Numerical simulations of magma chamber dynamics at Campi Flegrei, and associated seismicity, deformation and gravity changes

Understanding the complex relationships between quantities measured by volcanic monitoring network and shallow magma processes is a crucial headway for the comprehension of volcanic processes and a more realistic evaluation of the associated hazard. This question is very relevant at Campi Flegrei, a volcanic quiescent caldera immediately north-west of Napoli (Italy). The system activity shows a high fumarole release and periodic ground slow movement (bradyseism) with high seismicity. This activity, with the high people density and the presence of military and industrial buildings, makes Campi Flegrei one of the areas with higher volcanic hazard in the world. In such a context my thesis has been focused on magma dynamics due to the refilling of shallow magma chambers, and on the geophysical signals detectable by seismic, deformative and gravimetric monitoring networks that are associated with this phenomenologies. Indeed, the refilling of magma chambers is a process frequently occurring just before a volcanic eruption; therefore, the faculty of identifying this dynamics by means of recorded signal analysis is important to evaluate the short term volcanic hazard. The space-time evolution of dynamics due to injection of new magma in the magma chamber has been studied performing numerical simulations with, and implementing additional features in, the code GALES (Longo et al., 2006), recently developed and still on the upgrade at the Istituto Nazionale di Geofisica e Vulcanologia in Pisa (Italy). GALES is a finite element code based on a physico-mathematical two dimensional, transient model able to treat fluids as multiphase homogeneous mixtures, compressible to incompressible. The fundamental equations of mass, momentum and energy balance are discretised both in time and space using the Galerkin Least-Squares and discontinuity-capturing stabilisation technique. The physical properties of the mixture are computed as a function of local conditions of magma composition, pressure and temperature.The model features enable to study a broad range of phenomenologies characterizing pre and sin-eruptive magma dynamics in a wide domain from the volcanic crater to deep magma feeding zones. The study of displacement field associated with the simulated fluid dynamics has been carried out with a numerical code developed by the Geophysical group at the University College Dublin (O’Brien and Bean, 2004b), with whom we started a very profitable collaboration. In this code, the seismic wave propagation in heterogeneous media with free surface (e.g. the Earth’s surface) is simulated using a discrete elastic lattice where particle interactions are controlled by the Hooke’s law. This method allows to consider medium heterogeneities and complex topography. The initial and boundary conditions for the simulations have been defined within a coordinate project (INGV-DPC 2004-06 V3_2 “Research on active volcanoes, precursors, scenarios, hazard and risk - Campi Flegrei”), to which this thesis contributes, and many researchers experienced on Campi Flegrei in volcanological, seismic, petrological, geochemical fields, etc. collaborate. Numerical simulations of magma and rock dynamis have been coupled as described in the thesis. The first part of the thesis consists of a parametric study aimed at understanding the eect of the presence in magma of carbon dioxide in magma in the convection dynamics. Indeed, the presence of this volatile was relevant in many Campi Flegrei eruptions, including some eruptions commonly considered as reference for a future activity of this volcano. A set of simulations considering an elliptical magma chamber, compositionally uniform, refilled from below by a magma with volatile content equal or dierent from that of the resident magma has been performed. To do this, a multicomponent non-ideal magma saturation model (Papale et al., 2006) that considers the simultaneous presence of CO2 and H2O, has been implemented in GALES. Results show that the presence of CO2 in the incoming magma increases its buoyancy force promoting convection ad mixing. The simulated dynamics produce pressure transients with frequency and amplitude in the sensitivity range of modern geophysical monitoring networks such as the one installed at Campi Flegrei . In the second part, simulations more related with the Campi Flegrei volcanic system have been performed. The simulated system has been defined on the basis of conditions consistent with the bulk of knowledge of Campi Flegrei and in particular of the Agnano-Monte Spina eruption (4100 B.P.), commonly considered as reference for a future high intensity eruption in this area. The magmatic system has been modelled as a long dyke refilling a small shallow magma chamber; magmas with trachytic and phonolitic composition and variable volatile content of H2O and CO2 have been considered. The simulations have been carried out changing the condition of magma injection, the system configuration (magma chamber geometry, dyke size) and the resident and refilling magma composition and volatile content, in order to study the influence of these factors on the simulated dynamics. Simulation results allow to follow each step of the gas-rich magma ascent in the denser magma, highlighting the details of magma convection and mixing. In particular, the presence of more CO2 in the deep magma results in more ecient and faster dynamics. Through this simulations the variation of the gravimetric field has been determined. Afterward, the space-time distribution of stress resulting from numerical simulations have been used as boundary conditions for the simulations of the displacement field imposed by the magmatic dynamics on rocks. The properties of the simulated domain (rock density, P and S wave velocities) have been based on data from literature on active and passive tomographic experiments, obtained through a collaboration with A. Zollo at the Dept. of Physics of the Federici II Univeristy in Napoli. The elasto-dynamics simulations allow to determine the variations of the space-time distribution of deformation and the seismic signal associated with the studied magmatic dynamics. In particular, results show that these dynamics induce deformations similar to those measured at Campi Flegrei and seismic signals with energies concentrated on the typical frequency bands observed in volcanic areas. The present work shows that an approach based on the solution of equations describing the physics of processes within a magmatic fluid and the surrounding rock system is able to recognise and describe the relationships between geophysical signals detectable on the surface and deep magma dynamics. Therefore, the results suggest that the combined study of geophysical data and informations from numerical simulations can allow in a near future a more ecient evaluation of the short term volcanic hazard.

