Spectrum of the Laplace-Beltrami Operator and the Phase Structure of Causal Dynamical Triangulation

We propose a new method to characterize the different phases observed in the non-perturbative numerical approach to quantum gravity known as Causal Dynamical Triangulation. The method is based on the analysis of the eigenvalues and the eigenvectors of the Laplace-Beltrami operator computed on the triangulations: it generalizes previous works based on the analysis of diffusive processes and proves capable of providing more detailed information on the geometric properties of the triangulations. In particular, we apply the method to the analysis of spatial slices, showing that the different phases can be characterized by a new order parameter related to the presence or absence of a gap in the spectrum of the Laplace-Beltrami operator, and deriving an effective dimensionality of the slices at the different scales. We also propose quantities derived from the spectrum that could be used to monitor the running to the continuum limit around a suitable critical point in the phase diagram, if any is found.Comment: 21 pages, 26 figures, 2 table

Spectral Methods and Running Scales in Causal Dynamical Triangulations

The spectrum of the Laplace-Beltrami operator, computed on the spatial slices of Causal Dynamical Triangulations, is a powerful probe of the geometrical properties of the configurations sampled in the various phases of the lattice theory. We study the behavior of the lowest eigenvalues of the spectrum and show that this can provide information about the running of length scales as a function of the bare parameters of the theory, hence about the critical behavior around possible second order transition points in the CDT phase diagram, where a continuum limit could be defined.Comment: 5 pages, 6 figure

Epidemics of Liquidity Shortages in Interbank Markets

Financial contagion from liquidity shocks has being recently ascribed as a prominent driver of systemic risk in interbank lending markets. Building on standard compartment models used in epidemics, in this work we develop an EDB (Exposed-Distressed-Bankrupted) model for the dynamics of liquidity shocks reverberation between banks, and validate it on electronic market for interbank deposits data. We show that the interbank network was highly susceptible to liquidity contagion at the beginning of the 2007/2008 global financial crisis, and that the subsequent micro-prudential and liquidity hoarding policies adopted by banks increased the network resilience to systemic risk---yet with the undesired side effect of drying out liquidity from the market. We finally show that the individual riskiness of a bank is better captured by its network centrality than by its participation to the market, along with the currently debated concept of "too interconnected to fail"

Spectral Methods in Causal Dynamical Triangulations

We show recent results of the application of spectral analysis in the setting of the Monte Carlo approach to Quantum Gravity known as Causal Dynamical Triangulations (CDT), discussing the behavior of the lowest lying eigenvalues of the Laplace-Beltrami operator computed on spatial slices. This kind of analysis provides information about running scales of the theory and about the critical behaviour around a possible second order transition in the CDT phase diagram, discussing the implications for the continuum limit.Comment: Proceeding of Science for parallel talk at the 37th International Symposium on Lattice Field Theory - Lattice2019, 16-22 June 2019, Wuhan, Chin

Conoscere e comprendere il territorio: ricerche archeologiche e topografiche tra Reggio Calabria e Motta San Giovanni

This thesis is the result of four years of researchs and describes the area between Reggio Calabria and Motta San Giovanni from prehistory to the present day through the study of material and documentary sources. This territory is located on the Strait of Messina and covers an area of approximately 40 km2 from the coast to the Aspromonte mountains. This land plays a role of particular interest in the history of settlements, productions and trades of southern Calabria. Rich in necropolis, castles, churches, ports, quarries and mines, this area is a privileged place for the archaeological and historical study and to understand both the relationship between settlements and natural resources that the transformations of the Calabrian landscape during the centuries

Is the compact object associated with HESS J1731-347 a strange quark star?

The analysis of the central compact object within the supernova remnant HESS J1731-347 suggests that it has a small radius and, even more interestingly, a mass of the order or smaller than one solar mass. This raises the question of which astrophysical process could lead to such a small mass, since the analysis of various types of SN explosions indicate that is it not possible to produce a neutron star with a mass smaller than about $1.17 M_\odot$. Here we show that masses of the order or smaller than one solar mass can be obtained in the case of strange quark stars and that it is possible to build a coherent model explaining not only the mass and the radius of that object, but also its slow cooling suggested in various analyses. We also show that an astrophysical path exists which leads to the formation of such an object, and we discuss the role played in that scenario by strangelets assumed to constitute the dark matter.Comment: 6 pages, 2 Figures, 1 Table. New version significantly expanded. One section and one figure adde

Merger of a Neutron Star with a Black Hole: one-family vs. two-families scenario

A kilonova signal is generally expected after a Black Hole - Neutron Star merger. The strength of the signal is related to the equation of state of neutron star matter and it increases with the stiffness of the latter. The recent results obtained by NICER suggest a rather stiff equation of state and the expected kilonova signal is therefore strong, at least if the mass of the Black Hole does not exceed $\sim 10 M_\odot$. We compare the predictions obtained by considering equations of state of neutron star matter satisfying the most recent observations and assuming that only one family of compact stars exists with the results predicted in the two-families scenario. In the latter a soft hadronic equation of state produces very compact stellar objects while a rather stiff quark matter equation of state produces massive strange quark stars, satisfying NICER results. The expected kilonova signal in the two-families scenario is very weak: the Strange Quark Star - Black Hole merger does not produce a kilonova signal because, according to simulations, the amount of mass ejected is negligible and the Hadronic Star - Black Hole merger produces a much weaker signal than in the one-family scenario because the hadronic equation of state is very soft. This prediction will be easily tested with the new generation of detectors.Comment: 5 pages, 4 figure