which created fractures and complex internal features in the structure of both impacting bodies. In this paper some consequences concerning the formation of dynamical families are discussed in detail. It is argued that the possible weak family solution recently suggested and seemingly able to reproduce the properties of a family such as Koronis may be consistent with the observed mass distribution but entails an overwhelming amount of fast rotators and binary asteroids. In turn this may also affect the observable spin distribution. Finally, the probability of a suitable parent collision is estimated, showing that this kind of events may take place but only a very few times during the whole history of the Solar System

The role of viscosity in AGN outflows in relation to jet periodicities

Aims. Adopting the Smoothed Particle Hydrodynamics (SPH) numerical method, we performed a grid of evolving models of a 3D axially-symmetric, viscous accretion disc around a supermassive black hole (SMBH) of $10^{6}\div 10^{9}~ M_{\odot}$. Such sort of simulations are typical of accretion discs in active galactic nuclei (AGN). In such disc models, we pay attention to the role of the specific angular momentum λ and the turbulent viscosity parameter α, according to the Shakura and Sunyaev prescription. One or two shock fronts in the radial inviscid flow develop, according to the assigned initial kinematic and thermodynamic conditions. Methods. By fixing the initial and boundary conditions on the flow at the disc outer edge, where the total energy, the specific angular momentum λ, and the initial velocity are concerned, we find pairs of (α, λ) values determining radial periodical oscillations in the shock front. In some cases, an outflow develops from the subsonic post-shock region, close to the black hole. Results. The link between the accretion disc and the jet refueling through the onset of a centrifugal shock front is evident. We also compare model variability periods with observed ones in the radio light curves of AGN

Determination of the Spin Vector of a Synthetic Asteroid

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