The language of action. How language translates the dynamics of our actions.

The general aim of the thesis was to investigate how and to what extent the characteristics of action organization are reflected in language, and how they influence language processing and understanding. Even though a huge amount of research has been devoted to the study of the motor effects of language, this issue is very debated in literature. Namely, the majority of the studies have focused on low-level motor effects such as effector-relatedness of action, whereas only a few studies have started to systematically investigate how specific aspects of action organization are encoded and reflected in language. After a review of previous studies on the relationship between language comprehension and action (chapter 1) and a critical discussion of some of them (chapter 2), the thesis is composed by three experimental chapters, each devoted to a specific aspect of action organization. Chapter 3 presents a study designed with the aim to disentangle the effective time course of the involvement of the motor system during language processing. Three kinematics experiments were designed in order to determine whether and, at which stage of motor planning and execution effector-related action verbs influence actions executed with either the same or a different effector. Results demonstrate that the goal of an action can be linguistically re-activated, producing a modulation of the motor response. In chapter 4, a second study investigates the interplay between the role of motor perspective (agent) and the organization of action in motor chains. More specifically, this kinematics study aims at deepening how goal can be translated in language, using as stimuli simple sentences composed by a pronoun (I, You, He/She) and a verb. Results showed that the perspective activated by the pronoun You reflects the motor pattern of the “agent” combined with the chain structure of the verb. These data confirm an early involvement of the motor system in language processing, suggesting that it is specifically modulated by the activation of the agent’s perspective. In chapter 5, the issue of perspective is specifically investigated, focusing on its role in language comprehension. In particular, this study aimed at determining how a specific perspective (induced for example by a personal pronoun) modulates motor behaviour during and after language processing. A classical compatibility effect (the Action-sentence compatibility effect) has been used to this aim. In three behavioural experiments the authors investigated how the ACE is modulated by taking first or third person perspective. Results from these experiments showed that the ACE effect occurs only when a first-person perspective is activated by the sentences used as stimuli. Overall, the data from this thesis contributed to disentangle several aspects of how action organization is translated in language, and then reactivated during language processing. This constitutes a new contribution to the field, adding lacking information on how specific aspects such as goal and perspective are linguistically described. In addition, these studies offer a new point of view to understand the functional implications of the involvement of the motor system during language comprehension, specifically from the point of view of our social interactions.

Dynamic identification of structures: experimental assessment of modal parameteres through methods in frequency domain, in time-frequency domain and model updating

