In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will be therefore devoted to the study of the entanglement entropy in one- dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting model. We will derive its Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap will be analysed. In the second part of the thesis we will instead study the dynamics of correlators after a quantum quench , which represent a powerful tool to measure how perturbations and signals propagate through a quantum chain. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, which will be both studied by means of a semi-classical approach. Moreover in the last chapter we will demonstrate a general result about the dynamics of correlation functions of local observables after a quantum quench in integrable systems. In particular we will show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations).

In the thesis, we discuss some aspects of 1D quantum systems related to entanglement entropies; in particular, we develop a new numerical method for the detection of crossovers in Luttinger liquids, and we discuss the behaviour of Rényi entropies in open conformal systems, when the boundary conditions preserve their conformal invariance.

In this thesis we discuss a representation of quantum mechanics and quantum and statistical field theory based on a functional renormalization flow equation for the one-particle-irreducible average effective action, and we employ it to get information on some specific systems.

Il presente lavoro si rivolge all’analisi del ruolo delle forme metaforiche nella divulgazione della fisica contemporanea. Il focus è sugli aspetti cognitivi: come possiamo spiegare concetti fisici formalmente complessi ad un audience di non-esperti senza ‘snaturarne’ i significati disciplinari (comunicazione di ‘buona fisica’)? L’attenzione è sulla natura stessa della spiegazione e il problema riguarda la valutazione dell’efficacia della spiegazione scientifica a non-professionisti. Per affrontare tale questione, ci siamo orientati alla ricerca di strumenti formali che potessero supportarci nell’analisi linguistica dei testi. La nostra attenzione si è rivolta al possibile ruolo svolto dalle forme metaforiche nella costruzione di significati disciplinarmente validi. Si fa in particolare riferimento al ruolo svolto dalla metafora nella comprensione di nuovi significati a partire da quelli noti, aspetto fondamentale nel caso dei fenomeni di fisica contemporanea che sono lontani dalla sfera percettiva ordinaria. In particolare, è apparsa particolarmente promettente come strumento di analisi la prospettiva della teoria della metafora concettuale. Abbiamo allora affrontato il problema di ricerca analizzando diverse forme metaforiche di particolare rilievo prese da testi di divulgazione di fisica contemporanea. Nella tesi viene in particolare discussa l’analisi di un case-study dal punto di vista della metafora concettuale: una analogia di Schrödinger per la particella elementare. I risultati dell’analisi suggeriscono che la metafora concettuale possa rappresentare uno strumento promettente sia per la valutazione della qualità delle forme analogiche e metaforiche utilizzate nella spiegazione di argomenti di fisica contemporanea che per la creazione di nuove e più efficaci metafore. Inoltre questa prospettiva di analisi sembra fornirci uno strumento per caratterizzare il concetto stesso di ‘buona fisica’. Riteniamo infine che possano emergere altri risultati di ricerca interessanti approfondendo l’approccio interdisciplinare tra la linguistica e la fisica. / The present work deals with the role of metaphorical thinking in the public communication of contemporary physics. We focus on the cognitive aspects: how to disseminate complicated formal physical concepts to a non-professional public maintaining the ‘correct’ disciplinary meaning, that is aiming at communication of ‘good physics’. The focus is on the nature of the explanation and the problem is how to evaluate the effectiveness of public scientific explanation of advanced physical topics to a non-professional audience. For this purpose we have looked for formal tools apt at analyzing the linguistic features of dissemination texts. We have drawn our attention to the role of analogical and metaphorical forms in the construction of ‘actual’ physical meanings because they obviously play an important role in introducing new concepts from previous ones when dealing with contemporary physics phenomena that are far from the ordinary perceptive domain. For the purpose of our investigation the conceptual metaphor perspective, within the framework of cognitive linguistics, appeared to be the most promising analytical tool. We investigate the research problem by analyzing a set of ‘relevant’ analogies and metaphors taken from popular science literature. In particular an analysis of a case study, within the framework of conceptual metaphor, is presented : Schrödinger’s analogy for ‘elementary particle’. The results of the analysis suggest that the conceptual metaphor perspective might be a potential tool both to assess the quality of analogical forms used in explanation of contemporary physics and to design new and ‘better’ analogies and metaphors. Besides, in a recursive process this analysis could help to focus on those meaningful cognitive aspects that characterize, and refine, a ‘complete’ and ‘correct’ physical concept. We think that fruitful results of inquiry might come from a deeper interdisciplinary approach between linguistics and physics.

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. / 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.

In this thesis the evolution of the techno-social systems analysis methods will be reported, through the explanation of the various research experience directly faced. The first case presented is a research based on data mining of a dataset of words association named Human Brain Cloud: validation will be faced and, also through a non-trivial modeling, a better understanding of language properties will be presented. Then, a real complex system experiment will be introduced: the WideNoise experiment in the context of the EveryAware european project. The project and the experiment course will be illustrated and data analysis will be displayed. Then the Experimental Tribe platform for social computation will be introduced . It has been conceived to help researchers in the implementation of web experiments, and aims also to catalyze the cumulative growth of experimental methodologies and the standardization of tools cited above. In the last part, three other research experience which already took place on the Experimental Tribe platform will be discussed in detail, from the design of the experiment to the analysis of the results and, eventually, to the modeling of the systems involved. The experiments are: CityRace, about the measurement of human traffic-facing strategies; laPENSOcosì, aiming to unveil the political opinion structure; AirProbe, implemented again in the EveryAware project framework, which consisted in monitoring air quality opinion shift of a community informed about local air pollution. At the end, the evolution of the technosocial systems investigation methods shall emerge together with the opportunities and the threats offered by this new scientific path.

