From ergodic to non-ergodic chaos in Rosenzweig-Porter model

The Rosenzweig-Porter model is a one-parameter family of random matrices with three different phases: ergodic, extended non-ergodic and localized. We characterize numerically each of these phases and the transitions between them. We focus on several quantities that exhibit non-analytical behaviour and show that they obey the scaling hypothesis. Based on this, we argue that non-ergodic chaotic and ergodic regimes are separated by a continuous phase transition, similarly to the transition between non-ergodic chaotic and localized phases.Comment: 12 page

Thermodynamics from a scaling Hamiltonian

There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both extensive and nonextensive thermodynamic perspectives. We use a model, whose Hamiltonian takes into account spins ferromagnetically coupled in a chain via a power law that decays at large interparticle distance $r$ as $1/r^{\alpha}$ for $\alpha\geq0$. Here, we review old nonextensive scaling. In addition, we propose a new Hamiltonian scaled by $2\frac{(N/2)^{1-\alpha}-1}{1-\alpha}$ that explicitly includes symmetry of the lattice and dependence on the size, $N$, of the system. The new approach enabled us to improve upon previous results. A numerical test is conducted through Monte Carlo simulations. In the model, periodic boundary conditions are adopted to eliminate surface effects.Comment: 12 pages, 2 figures, submitted for publication to Phys. Rev.

Mapping the structural diversity of C60 carbon clusters and their infrared spectra

The current debate about the nature of the carbonaceous material carrying the infrared (IR) emission spectra of planetary and proto-planetary nebulae, including the broad plateaus, calls for further studies on the interplay between structure and spectroscopy of carbon-based compounds of astrophysical interest. The recent observation of C60 buckminsterfullerene in space suggests that carbon clusters of similar size may also be relevant. In the present work, broad statistical samples of C60 isomers were computationally determined without any bias using a reactive force field, their IR spectra being subsequently obtained following local optimization with the density-functional-based tight-binding theory. Structural analysis reveals four main structural families identified as cages, planar polycyclic aromatics, pretzels, and branched. Comparison with available astronomical spectra indicates that only the cage family could contribute to the plateau observed in the 6-9 micron region. The present framework shows great promise to explore and relate structural and spectroscopic features in more diverse and possibly hydrogenated carbonaceous compounds, in relation with astronomical observations

Size effect in the ionization energy of PAH clusters

We report the first experimental measurement of the near-threshold photo-ionization spectra of polycyclic aromatic hydrocarbon clusters made of pyrene C16H10 and coronene C24H12, obtained using imaging photoelectron photoion coincidence spectrometry with a VUV synchrotron beamline. The experimental results of the ionization energy are confronted to calculated ones obtained from simulations using dedicated electronic structure treatment for large ionized molecular clusters. Experiment and theory consistently find a decrease of the ionization energy with cluster size. The inclusion of temperature effects in the simulations leads to a lowering of this energy and to a quantitative agreement with the experiment. In the case of pyrene, both theory and experiment show a discontinuity in the IE trend for the hexamer