Among the experimental methods commonly used to define the behaviour of a full scale system, dynamic tests are the most complete and efficient procedures. A dynamic test is an experimental process, which would define a set of characteristic parameters of the dynamic behaviour of the system, such as natural frequencies of the structure, mode shapes and the corresponding modal damping values associated. An assessment of these modal characteristics can be used both to verify the theoretical assumptions of the project, to monitor the performance of the structural system during its operational use. The thesis is structured in the following chapters: The first introductive chapter recalls some basic notions of dynamics of structure, focusing the discussion on the problem of systems with multiply degrees of freedom (MDOF), which can represent a generic real system under study, when it is excited with harmonic force or in free vibration. The second chapter is entirely centred on to the problem of dynamic identification process of a structure, if it is subjected to an experimental test in forced vibrations. It first describes the construction of FRF through classical FFT of the recorded signal. A different method, also in the frequency domain, is subsequently introduced; it allows accurately to compute the FRF using the geometric characteristics of the ellipse that represents the direct input-output comparison. The two methods are compared and then the attention is focused on some advantages of the proposed methodology. The third chapter focuses on the study of real structures when they are subjected to experimental test, where the force is not known, like in an ambient or impact test. In this analysis we decided to use the CWT, which allows a simultaneous investigation in the time and frequency domain of a generic signal x(t). The CWT is first introduced to process free oscillations, with excellent results both in terms of frequencies, dampings and vibration modes. The application in the case of ambient vibrations defines accurate modal parameters of the system, although on the damping some important observations should be made. The fourth chapter is still on the problem of post processing data acquired after a vibration test, but this time through the application of discrete wavelet transform (DWT). In the first part the results obtained by the DWT are compared with those obtained by the application of CWT. Particular attention is given to the use of DWT as a tool for filtering the recorded signal, in fact in case of ambient vibrations the signals are often affected by the presence of a significant level of noise. The fifth chapter focuses on another important aspect of the identification process: the model updating. In this chapter, starting from the modal parameters obtained from some environmental vibration tests, performed by the University of Porto in 2008 and the University of Sheffild on the Humber Bridge in England, a FE model of the bridge is defined, in order to define what type of model is able to capture more accurately the real dynamic behaviour of the bridge. The sixth chapter outlines the necessary conclusions of the presented research. They concern the application of a method in the frequency domain in order to evaluate the modal parameters of a structure and its advantages, the advantages in applying a procedure based on the use of wavelet transforms in the process of identification in tests with unknown input and finally the problem of 3D modeling of systems with many degrees of freedom and with different types of uncertainty.

Harmful algae and their potential impacts on the coastal ecosystem: growth and toxin production dynamics

The main goal of the present thesis was to study some harmful algal species which cause blooms in Italian coastal waters, leading to consequences for human health, coastal ecosystem, fishery and tourism. In particular, in the first part of this thesis the toxicity of Adriatic strains of the raphidophyte Fibrocapsa japonica was investigated. Despite several hypotheses have been proposed for the toxic mechanism of the raphidophytes, especially for the species Chattonella antiqua and C. marina, which have been studied more extensively, just a few studies on the toxic effects of these species for different organisms were reported. Moreover, a careful reading of the literature evidenced as any ichthyotoxic events reported worldwide can be linked to F. japonica blooms. Although recently several studies were performed on F. japonica strains from the USA, Japan, Australia, New Zealand, the Netherlands, Germany, and France in order to characterize their growth and toxicity features, the work reported in this thesis results one of the first investigation on the toxic effects of F. japonica for different organisms, such as bacteria, crustaceans and fish. Mortality effects, together with haemolysis of fish erythrocytes, probably due to the relatively high amount of PUFAs produced by this species, were observed. Mortality for fish, however, was reported only at a high cell density and after a long exposition period (9-10 days); moreover a significant increase of H2O2 obtained in the tanks where sea basses were exposed to F. japonica was also relevant. This result may justify the absence of ichthyotoxic events in the Italian coasts, despite F. japonica blooms detected in these areas were characterized by high cell densities. This work reports also a first complete characterization of the fatty acids produced and extracellularly released by the Adriatic F. japonica, and results were also compared with the fatty acid profile of other strains. The absence of known brevetoxins in F. japonica algal extracts was also highlighted, leading to the hypothesis that the toxicity of F. japonica may be due to a synergic effect of PUFAs and ROS. Another microalgae that was studied in this thesis is the benthic dinoflagellate Ostreopsis cf. ovata. This species was investigated with the aim to investigate the effect of environmental parameters on its growth and toxicity. O. cf. ovata, in fact, shows different blooming periods along the Italian coasts and even the reported toxic effects are variable. The results of this work confirmed the high variability in the growth dynamic and toxin content of several Italian strains which were isolated in recent years along the Adriatic and Tyrrhenian Seas. Moreover, the effects of temperature and salinity on the behaviour of the different isolates are in good agreement with the results obtained from field surveys, which evidence as the environmental parameters are important factors modulating O. cf. ovata proliferation. Another relevant result that was highlighted is the anomaly in the production of palytoxin-like compounds reported by one of the studied isolate, in particular the one isolated in 2008 in Ancona (Adriatic Sea). Only this strain reported the absence of two (ovatoxin-b and –c) of the five ovatoxins so far known in the toxin profile and a different relative abundance of the other toxins. The last aspect that was studied in this thesis regards the toxin biosythesis. In fact, toxins produced (palytoxin-like compounds) or supposed to be produced (brevetoxin-like compounds) by O. cf. ovata and F. japonica, respectively, are polyketides, which are highly oxygenated compounds synthesized by complex enzymes known as polyketide synthase (PKS) enzymes. These enzymes are multi-domain complexes that structurally and functionally resemble the fatty acid synthases (FASs). This work reports the first study of PKS proteins in the dinoflagellates O. cf. ovata, C. monotis and in the raphidophyte F. japonica. For the first time some PKSs were identified in these species, confirming the presence of PKS proteins predicted by the in silico translation of the transcripts found in K. brevis also in other species. The identification of O. cf. ovata PKSs and the localization of the palytoxin-like compounds produced by this dinoflagellate in a similar location (chloroplast) as that observed for other dinoflagellate and cyanobacterial toxins provides some indication that these proteins may be involved in polyketide biosynthesis. However, their potential function as fatty acid synthases cannot be ruled out, as plant fatty acid synthesis also occurs within chloroplasts. This last hypothesis is also supported by the fact that in all the investigated species, and in particular in F. japonica, PKS proteins were present. Therefore, these results provide an important contribution to the study of the polyketides and of the involvement of PKS proteins in the toxin biosynthesis.

