Entanglement Entropies in One-Dimensional Systems

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.

Design of a new harrow type wool transport mechanism to reduce fibre entanglement

The wool is entangled at several stages of its processing. In the conventional scouring machines, the prongs or the rakes agitate the wool and lead the fiber entanglement. Several scouring systems have been commercialized in order to reduce the fiber entanglement. In spite of the existing technologies, the conventional scouring machines are widely used in wool processing. In this thesis, a new approach for the harrow type wool transport mechanism has been introduced. The proposed mechanism has been designed based on the motion of the conventional harrow type wool transport mechanism by exploiting new synthesis concepts. The developed structure has been synthesized based on the Hrones and Nelson's "Atlas of four bar linkages". The four bar linkage has been applied for the desired trajectory of the developed wool transport mechanism. The prongs of the developed mechanism immerse the wool into the scouring liquor and gently propel forward toward the end of the machine with approximately straight line motion in a certain length instead of circular or elliptical motion typical of the conventional machines.

The stratigraphic record of the quaternary sea level fluctuations and the impact of the post-glacial sea level rise (Termination I) in the Adriatic basin (Mediterranean sea)

The modern stratigraphy of clastic continental margins is the result of the interaction between several geological processes acting on different time scales, among which sea level oscillations, sediment supply fluctuations and local tectonics are the main mechanisms. During the past three years my PhD was focused on understanding the impact of each of these process in the deposition of the central and northern Adriatic sedimentary successions, with the aim of reconstructing and quantifying the Late Quaternary eustatic fluctuations. In the last few decades, several Authors tried to quantify past eustatic fluctuations through the analysis of direct sea level indicators, among which drowned barrier-island deposits or coral reefs, or indirect methods, such as Oxygen isotope ratios (δ18O) or modeling simulations. Sea level curves, obtained from direct sea level indicators, record a composite signal, formed by the contribution of the global eustatic change and regional factors, as tectonic processes or glacial-isostatic rebound effects: the eustatic signal has to be obtained by removing the contribution of these other mechanisms. To obtain the most realistic sea level reconstructions it is important to quantify the tectonic regime of the central Adriatic margin. This result has been achieved integrating a numerical approach with the analysis of high-resolution seismic profiles. In detail, the subsidence trend obtained from the geohistory analysis and the backstripping of the borehole PRAD1.2 (the borehole PRAD1.2 is a 71 m continuous borehole drilled in -185 m of water depth, south of the Mid Adriatic Deep - MAD - during the European Project PROMESS 1, Profile Across Mediterranean Sedimentary Systems, Part 1), has been confirmed by the analysis of lowstand paleoshorelines and by benthic foraminifera associations investigated through the borehole. This work showed an evolution from inner-shelf environment, during Marine Isotopic Stage (MIS) 10, to upper-slope conditions, during MIS 2. Once the tectonic regime of the central Adriatic margin has been constrained, it is possible to investigate the impact of sea level and sediment supply fluctuations on the deposition of the Late Pleistocene-Holocene transgressive deposits. The Adriatic transgressive record (TST - Transgressive Systems Tract) is formed by three correlative sedimentary bodies, deposited in less then 14 kyr since the Last Glacial Maximum (LGM); in particular: along the central Adriatic shelf and in the adjacent slope basin the TST is formed by marine units, while along the northern Adriatic shelf the TST is represented by costal deposits in a backstepping configuration. The central Adriatic margin, characterized by a thick transgressive sedimentary succession, is the ideal site to investigate the impact of late Pleistocene climatic and eustatic fluctuations, among which Meltwater Pulses 1A and 1B and the Younger Dryas cold event. The central Adriatic TST is formed by a tripartite deposit bounded by two regional unconformities. In particular, the middle TST unit includes two prograding wedges, deposited in the interval between the two Meltwater Pulse events, as highlighted by several 14C age estimates, and likely recorded the Younger Dryas cold interval. Modeling simulations, obtained with the two coupled models HydroTrend 3.0 and 2D-Sedflux 1.0C (developed by the Community Surface Dynamics Modeling System - CSDMS), integrated by the analysis of high resolution seismic profiles and core samples, indicate that: 1 - the prograding middle TST unit, deposited during the Younger Dryas, was formed as a consequence of an increase in sediment flux, likely connected to a decline in vegetation cover in the catchment area due to the establishment of sub glacial arid conditions; 2 - the two-stage prograding geometry was the consequence of a sea level still-stand (or possibly a fall) during the Younger Dryas event. The northern Adriatic margin, characterized by a broad and gentle shelf (350 km wide with a low angle plunge of 0.02° to the SE), is the ideal site to quantify the timing of each steps of the post LGM sea level rise. The modern shelf is characterized by sandy deposits of barrier-island systems in a backstepping configuration, showing younger ages at progressively shallower depths, which recorded the step-wise nature of the last sea level rise. The age-depth model, obtained by dated samples of basal peat layers, is in good agreement with previous published sea level curves, and highlights the post-glacial eustatic trend. The interval corresponding to the Younger Dyas cold reversal, instead, is more complex: two coeval coastal deposits characterize the northern Adriatic shelf at very different water depths. Several explanations and different models can be attempted to explain this conundrum, but the problem remains still unsolved.

