Integrals of motion in the Many-Body localized phase

We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum $\{0,1\}$, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization-delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.Comment: 65 pages, 12 figures. Corrected typos, added reference

Coexistence of periods in a bisecting bifurcation

The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally stable limit cycles with different periods in the attractor is explained.Comment: 13 pages, 5 figure

Families of piecewise linear maps with constant Lyapunov exponent

We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.Comment: 26 pages, 13 figure

Understanding the relationship between the environment of the black hole and the radio jet: optical spectroscopy of compact AGN

We aim to investigate the relationship between radio jet activity on parsec-scales and the characteristics of both the bright active galactic nuclei (AGN) and their broad line regions (BLR). For this purpose, we combine 2cm Very Long Baseline Array observations of AGN with their optical spectral observations. This would enable us to investigate the optical spectra of a set of 172 relativistically beamed, flat-spectrum AGN with the nuclear disk oriented near to the plane of sky. Here, we present first results from optical spectroscopic observations of the brightest AGN from the 2 cm VLBA survey, and show a diversity of their spectral morphologies.Comment: 2 pages, to be published in the Proceedings of "Multiwavelength AGN Surveys", Cozumel, Dec 8 - 12, 200

Localized systems coupled to small baths: from Anderson_{nderson} to Zeno_{eno}

We investigate what happens if an Anderson localized system is coupled to a small bath, with a discrete spectrum, when the coupling between system and bath is specially chosen so as to never localize the bath. We find that the effect of the bath on localization in the system is a non-monotonic function of the coupling between system and bath. At weak couplings, the bath facilitates transport by allowing the system to 'borrow' energy from the bath. But above a certain coupling the bath produces localization, because of an orthogonality catastrophe, whereby the bath 'dresses' the system and hence suppresses the hopping matrix element. We call this last regime the regime of "Zeno-localization", since the physics of this regime is akin to the quantum Zeno effect, where frequent measurements of the position of a particle impede its motion. We confirm our results by numerical exact diagonalization

Radio-optical scrutiny of the central engine in compact AGN

We combine Very-Long-Baseline Interferometry (VLBI) data for $\sim100$ active galactic nuclei (AGN) available from the Very Large Baseline Array (VLBA) 2 cm imaging survey and optical spectroscopy to investigate the relationships in the emission-line region--central engine--radio jet system. Here, we present the diversity of spectral types among the brightest AGN in our sample. We also discuss correlations between the mass of the central engine and properties of the parsec-scale radio jet for 24 AGN selected by the presence of H$\beta$ broad-emission lines in their spectra.Comment: 4 pages, 5 figures, to appear in the proceedings of the Workshop on "Multiband Approach to AGN" held in Bonn (Germany), 30 September - 2 October 2004, to be published in "Memorie della Societa Astronomica Italiana

Classification of symmetric periodic trajectories in ellipsoidal billiards

We classify nonsingular symmetric periodic trajectories (SPTs) of billiards inside ellipsoids of R^{n+1} without any symmetry of revolution. SPTs are defined as periodic trajectories passing through some symmetry set. We prove that there are exactly 2^{2n}(2^{n+1}-1) classes of such trajectories. We have implemented an algorithm to find minimal SPTs of each of the 12 classes in the 2D case (R^2) and each of the 112 classes in the 3D case (R^3). They have periods 3, 4 or 6 in the 2D case; and 4, 5, 6, 8 or 10 in the 3D case. We display a selection of 3D minimal SPTs. Some of them have properties that cannot take place in the 2D case.Comment: 26 pages, 77 figures, 17 table

New records of moths (Insecta, Lepidoptera) from urban gardens on Terceira Island with new data on recently introduced species to the Azores

The urban Duque da Terceira Garden, in the main town of Angra do Heroísmo (Terceira, Azores), was investigated to describe the species composition of moths (Insecta, Lepidoptera). Moths were sampled with two methods: SLAM traps (between April and September 2017) and light trapping (two sessions in the summer of 2017). A total of 42 taxa were sampled with the addition of 19 new records for Duque da Terceira Garden, five of which were also new records for Terceira Island. The five species recorded as new for Terceira were subjected to an exhaustive taxonomic analysis. In addition, we revised the colonization status of some species. Our results show that urban gardens may help the establishment of exotic species and that it is necessary to monitor and control how these species established in urban environments.info:eu-repo/semantics/publishedVersio

The high-d landscapes paradigm: spin-glasses, and beyond

We review recent developments on the characterization of random landscapes in high-dimension. We focus in particular on the problem of characterizing the landscape topology and geometry, discussing techniques to count and classify its stationary points and stressing connections with the statistical physics of disordered systems and with random matrix theory.Comment: Contribution to the book Spin Glass Theory and Far Beyond: Replica Symmetry Breaking after 40 Year