The Simon effect and its time courses: an investigation

The objective of the current thesis is to investigate the temporal dynamics (i.e., time courses) of the Simon effect, both from a theoretical and experimental point of view, for a better understanding of whether a) one or more process are responsible for the Simon effect and b) how this/these mechanism/s differently influence performance. In the first theoretical (i.e., “Theoretical Overview”) part, I examined in detail the process and justification for analyzing the temporal dynamics of the Simon effect and the assumptions that underlie interpretation of the results which have been obtained in the existing literature so far. In the second part (“Experimental Investigations”), though, I experimentally investigated several issues which the existing literature left unsolved, in order to get further evidence in favor or in contrast with the mainstream models which are currently used to account for the different Simon effect time courses. Some points about the experiments are worth mentioning: First, all the experiments were conducted in the laboratory, facing participants with stimuli presented on a PC screen and then recording their responses. Both stimuli presentation and response collection was controlled by the E-Prime software. The dependent variables of interest were always behavioral measures of performance, such as velocity and accuracy. Second, the most part of my experiments had been conducted at the Communication Sciences Department (University of Bologna), under Prof. Nicoletti’s supervision. The remaining part, though, had been conducted at the Psychological Sciences Department of Purdue University (West Lafayette, Indiana, USA), where I collaborated for one year as a visiting student with Prof. Proctor and his team. Third, my experimental pool was entirely composed by healthy and young students, since the cognitive functioning of elderly people was not the target of my research.

A Multilevel Model with Time Series Components for the Analysis of Tribal Art Prices

In the present work we perform an econometric analysis of the Tribal art market. To this aim, we use a unique and original database that includes information on Tribal art market auctions worldwide from 1998 to 2011. In Literature, art prices are modelled through the hedonic regression model, a classic fixed-effect model. The main drawback of the hedonic approach is the large number of parameters, since, in general, art data include many categorical variables. In this work, we propose a multilevel model for the analysis of Tribal art prices that takes into account the influence of time on artwork prices. In fact, it is natural to assume that time exerts an influence over the price dynamics in various ways. Nevertheless, since the set of objects change at every auction date, we do not have repeated measurements of the same items over time. Hence, the dataset does not constitute a proper panel; rather, it has a two-level structure in that items, level-1 units, are grouped in time points, level-2 units. The main theoretical contribution is the extension of classical multilevel models to cope with the case described above. In particular, we introduce a model with time dependent random effects at the second level. We propose a novel specification of the model, derive the maximum likelihood estimators and implement them through the E-M algorithm. We test the finite sample properties of the estimators and the validity of the own-written R-code by means of a simulation study. Finally, we show that the new model improves considerably the fit of the Tribal art data with respect to both the hedonic regression model and the classic multilevel model.

