The problem of quantum chaotic scattering with direct processes reduced to the one without

We show that the study of the statistical properties of the scattering matrix S for quantum chaotic scattering in the presence of direct processes (charaterized by a nonzero average S matrix ) can be reduced to the simpler case where direct processes are absent ( = 0). Our result is verified with a numerical simulation of the two-energy autocorrelation for two-dimensional S matrices. It is also used to extend Wigner's time delay distribution for one-dimensional S matrices, recently found for = 0, to the case not equal to zero; this extension is verified numerically. As a consequence of our result, future calculations can be restricted to the simpler case of no direct processes.Comment: 9 pages (Latex) and 1 EPS figure. Submitted to Europhysics Letters. The conjecture proposed in the previous version is proved; thus the present version contains a more satisfactory presentation of the proble

Measurement and Ergodicity in Quantum Mechanics

The experimental realization of successive non-demolition measurements on single microscopic systems brings up the question of ergodicity in Quantum Mechanics (QM). We investigate whether time averages over one realization of a single system are related to QM averages over an ensemble of similarly prepared systems. We adopt a generalization of von Neumann model of measurement, coupling the system to $N$ "probes" --with a strength that is at our disposal-- and detecting the latter. The model parallels the procedure followed in experiments on Quantum Electrodynamic cavities. The modification of the probability of the observable eigenvalues due to the coupling to the probes can be computed analytically and the results compare qualitatively well with those obtained numerically by the experimental groups. We find that the problem is not ergodic, except in the case of an eigenstate of the observable being studied.Comment: In press in J. Phys. A: Math. Theo

Undulation textures at the phase transitions of some alkyloxybenzoic acids

We observed undulated smectic textures for some compounds of the 4,n-alkyloxybenzoic (nOBAC) acid series, at transitions between the smectic and the isotropic phase and between the smectic and nematic phase. Studied compounds were 12OBAC, 16OBAC and a binary mixture of 12- and 16OBAC. The undulations are dressing a usual Schlieren texture. In the case of the binary mixture, an interesting fingerprint pattern is observed too

Tidal synchronization of an anelastic multi-layered body: Titan's synchronous rotation

This paper presents one analytical tidal theory for a viscoelastic multi-layered body with an arbitrary number of homogeneous layers. Starting with the static equilibrium figure, modified to include tide and differential rotation, and using the Newtonian creep approach, we find the dynamical equilibrium figure of the deformed body, which allows us to calculate the tidal potential and the forces acting on the tide generating body, as well as the rotation and orbital elements variations. In the particular case of the two-layer model, we study the tidal synchronization when the gravitational coupling and the friction in the interface between the layers is added. For high relaxation factors (low viscosity), the stationary solution of each layer is synchronous with the orbital mean motion (n) when the orbit is circular, but the spin rates increase if the orbital eccentricity increases. For low relaxation factors (high viscosity), as in planetary satellites, if friction remains low, each layer can be trapped in different spin-orbit resonances with frequencies n/2,n,3n/2,... . We apply the theory to Titan. The main results are: i) the rotational constraint does not allow us confirm or reject the existence of a subsurface ocean in Titan; and ii) the crust-atmosphere exchange of angular momentum can be neglected. Using the rotation estimate based on Cassini's observation, we limit the possible value of the shell relaxation factor, when a subsurface ocean is assumed, to 10^-9 Hz, which correspond to a shell's viscosity 10^18 Pa s, depending on the ocean's thickness and viscosity values. In the case in which the ocean does not exist, the maximum shell relaxation factor is one order of magnitude smaller and the corresponding minimum shell's viscosity is one order higher.Comment: Accepted for publication in Celestial Mechanics and Dynamical Astronomy. Referee's comments addressed in this versio

Scalar self-energy for a charged particle in global monopole spacetime with a spherical boundary

We analyze combined effects of the geometry produced by global monopole and a concentric spherical boundary on the self-energy of a point-like scalar charged test particle at rest. We assume that the boundary is outside the monopole's core with a general spherically symmetric inner structure. An important quantity to this analysis is the three-dimensional Green function associated with this system. For both Dirichlet and Neumann boundary conditions obeyed by the scalar field on the sphere, the Green function presents a structure that contains contributions due to the background geometry of the spacetime and the boundary. Consequently the corresponding induced scalar self-energy present also similar structure. For points near the sphere the boundary-induced part dominates and the self-force is repulsive/attractive with respect to the boundary for Dirichlet/Neumann boundary condition. In the region outside the sphere at large distances from it, the boundary-free part in the self-energy dominates and the corresponding self-force can be either attractive or repulsive with dependence of the curvature coupling parameter for scalar field. In particular, for the minimal coupling we show the presence of a stable equilibrium point for Dirichlet boundary condition. In the region inside the sphere the nature of the self-force depends on the specific model for the monopole's core. As illustrations of the general procedure adopted we shall consider two distinct models, namely flower-pot and the ballpoint-pen ones.Comment: 26 pages, 7 figures. Paper accepted for publication in CQG with minor revision. arXiv admin note: text overlap with arXiv:1009.019

Vacuum polarization by a flat boundary in cosmic string spacetime

In this paper we analyze the vacuum expectation values of the field squared and the energy-momentum tensor associated to a massive scalar field in a higher dimensional cosmic string spacetime, obeying Dirichlet or Neumann boundary conditions on the surface orthogonal to the string. In order to develop this analysis the corresponding Green function is obtained. The Green function is given by the sum of two expressions: the first one corresponds to the standard Green function in the boundary-free cosmic string spacetime and the second contribution is induced by the boundary. The boundary induced parts have opposite signs for Dirichlet and Neumann scalars. Because the analysis of vacuum polarization effects in the boundary-free cosmic string spacetime have been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions is investigated. We show that the non-trivial topology due to the cosmic string enhances the boundary induced vacuum polarization effects for both field squared and the energy-momentum tensor, compared to the case of a boundary in Minkowski spacetime. The presence of the cosmic string induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is investigated.Comment: 19 pages, 5 figure