Quantum Correlations in Field Theory and Integrable Systems

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).

Perturbative and non perturbative effects in the Standard Model and orbifolded ADS/CFT based theories

We study some perturbative and nonperturbative effects in the framework of the Standard Model of particle physics. In particular we consider the time dependence of the Higgs vacuum expectation value given by the dynamics of the StandardModel and study the non-adiabatic production of both bosons and fermions, which is intrinsically non-perturbative. In theHartree approximation, we analyze the general expressions that describe the dissipative dynamics due to the backreaction of the produced particles. Then, we solve numerically some relevant cases for the Standard Model phenomenology in the regime of relatively small oscillations of the Higgs vacuum expectation value (vev). As perturbative effects, we consider the leading logarithmic resummation in small Bjorken x QCD, concentrating ourselves on the Nc dependence of the Green functions associated to reggeized gluons. Here the eigenvalues of the BKP kernel for states of more than three reggeized gluons are unknown in general, contrary to the large Nc limit (planar limit) case where the problem becomes integrable. In this contest we consider a 4-gluon kernel for a finite number of colors and define some simple toy models for the configuration space dynamics, which are directly solvable with group theoretical methods. In particular we study the depencence of the spectrum of thesemodelswith respect to the number of colors andmake comparisons with the planar limit case. In the final part we move on the study of theories beyond the Standard Model, considering models built on AdS5 S5/Γ orbifold compactifications of the type IIB superstring, where Γ is the abelian group Zn. We present an appealing three family N = 0 SUSY model with n = 7 for the order of the orbifolding group. This result in a modified Pati–Salam Model which reduced to the StandardModel after symmetry breaking and has interesting phenomenological consequences for LHC.

Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Falegnami e muratori a Bologna nel Medioevo: statuti e matricole (1248-1377)

La finalità della tesi è stata quella d'improntare una riflessione sulle società legate all'edilizia nel momento di apice politico ed economico di una città, attiva e importante nel basso Medioevo, come Bologna. Questo tipo di studio, già intrapreso per alcune città dell'Italia centro settentrionale, risulta necessario per comprendere alcune dinamiche politiche, economiche e produttive della realtà cittadina. In particolare, gli obiettivi sono stati quelli di coniugare la vita corporativa dell'arte all'organizzazione lavorativa, individuando gli aspetti legati all'ambito produttivo e valutando, l'evoluzione della società nel passaggio dal Duecento al Trecento. Gli statuti e le matricole, principali fonti compilate dalle due società delle arti e giunte ai nostri giorni, salvo rare eccezioni, completamente inedite sono stati il principale punto di partenza dello studio. Il risultato è la sintesi di alcuni spunti di riflessione emersi dai documenti, quali la mentalità degli uomini che si approcciavano alle arti, le gerarchie nate all'interno delle stesse società, il loro cambiamento e quello legato alla percezione di comunità nel corso dei secoli oltre agli aspetti più prettamente lavorativi e artigianali.

Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

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.

Centro-sinistra e autonomia speciale. La DC trentina tra il 1955 e il 1968

La tesi è una ricerca di storia politica che affianca due diverse “storie” di centro-sinistra, quella nazionale e quella che vide protagonista la Democrazia Cristiana del Trentino. Lo studio analizza i fatti attraverso il filtro delle DC come se quello trentino e quello nazionale fossero due partiti, per poi tentare di capire ciò che accadeva alla loro sinistra alla ricerca dei diversi pesi e dei differenti equilibri che al centro e alla periferia si manifestavano nei rapporti con il PSI e con il PCI, e per osservare le reazioni della Chiesa così da valutare se le gerarchie romane e quelle trentine interagirono in modo differente sugli sviluppi delle rispettive esperienze politiche di quegli anni. Il testo è organizzato in quattro capitoli. Il primo e il secondo (speculari e dedicati allo stesso lustro: 1955-1960) rappresentano un confronto tra i differenti iter d’avvicinamento al centro-sinistra che la politica nazionale e quella trentina sperimentarono nella seconda metà degli anni Cinquanta. Nel terzo capitolo (1960-1964) e nel quarto (1964-1968) le vicende nazionali e quelle locali sono invece raccontate in modo intrecciato, ripercorrendo le diverse fasi dell’alleanza tra Democrazia Cristiana e Partito Socialista, e nel contempo dando conto della trasformazione del Trentino da una realtà di tipo agricolo ad una di tipo industriale, del passaggio da una comunità di tipo cattolico tradizionale ad una che si accinge a vivere in un contesto secolarizzato, e da una società che si autopercepisce come periferica ad una che ospita una delle contestazioni studentesche più peculiari, incisive e note d’Italia.