The coupling between electron transfer and Protein/Solvent Dynamics in Photosynthetic Reaction Centers: Spectroscopic Studies in Amorphous Matrices

We investigated at the molecular level protein/solvent interactions and their relevance in protein function through the use of amorphous matrices at room temperature. As a model protein, we used the bacterial photosynthetic reaction center (RC) of Rhodobacter sphaeroides, a pigment protein complex which catalyzes the light-induced charge separation initiating the conversion of solar into chemical energy. The thermal fluctuations of the RC and its dielectric conformational relaxation following photoexcitation have been probed by analyzing the recombination kinetics of the primary charge-separated (P+QA-) state, using time resolved optical and EPR spectroscopies. We have shown that the RC dynamics coupled to this electron transfer process can be progressively inhibited at room temperature by decreasing the water content of RC films or of RC-trehalose glassy matrices. Extensive dehydration of the amorphous matrices inhibits RC relaxation and interconversion among conformational substates to an extent comparable to that attained at cryogenic temperatures in water-glycerol samples. An isopiestic method has been developed to finely tune the hydration level of the system. We have combined FTIR spectral analysis of the combination and association bands of residual water with differential light-minus-dark FTIR and high-field EPR spectroscopy to gain information on thermodynamics of water sorption, and on structure/dynamics of the residual water molecules, of protein residues and of RC cofactors. The following main conclusions were reached: (i) the RC dynamics is slaved to that of the hydration shell; (ii) in dehydrated trehalose glasses inhibition of protein dynamics is most likely mediated by residual water molecules simultaneously bound to protein residues and sugar molecules at the protein-matrix interface; (iii) the local environment of cofactors is not involved in the conformational dynamics which stabilizes the P+QA-; (iv) this conformational relaxation appears to be rather delocalized over several aminoacidic residues as well as water molecules weakly hydrogen-bonded to the RC.

The Dynamics of Passive Torsional Fatigue Test Rigs: Innovative Applications of Universal Joints

The dynamics of a passive back-to-back test rig have been characterised, leading to a multi-coordinate approach for the analysis of arbitrary test configurations. Universal joints have been introduced into a typical pre-loaded back-to-back system in order to produce an oscillating torsional moment in a test specimen. Two different arrangements have been investigated using a frequency-based sub-structuring approach: the receptance method. A numerical model has been developed in accordance with this theory, allowing interconnection of systems with two-coordinates and closed multi-loop schemes. The model calculates the receptance functions and modal and deflected shapes of a general system. Closed form expressions of the following individual elements have been developed: a servomotor, damped continuous shaft and a universal joint. Numerical results for specific cases have been compared with published data in literature and experimental measurements undertaken in the present work. Due to the complexity of the universal joint and its oscillating dynamic effects, a more detailed analysis of this component has been developed. Two models have been presented. The first represents the joint as two inertias connected by a massless cross-piece. The second, derived by the dynamic analysis of a spherical four-link mechanism, considers the contribution of the floating element and its gyroscopic effects. An investigation into non-linear behaviour has led to a time domain model that utilises the Runge-Kutta fourth order method for resolution of the dynamic equations. It has been demonstrated that the torsional receptances of a universal joint, derived using the simple model, result in representation of the joint as an equivalent variable inertia. In order to verify the model, a test rig has been built and experimental validation undertaken. The variable inertia of a universal joint has lead to a novel application of the component as a passive device for the balancing of inertia variations in slider-crank mechanisms.

