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).

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.

Reconstructing Quantum Field Theory from an Educational Perspective

The research work concerns the analysis of the foundations of Quantum Field Theory carried out from an educational perspective. The whole research has been driven by two questions: • How the concept of object changes when moving from classical to contemporary physics? • How are the concepts of field and interaction shaped and conceptualized within contemporary physics? What makes quantum field and interaction similar to and what makes them different from the classical ones? The whole work has been developed through several studies: 1. A study aimed to analyze the formal and conceptual structures characterizing the description of the continuous systems that remain invariant in the transition from classical to contemporary physics. 2. A study aimed to analyze the changes in the meanings of the concepts of field and interaction in the transition to quantum field theory. 3. A detailed study of the Klein-Gordon equation aimed at analyzing, in a case considered emblematic, some interpretative (conceptual and didactical) problems in the concept of field that the university textbooks do not address explicitly. 4. A study concerning the application of the “Discipline-Culture” Model elaborated by I. Galili to the analysis of the Klein-Gordon equation, in order to reconstruct the meanings of the equation from a cultural perspective. 5. A critical analysis, in the light of the results of the studies mentioned above, of the existing proposals for teaching basic concepts of Quantum Field Theory and particle physics at the secondary school level or in introductory physics university courses.

Photo- and redox-active supramolecular systems containing metal complexes

The aim of this Ph.D. project has been the photophysical and photochemical characterization of new photo- and redox-active supramolecular systems. In particular we studied two different classes of compounds: metal complexes and dendrimers. Two different families of bis-cyclometalated neutral Ir(III) complexes are presented and their photophysical properties are discussed. The first family of complexes contains two 2-phenylpyridyl (ppy) or 2-(4,6-difluorophenyl)pyridyl (F2ppy) cyclometalated ligands and an ancillary ligand constituted by a phenol-oxazoline (phox), which can be substituted in the third position with a fluorine group (Fphox). In the second part of this study, we present another family of bis-cyclometalated Ir(III) complexes in which the ancillary ligand could be a chiral or an achiral bis-oxazoline (box). We report on their structural, electrochemical, photophysical, and photochemical properties. Complexes containing phox and Fphox ancillary ligands show blue luminescence with very high quantum yield, while complexes with box ligands do not show particularly interesting photophysical properties. Surprisingly these complexes give an unexpected photoreaction when irradiated with UV light in presence of dioxygen. This photoreaction originates a stable, strong blue emitting and particularly interesting photoproduct. Three successive generations of a family of polyethyleneglycol (PEG)-coated Pd(II) tetrabenzoporphyrin (PdTBP)-based dendritic nanoprobes are presented, and their ability to sensitize singlet oxygen and inflict cellular photodamage are discussed. It was found that the size of the dendrimer has practically no effect on the singlet oxygen sensitization efficiency, that approximate the unity, in spite of the strong attenuation of the triplet quenching rate with an increase in the dendrimer generation. Nevertheless, when compared against a commonly used singlet oxygen sensitizer, as Photofrin, the phosphorescent probes were found to be non-phototoxic. The lack of phototoxicity is presumably due to the inability of PEGylated probes to associate with cell surfaces and/or penetrate cellular membranes. The results suggest that protected phosphorescent probes can be safely used for oxygen measurements in biological systems in vivo. A new family of two photoswitchable (G0(Azo) and G1(Azo)) dendrimers with an azobenzene core, two cyclam units as coordination sites for metal ions, and luminescent naphthalene units at the periphery have been characterized and their coordination abilities have been studied. Because of their proximity, the various functional groups of the dendrimer may interact, so that the properties of the dendrimers are different from those exhibited by the separated functional units. Both the naphthalene fluorescence and the azobenzene photoisomerization can be observed in the dendrimer, but it has been shown that (i) the fluorescent excited state of the naphthalene units is substantially quenched by excimer and exciplex formation and by energy transfer to the azobenzene units, and (ii) in the latter case the fluorescence quenching is accompanied by the photosensitized isomerization of the trans → cis, and, with higher efficiency, the cis → trans reaction. Complexation of these dendrimers, both trans and cis isomers, with Zn(II) ions shows that complexes of 1:1 and 2:1 metal per dendrimer stoichiometry are formed showing different photophysical and photochemical properties compared to the corresponding free ligands. Practically unitary efficiency of the sensitized isomerization of trans → cis and cis → trans reaction is observed, as well as a slight increase in the naphthalene monomer emission. These results are consistent with the coordination of the cyclam amine units with Zn(II), which prevents exciplex formation. No indication of a concomitant coordination of both cyclam to a single metal ion has been obtained both for trans and cis isomer.