Shilnikov problem in Filippov dynamical systems

In this paper we introduce the concept of sliding Shilnikov orbits for $3$D Filippov systems. In short, such an orbit is a piecewise smooth closed curve, composed by Filippov trajectories, which slides on the switching surface and connects a Filippov equilibrium to itself, namely a pseudo saddle-focus. A version of the Shilnikov's Theorem is provided for such systems. Particularly, we show that sliding Shilnikov orbits occur in generic one-parameter families of Filippov systems, and that arbitrarily close to a sliding Shilnikov orbit there exist countably infinitely many sliding periodic orbits. Here, no additional Shilnikov-like assumption is needed in order to get this last result. In addition, we show the existence of sliding Shilnikov orbits in discontinuous piecewise linear differential systems. As far as we know, the examples of Fillippov systems provided in this paper are the first exhibiting such a sliding phenomenon

Generation of an ultrastable 578 nm laser for Yb lattice clock

In this paper we described the development and the characterization of a 578 nm laser source to be the clock laser for an Ytterbium Lattice Optical clock. Two independent laser sources have been realized and the characterization of the stability with a beat note technique is presente

Dielectric correction to the Chiral Magnetic Effect

We derive an electric current density $j_{em}$ in the presence of a magnetic field $B$ and a chiral chemical potential $\mu_5$. We show that $j_{em}$ has not only the anomaly-induced term $\propto \mu_5 B$ (i.e. Chiral Magnetic Effect) but also a non-anomalous correction which comes from interaction effects and expressed in terms of the susceptibility. We find the correction characteristically dependent on the number of quark flavors. The numerically estimated correction turns out to be a minor effect on heavy-ion collisions but can be tested by the lattice QCD simulation.Comment: 4 pages, 1 figur

Socially excessive bankruptcy costs and the benefits of interest rate ceilings on loans

The authors study the capital accumulation and welfare implications of ceilings on loan interest rates in a dynamic general equilibrium model. Binding ceilings on loan rates reduce the probability of bankruptcy. Lower bankruptcy rates result in lower bankruptcy and liquidation costs. The authors state conditions under which the resources freed by this cost-saving result increase the steady state capital stock, reduce steady state credit rationing, and raise the steady state welfare of all agents. The authors also argue that the conditions stated are likely to be satisfied in practice. Finally, their results hold even if initially there is capital over-accumulation.Loans ; Interest rates ; Bankruptcy

Optimal quantum repeaters for qubits and qudits

A class of optimal quantum repeaters for qubits is suggested. The schemes are minimal, i.e. involve a single additional probe qubit, and optimal, i.e. provide the maximum information adding the minimum amount of noise. Information gain and state disturbance are quantified by fidelities which, for our schemes, saturate the ultimate bound imposed by quantum mechanics for randomly distributed signals. Special classes of signals are also investigated, in order to improve the information-disturbance trade-off. Extension to higher dimensional signals (qudits) is straightforward.Comment: Revised version. To appear in PR

Shear viscosity of neutron matter from realistic nucleon-nucleon interactions

The calculation of transport properties of Fermi liquids, based on the formalism developed by Abrikosov and Khalatnikov, requires the knowledge of the probability of collisions between quasiparticles in the vicinity of the Fermi surface. We have carried out a numerical study of the shear viscosity of pure neutron matter, whose value plays a pivotal role in determining the stability of rotating neutron stars, in which these processes are described using a state-of-the-art nucleon-nucleon potential model. Within our approach medium modifications of the scattering cross section are consistently taken into account, through an effective interaction obtained from the matrix elements of the bare interaction between correlated states. Inclusion of medium effects lead to a large increase of the viscosity at densities larger than $\sim 0.1$ fm^{-3}.Comment: 4 pages, 4 figures. Corrected typo