Modeling the spatial dynamics of economic models

The advances that have been characterizing spatial econometrics in recent years are mostly theoretical and have not found an extensive empirical application yet. In this work we aim at supplying a review of the main tools of spatial econometrics and to show an empirical application for one of the most recently introduced estimators. Despite the numerous alternatives that the econometric theory provides for the treatment of spatial (and spatiotemporal) data, empirical analyses are still limited by the lack of availability of the correspondent routines in statistical and econometric software. Spatiotemporal modeling represents one of the most recent developments in spatial econometric theory and the finite sample properties of the estimators that have been proposed are currently being tested in the literature. We provide a comparison between some estimators (a quasi-maximum likelihood, QML, estimator and some GMM-type estimators) for a fixed effects dynamic panel data model under certain conditions, by means of a Monte Carlo simulation analysis. We focus on different settings, which are characterized either by fully stable or quasi-unit root series. We also investigate the extent of the bias that is caused by a non-spatial estimation of a model when the data are characterized by different degrees of spatial dependence. Finally, we provide an empirical application of a QML estimator for a time-space dynamic model which includes a temporal, a spatial and a spatiotemporal lag of the dependent variable. This is done by choosing a relevant and prolific field of analysis, in which spatial econometrics has only found limited space so far, in order to explore the value-added of considering the spatial dimension of the data. In particular, we study the determinants of cropland value in Midwestern U.S.A. in the years 1971-2009, by taking the present value model (PVM) as the theoretical framework of analysis.

Hydrodynamical simulations of early-type galaxies: effects of galaxy shape and stellar dynamics on hot coronae

Early-Type galaxies (ETGs) are embedded in hot (10^6-10^7 K), X-ray emitting gaseous haloes, produced mainly by stellar winds and heated by Type Ia supernovae explosions, by the thermalization of stellar motions and occasionally by the central super-massive black hole (SMBH). In particular, the thermalization of the stellar motions is due to the interaction between the stellar and the SNIa ejecta and the hot interstellar medium (ISM) already residing in the ETG. A number of different astrophysical phenomena determine the X-ray properties of the hot ISM, such as stellar population formation and evolution, galaxy structure and internal kinematics, Active Galactic Nuclei (AGN) presence, and environmental effects. With the aid of high-resolution hydrodynamical simulations performed on state-of-the-art galaxy models, in this Thesis we focus on the effects of galaxy shape, stellar kinematics and star formation on the evolution of the X-ray coronae of ETGs. Numerical simulations show that the relative importance of flattening and rotation are functions of the galaxy mass: at low galaxy masses, adding flattening and rotation induces a galactic wind, thus lowering the X-ray luminosity; at high galaxy masses the angular momentum conservation keeps the central regions of rotating galaxies at low density, whereas in non-rotating models a denser and brighter atmosphere is formed. The same dependence from the galaxy mass is present in the effects of star formation (SF): in light galaxies SF contributes to increase the spread in Lx, while at high galaxy masses the halo X-ray properties are marginally sensitive to SF effects. In every case, the star formation rate at the present epoch quite agrees with observations, and the massive, cold gaseous discs are partially or completely consumed by SF on a time-scale of few Gyr, excluding the presence of young stellar discs at the present epoch.

Identity dynamics and the emergence of new organizational arrangements: A multi-level study

Organizational and institutional scholars have advocated the need to examine how processes originating at an individual level can change organizations or even create new organizational arrangements able to affect institutional dynamics (Chreim et al., 2007; Powell & Colyvas, 2008; Smets et al., 2012). Conversely, research on identity work has mainly investigated the different ways individuals can modify the boundaries of their work in actual occupations, thus paying particular attention to ‘internal’ self-crafting (e.g. Wrzesniewski & Dutton, 2001). Drawing from literatures on possible and alternative self and on positive organizational scholarship (e.g., Obodaru, 2012; Roberts & Dutton, 2009), my argument is that individuals’ identity work can go well beyond the boundaries of internal self-crafting to the creation of new organizational arrangements. In this contribution I analyze, through multiple case studies, healthcare professionals who spontaneously participated in the creation of new organizational arrangements, namely health structures called Community Hospitals. The contribution develops this form of identity work by building a grounded model. My findings disclose the process that leads from the search for the enactment of different self-concepts to positive identities, through the creation of a new organizational arrangement. I contend that this is a particularly complex form of collective identity work because it requires, to be successful, concerted actions of several internal, external and institutional actors, and it also requires balanced tensions that – at the same time - enable individuals’ aspirations and organizational equilibrium. I name this process organizational collective crafting. Moreover I inquire the role of context in supporting the triggering power of those unrealized selves. I contribute to the comprehension of the consequences of self-comparisons, organizational identity variance, and positive identity. The study bears important insights on how identity work originating from individuals can influence organizational outcomes and larger social systems.

Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.