Learning Methods and Algorithms for Semantic Text Classification across Multiple Domains

Information is nowadays a key resource: machine learning and data mining techniques have been developed to extract high-level information from great amounts of data. As most data comes in form of unstructured text in natural languages, research on text mining is currently very active and dealing with practical problems. Among these, text categorization deals with the automatic organization of large quantities of documents in priorly defined taxonomies of topic categories, possibly arranged in large hierarchies. In commonly proposed machine learning approaches, classifiers are automatically trained from pre-labeled documents: they can perform very accurate classification, but often require a consistent training set and notable computational effort. Methods for cross-domain text categorization have been proposed, allowing to leverage a set of labeled documents of one domain to classify those of another one. Most methods use advanced statistical techniques, usually involving tuning of parameters. A first contribution presented here is a method based on nearest centroid classification, where profiles of categories are generated from the known domain and then iteratively adapted to the unknown one. Despite being conceptually simple and having easily tuned parameters, this method achieves state-of-the-art accuracy in most benchmark datasets with fast running times. A second, deeper contribution involves the design of a domain-independent model to distinguish the degree and type of relatedness between arbitrary documents and topics, inferred from the different types of semantic relationships between respective representative words, identified by specific search algorithms. The application of this model is tested on both flat and hierarchical text categorization, where it potentially allows the efficient addition of new categories during classification. Results show that classification accuracy still requires improvements, but models generated from one domain are shown to be effectively able to be reused in a different one.

Una scienza plausibile per un oggetto sfuggente. Popolazione, societa e governo nel pensiero politico di T.R. Malthus

Questa tesi è un’analisi storico-concettuale del pensiero politico di Thomas Robert Malthus. Si vedrà in particolar modo come la crisi rivoluzionaria tardo settecentesca, cui si sommano i rivolgimenti economici e sociali connessi alla nascita della produzione manifatturiera, spinge l’autore a ripensare alcuni concetti fondamentali del pensiero politico moderno. Popolazione, società, governo e costituzione sono gli oggetti principali di questa ricerca: il principio di popolazione è la legge scientifica cui il reverendo Malthus ricorre per elaborare le proprie teorie sul governo, il quale deve sempre porsi come scopo quello di preservare – o migliorare – la costituzione della società. La presenza politica di masse di poveri in società conduce l’autore alla ricerca di un principio scientifico in grado di fondare nella natura le gerarchie e la disuguaglianza da più parti contestate; in quanto dipendono da «leggi fondamentali», per Malthus le gerarchie e la disuguaglianza che da esse deriva sono un tratto costitutivo della società. La teologia, la morale e l’economia politica sono scienze di cui l’autore si serve per argomentare intorno all’incontestabile natura della povertà e della disuguaglianza tra i sessi, e per affermare le modalità di una loro proficua amministrazione. In India e in Irlanda, poi, le condizioni naturali di cui il principio di popolazione suggella la necessità si scoprono soggette a sfide del tutto originali rispetto a quelle osservabili in Inghilterra. Lì, allora, lo sforzo malthusiano di costruire una scienza all’altezza della complessità dell’oggetto sociale rivela con somma chiarezza la propria ambizione di naturalizzare la politica e garantire le condizioni di disciplinamento degli individui al lavoro e alla subordinazione. Il dispositivo di naturalizzazione che giace al cuore del sistema malthusiano rappresenta la cifra del problema Malthus che apre questa ricerca e ne scandisce i momenti salienti.

Non perturbative aspects of non equilibrium physics in two dimensional models

The present manuscript focuses on out of equilibrium physics in two dimensional models. It has the purpose of presenting some results obtained as part of out of equilibrium dynamics in its non perturbative aspects. This can be understood in two different ways: the former is related to integrability, which is non perturbative by nature; the latter is related to emergence of phenomena in the out of equilibirum dynamics of non integrable models that are not accessible by standard perturbative techniques. In the study of out of equilibirum dynamics, two different protocols are used througout this work: the bipartitioning protocol, within the Generalised Hydrodynamics (GHD) framework, and the quantum quench protocol. With GHD machinery we study the Staircase Model, highlighting how the hydrodynamic picture sheds new light into the physics of Integrable Quantum Field Theories; with quench protocols we analyse different setups where a non-perturbative description is needed and various dynamical phenomena emerge, such as the manifistation of a dynamical Gibbs effect, confinement and the emergence of Bloch oscillations preventing thermalisation.