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).

Fluxus. Prima, durante, dopo

Fluxus è stato definito il più radicale e sperimentale movimento artistico degli anni Sessanta. Dalla prima comparsa ad oggi è stato osannato, analizzato, dimenticato e riscoperto molte volte, tuttora però rimane una delle più grandi incognite critiche della storia dell’arte del Novecento. La ricerca si sviluppa secondo uno schema tripartito: indagare origini, ascendenze e ispirazioni; collocare e contestualizzare il periodo di nascita e sviluppo; esaminare influenze e lasciti. Attraverso un confronto di manifesti, scritti autografi e opere si è cercato di verificare punti di contatto e di continuità tra Fluxus e le Avanguardie Storiche, con particolare riferimento a Futurismo e Dadaismo. Successivamente si è cercato di ricostruire le dinamiche che hanno portato, alla fine degli anni Cinquanta, al definirsi di un terreno fertile dal quale sono germinate esperienze strettamente legate quali Happening, Performance Art e lo stesso Fluxus, del quale si sono ripercorsi i cosiddetti “anni eroici” per evidenziarne le caratteristiche salienti. Nella terza sezione sono state individuate diverse ipotesi di continuazione dell’attitudine Fluxus, dal percorso storico-filologico dei precoci tentativi di musealizzazione, alle eredità dirette e indirette sulle generazioni successive di artisti, fino alla individuazione di idee e concetti la cui attualità rende Fluxus un elemento imprescindibile per la comprensione della cultura contemporanea.

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.

Exploring Quantum Speed-up Through Cluster-state Computers

The aim of this thesis is to investigate the nature of quantum computation and the question of the quantum speed-up over classical computation by comparing two different quantum computational frameworks, the traditional quantum circuit model and the cluster-state quantum computer. After an introductory survey of the theoretical and epistemological questions concerning quantum computation, the first part of this thesis provides a presentation of cluster-state computation suitable for a philosophical audience. In spite of the computational equivalence between the two frameworks, their differences can be considered as structural. Entanglement is shown to play a fundamental role in both quantum circuits and cluster-state computers; this supports, from a new perspective, the argument that entanglement can reasonably explain the quantum speed-up over classical computation. However, quantum circuits and cluster-state computers diverge with regard to one of the explanations of quantum computation that actually accords a central role to entanglement, i.e. the Everett interpretation. It is argued that, while cluster-state quantum computation does not show an Everettian failure in accounting for the computational processes, it threatens that interpretation of being not-explanatory. This analysis presented here should be integrated in a more general work in order to include also further frameworks of quantum computation, e.g. topological quantum computation. However, what is revealed by this work is that the speed-up question does not capture all that is at stake: both quantum circuits and cluster-state computers achieve the speed-up, but the challenges that they posit go besides that specific question. Then, the existence of alternative equivalent quantum computational models suggests that the ultimate question should be moved from the speed-up to a sort of “representation theorem” for quantum computation, to be meant as the general goal of identifying the physical features underlying these alternative frameworks that allow for labelling those frameworks as “quantum computation”.