Higher gauge theory arises naturally in superstring theory, but many of its features remain obscure. In this thesis, after an exposition of the bacis tools in local higher gauge theory, a higher gauge Chern-Simons model is defined. We discuss the classical equations of motion as well as the behaviour of the gauge anomaly. We perform canonical quantization and we introduce two possible quantization schemes for the model. We also expound higher parallel transport in higher gauge theory, and we speculate that it can provide Wilson surfaces as topological observables for the higher gauge Chern-Simons theory.

In this thesis, my work in the Compact Muon Solenoid (CMS) experiment on the search for the neutral Minimal Supersymmetric Standard Model (MSSM) Higgs decaying into two muons is presented. The search is performed on the full data collected during the years 2011 and 2012 by CMS in proton-proton collisions at CERN Large Hadron Collider (LHC). The MSSM is explored within the most conservative benchmark scenario, m_h^{max}, and within its modified versions, m_h^{mod +} and m_h^{mod -}. The search is sensitive to MSSM Higgs boson production in association with a b\bar{b} quark pair and to the gluon-gluon fusion process. In the m_h^{max} scenario, the results exclude values of tanB larger than 15 in the m_A range 115-200 GeV, and values of tanB greater than 30 in the m_A range up to 300 GeV. There are no significant differences in the results obtained within the three different scenarios considered. Comparisons with other neutral MSSM Higgs searches are shown.

Sono indagate le implicazioni teoriche e sperimentali derivanti dall'assunzione, nella teoria della relatività speciale, di un criterio di sincronizzazione (detta assoluta) diverso da quello standard. La scelta della sincronizzazione assoluta è giustificata da alcune considerazioni di carattere epistemologico sullo status di fenomeni quali la contrazione delle lunghezze e la dilatazione del tempo. Oltre che a fornire una diversa interpretazione, la sincronizzazione assoluta rappresenta una estensione del campo di applicazione della relatività speciale in quanto può essere attuata anche in sistemi di riferimento accelerati. Questa estensione consente di trattare in maniera unitaria i fenomeni sia in sistemi di riferimento inerziali che accelerati. L'introduzione della sincronizzazione assoluta implica una modifica delle trasformazioni di Lorentz. Una caratteristica di queste nuove trasformazioni (dette inerziali) è che la trasformazione del tempo è indipendente dalle coordinate spaziali. Le trasformazioni inerziali sono ottenute nel caso generale tra due sistemi di riferimento aventi velocità (assolute) u1 e u2 comunque orientate. Viene mostrato che le trasformazioni inerziali possono formare un gruppo pur di prendere in considerazione anche riferimenti non fisicamente realizzabili perché superluminali. È analizzato il moto rigido secondo Born di un corpo esteso considerando la sincronizzazione assoluta. Sulla base delle trasformazioni inerziali si derivano le trasformazioni per i campi elettromagnetici e le equazioni di questi campi (che sostituiscono le equazioni di Maxwell). Si mostra che queste equazioni contengono soluzioni in assenza di cariche che si propagano nello spazio come onde generalmente anisotrope in accordo con quanto previsto dalle trasformazioni inerziali. L'applicazione di questa teoria elettromagnetica a sistemi accelerati mostra l'esistenza di fenomeni mai osservati che, pur non essendo in contraddizione con la relatività standard, ne forzano l'interpretazione. Viene proposto e descritto un esperimento in cui uno di questi fenomeni è misurabile. / Theoretical and experimental implications in the theory of special relativity resulting from the assumption of synchronization criterion (called absolute) other than the standard, are investigated. The choice of the absolute synchronization is justified by considerations of epistemological status of phenomena such as length contraction and time dilation. The absolute synchronization provides a different interpretation of the theory and is an extension of the scope of special relativity as it can be implemented even in accelerated frames of reference. Therefore it is possible to treat in a unified way the phenomena in both inertial and accelerated frame. The introduction of the absolute synchronization implies a modification of the Lorentz transformations. A characteristic of these new transformations (called inertial) is that the transformation of time is independent of the spatial coordinates . The inertial transformations are obtained in the general case between two systems having (absolute) velocity u1 and u2 in any orientation . It is shown that the inertial transformations can have a group structure if unphysical superluminal frames are considered too. The Born rigid motion of an extended body is analyzed by applying the absolute synchronization. Transformations for electromagnetic fields and the equations of these fields (substituting Maxwell's equations) are derived on the basis of inertial transformations. It is shown that these equations contain solutions in the absence of charges that propagate through space as waves generally anisotropic as provided by the inertial transformations in the propagation of light. The application of electromagnetic theory to accelerated systems show the existence of phenomena never observed before. These phenomena, although not in contradiction with standard relativity, force the interpretation of the theory. An experiment in which one of these phenomena is measurable is proposed and described in this thesis.

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.