Quantum integrability as a new method for exact results on N=2 supersymmetric gauge theories and black holes

In this thesis I show a triple new connection we found between quantum integrability, N=2 supersymmetric gauge theories and black holes perturbation theory. I use the approach of the ODE/IM correspondence between Ordinary Differential Equations (ODE) and Integrable Models (IM), first to connect basic integrability functions - the Baxter’s Q, T and Y functions - to the gauge theory periods. This fundamental identification allows several new results for both theories, for example: an exact non linear integral equation (Thermodynamic Bethe Ansatz, TBA) for the gauge periods; an interpretation of the integrability functional relations as new exact R-symmetry relations for the periods; new formulas for the local integrals of motion in terms of gauge periods. This I develop in all details at least for the SU(2) gauge theory with Nf=0,1,2 matter flavours. Still through to the ODE/IM correspondence, I connect the mathematically precise definition of quasinormal modes of black holes (having an important role in gravitational waves’ obervations) with quantization conditions on the Q, Y functions. In this way I also give a mathematical explanation of the recently found connection between quasinormal modes and N=2 supersymmetric gauge theories. Moreover, it follows a new simple and effective method to numerically compute the quasinormal modes - the TBA - which I compare with other standard methods. The spacetimes for which I show these in all details are in the simplest Nf=0 case the D3 brane in the Nf=1,2 case a generalization of extremal Reissner-Nordström (charged) black holes. Then I begin treating also the Nf=3,4 theories and argue on how our integrability-gauge-gravity correspondence can generalize to other types of black holes in either asymptotically flat (Nf=3) or Anti-de-Sitter (Nf=4) spacetime. Finally I begin to show the extension to a 4-fold correspondence with also Conformal Field Theory (CFT), through the renowned AdS/CFT correspondence.

Gandhi nell'Atlantico Nero: geografie, movimenti, concetti

Questo lavoro ricostruisce l'uso strategico di Gandhi come “significante” nel pensiero politico dell'Atlantico Nero, nella lotta contro la supremazia bianca e nei processi di decolonizzazione. Le pratiche discorsive che hanno stretto alleanze metaforiche con il movimento gandhiano sono evidenziate come un mezzo con cui il discorso politico nero attraversa la linea di separazione tra metropoli e colonie, e sovverte la costruzione spaziale della modernità. L’analisi spazia dall'indomani della Prima guerra mondiale alla seconda metà degli anni Cinquanta. Questa parte di Secolo breve fu caratterizzata dalle due guerre mondiali, dalla Lega contro l'imperialismo e dai congressi panafricani - importanti punti di svolta che consolidarono la consapevolezza di un'esperienza comune di oppressione e sfruttamento razziale. La ricerca si concentra sui circuiti e movimenti editoriali e associativi, come i congressi panafricani (1919-1945), il movimento “New Negro”, l’UNIA di Marcus Garvey, il sindacalismo nero e i movimenti di liberazione africani - in particolare la Positive Action in Ghana, il movimento zikista in Nigeria e la Defiance Campaign in Sud Africa. Nel complesso quadro di gerarchie e idiosincrasie dell'Atlantico Nero, gli scarti semantici dell'uso di Gandhi come tropo politico sono connessi con diverse prospettive e visioni di solidarietà.

Modelling the infrastructure of the “Śivadharma Database”

A Digital Scholarly Edition is a conceptually and structurally sophisticated entity. Throughout the centuries, diverse methodologies have been employed to reconstruct a text transmitted through one or multiple sources, resulting in various edition types. With the advent of digital technology in philology, these practices have undergone a significant transformation, compelling scholars to reconsider their approach in light of the web. In the digital age, philologists are expected to possess (too) advanced technical skills to prepare interactive and enriched editions, even though, in most cases, only mechanical or documentary editions are published online. The Śivadharma Database is a web Content Management System (CMS) designed to facilitate the preparation, publication, and updating of Digital Scholarly Editions. By providing scholars with a user-friendly CRUD web application to reconstruct and annotate a text, they can prepare their textus with additional components such as apparatus, notes, translations, citations, and parallels. It is possible by leveraging an annotation system based on HTML and graph data structure. This choice is made because the text entity is multidimensional and multifaceted, even if its sequential presentation constrains it. In particular, editions of South Asian texts of the Śivadharma corpus, the case study of this research, contain a series of phenomena that are difficult to manage formally, such as overlapping hierarchies. Hence, it becomes necessary to establish the data structure best suited to represent this complexity. In Śivadharma Database, the textus is an HTML file readily displayable. Textual fragments, annotated via an interface without requiring philologists to write code and saved in the backend, form the atomic unit of multiple relationships organised in a graph database. This approach enables the formal representation of complex and overlapping textual phenomena, allowing for good annotation expressiveness with minimal effort to learn the relevant technologies during the editing workflow.