First clear evidence of quantum chaos in the bound states of an atomic nucleus

We study the spectral fluctuations of the $^{208}$Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of $6.20$ MeV recently identified at the Maier-Leibnitz-Laboratorium at Garching, Germany. For natural parity states the results are very close to the predictions of Random Matrix Theory (RMT) for the nearest-neighbor spacing distribution. A quantitative estimate of the agreement is given by the Brody parameter $\omega$, which takes the value $\omega=0$ for regular systems and $\omega \simeq 1$ for chaotic systems. We obtain $\omega=0.85 \pm 0.02$ which is, to our knowledge, the closest value to chaos ever observed in experimental bound states of nuclei. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in $^{208}$Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition our results show that chaotic and non-chaotic nuclear states coexist in the same energy region of the spectrum.Comment: 9 pages, 1 figur

A Motivating Exploration on Lunar Craters and Low-Energy Dynamics in the Earth -- Moon System

It is known that most of the craters on the surface of the Moon were created by the collision of minor bodies of the Solar System. Main Belt Asteroids, which can approach the terrestrial planets as a consequence of different types of resonance, are actually the main responsible for this phenomenon. Our aim is to investigate the impact distributions on the lunar surface that low-energy dynamics can provide. As a first approximation, we exploit the hyberbolic invariant manifolds associated with the central invariant manifold around the equilibrium point L_2 of the Earth - Moon system within the framework of the Circular Restricted Three - Body Problem. Taking transit trajectories at several energy levels, we look for orbits intersecting the surface of the Moon and we attempt to define a relationship between longitude and latitude of arrival and lunar craters density. Then, we add the gravitational effect of the Sun by considering the Bicircular Restricted Four - Body Problem. As further exploration, we assume an uniform density of impact on the lunar surface, looking for the regions in the Earth - Moon neighbourhood these colliding trajectories have to come from. It turns out that low-energy ejecta originated from high-energy impacts are also responsible of the phenomenon we are considering.Comment: The paper is being published in Celestial Mechanics and Dynamical Astronomy, vol. 107 (2010

Propagation of spatially entangled qudits through free space

We show the propagation of entangled states of high-dimensional quantum systems. The qudits states were generated using the transverse correlation of the twin photons produced by spontaneous parametric down-conversion. Their free-space distribution was performed at the laboratory scale and the propagated states maintained a high-fidelity with their original form. The use of entangled qudits allow an increase in the quantity of information that can be transmitted and may also guarantee more privacy for communicating parties. Therefore, studies about propagating entangled states of qudits are important for the effort of building quantum communication networks.Comment: 5 Pages, 4 Figures, REVTeX

Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory

By using unitarized two-loop Chiral Perturbation Theory partial waves to describe pion-pion scattering we find that the dominant component of the lightest scalar meson does not follow the q-qbar dependence on the number of colors that, in contrast, is obeyed by the lightest vectors. The method suggests that a subdominant q-qbar component of the f_0(600) possibly originates around 1 GeV.Comment: 4 pages, 1 Figure. To appear in Phys. Rev. Let

Statistical Analysis of Water Masers in Star-Forming Regions: Cepheus A and W75 N

We have done a statistical analysis of Very Long Baseline Array (VLBA) data of water masers in the star-forming regions (SFRs) Cepheus A and W75 N, using correlation functions to study the spatial clustering and Doppler-velocity distribution of these masers. Two-point spatial correlation functions show a characteristic scale size for clusters of water maser spots < or ~1 AU, similar to the values found in other SFRs. This suggests that the scale for water maser excitation tends to be < or ~1 AU. Velocity correlation functions show power-law dependences with indices that can be explained by regular velocity fields, such as expansion and/or rotation. These velocity fields are similar to those indicated by the water maser proper-motion measurements; therefore, the velocity correlation functions appear to reveal the organized motion of water maser spots on scales larger than 1 AU.Comment: 16 pages, 8 figures, and 3 tables. Accepted by The Astrophysical Journa

Optimal map of the modular structure of complex networks

Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking, modules are islands of highly connected nodes separated by a relatively small number of links. Every module can have contributions of links from any node in the network. The challenge is to disentangle these contributions to understand how the modular structure is built. The main problem is that the analysis of a certain partition into modules involves, in principle, as many data as number of modules times number of nodes. To confront this challenge, here we first define the contribution matrix, the mathematical object containing all the information about the partition of interest, and after, we use a Truncated Singular Value Decomposition to extract the best representation of this matrix in a plane. The analysis of this projection allow us to scrutinize the skeleton of the modular structure, revealing the structure of individual modules and their interrelations.Comment: 21 pages, 10 figure

Robustness of Cooperation in the Evolutionary Prisoner's Dilemma on Complex Networks

Recent studies on the evolutionary dynamics of the Prisoner's Dilemma game in scale-free networks have demonstrated that the heterogeneity of the network interconnections enhances the evolutionary success of cooperation. In this paper we address the issue of how the characterization of the asymptotic states of the evolutionary dynamics depends on the initial concentration of cooperators. We find that the measure and the connectedness properties of the set of nodes where cooperation reaches fixation is largely independent of initial conditions, in contrast with the behavior of both the set of nodes where defection is fixed, and the fluctuating nodes. We also check for the robustness of these results when varying the degree heterogeneity along a one-parametric family of networks interpolating between the class of Erdos-Renyi graphs and the Barabasi-Albert networks.Comment: 18 pages, 6 figures, revised version accepted for publication in New Journal of Physics (2007

Theoretical derivation of 1/f noise in quantum chaos

It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is different for chaotic and integrable systems. Using random matrix theory we derive theoretical expressions that explain the power spectrum behavior at all frequencies. These expressions reproduce to a good approximation the power laws of type 1/f (1/f^2) characteristics of chaotic (integrable) systems, observed in almost the whole frequency domain. Although we use random matrix theory to derive these results, they are also valid for semiclassical systems.Comment: 5 pages (Latex), 3 figure