3 resultados para Pseudospin and spin symmetry

em AMS Tesi di Dottorato - Alm@DL - Università di Bologna


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Supramolecular chemistry is a multidisciplinary field which impinges on other disciplines, focusing on the systems made up of a discrete number of assembled molecular subunits. The forces responsible for the spatial organization are intermolecular reversible interactions. The supramolecular architectures I was interested in are Rotaxanes, mechanically-interlocked architectures consisting of a "dumbbell shaped molecule", threaded through a "macrocycle" where the stoppers at the end of the dumbbell prevent disassociation of components and catenanes, two or more interlocked macrocycles which cannot be separated without breaking the covalent bonds. The aim is to introduce one or more paramagnetic units to use the ESR spectroscopy to investigate complexation properties of these systems cause this technique works in the same time scale of supramolecular assemblies. Chapter 1 underlines the main concepts upon which supramolecular chemistry is based, clarifying the nature of supramolecular interactions and the principles of host-guest chemistry. In chapter 2 it is pointed out the use of ESR spectroscopy to investigate the properties of organic non-covalent assemblies in liquid solution by spin labels and spin probes. The chapter 3 deals with the synthesis of a new class of p-electron-deficient tetracationic cyclophane ring, carrying one or two paramagnetic side-arms based on 2,2,6,6-tetramethylpiperidine-N-oxyl (TEMPO) moiety. In the chapter 4, the Huisgen 1,3-dipolar cycloaddition is exploited to synthesize rotaxanes having paramagnetic cyclodextrins as wheels. In the chapter 5, the catalysis of Huisgen’s cycloaddition by CB[6] is exploited to synthesize paramagnetic CB[6]-based [3]-rotaxanes. In the chapter 6 I reported the first preliminary studies of Actinoid series as a new class of templates in catenanes’ synthesis. Being f-block elements, so having the property of expanding the valence state, they constitute promising candidates as chemical templates offering the possibility to create a complex with coordination number beyond 6.

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The main object of this thesis is the analysis and the quantization of spinning particle models which employ extended ”one dimensional supergravity” on the worldline, and their relation to the theory of higher spin fields (HS). In the first part of this work we have described the classical theory of massless spinning particles with an SO(N) extended supergravity multiplet on the worldline, in flat and more generally in maximally symmetric backgrounds. These (non)linear sigma models describe, upon quantization, the dynamics of particles with spin N/2. Then we have analyzed carefully the quantization of spinning particles with SO(N) extended supergravity on the worldline, for every N and in every dimension D. The physical sector of the Hilbert space reveals an interesting geometrical structure: the generalized higher spin curvature (HSC). We have shown, in particular, that these models of spinning particles describe a subclass of HS fields whose equations of motions are conformally invariant at the free level; in D = 4 this subclass describes all massless representations of the Poincar´e group. In the third part of this work we have considered the one-loop quantization of SO(N) spinning particle models by studying the corresponding partition function on the circle. After the gauge fixing of the supergravity multiplet, the partition function reduces to an integral over the corresponding moduli space which have been computed by using orthogonal polynomial techniques. Finally we have extend our canonical analysis, described previously for flat space, to maximally symmetric target spaces (i.e. (A)dS background). The quantization of these models produce (A)dS HSC as the physical states of the Hilbert space; we have used an iterative procedure and Pochhammer functions to solve the differential Bianchi identity in maximally symmetric spaces. Motivated by the correspondence between SO(N) spinning particle models and HS gauge theory, and by the notorious difficulty one finds in constructing an interacting theory for fields with spin greater than two, we have used these one dimensional supergravity models to study and extract informations on HS. In the last part of this work we have constructed spinning particle models with sp(2) R symmetry, coupled to Hyper K¨ahler and Quaternionic-K¨ahler (QK) backgrounds.

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In this work I reported recent results in the field of Statistical Mechanics of Equilibrium, and in particular in Spin Glass models and Monomer Dimer models . We start giving the mathematical background and the general formalism for Spin (Disordered) Models with some of their applications to physical and mathematical problems. Next we move on general aspects of the theory of spin glasses, in particular to the Sherrington-Kirkpatrick model which is of fundamental interest for the work. In Chapter 3, we introduce the Multi-species Sherrington-Kirkpatrick model (MSK), we prove the existence of the thermodynamical limit and the Guerra's Bound for the quenched pressure together with a detailed analysis of the annealed and the replica symmetric regime. The result is a multidimensional generalization of the Parisi's theory. Finally we brie y illustrate the strategy of the Panchenko's proof of the lower bound. In Chapter 4 we discuss the Aizenmann-Contucci and the Ghirlanda-Guerra identities for a wide class of Spin Glass models. As an example of application, we discuss the role of these identities in the proof of the lower bound. In Chapter 5 we introduce the basic mathematical formalism of Monomer Dimer models. We introduce a Gaussian representation of the partition function that will be fundamental in the rest of the work. In Chapter 6, we introduce an interacting Monomer-Dimer model. Its exact solution is derived and a detailed study of its analytical properties and related physical quantities is performed. In Chapter 7, we introduce a quenched randomness in the Monomer Dimer model and show that, under suitable conditions the pressure is a self averaging quantity. The main result is that, if we consider randomness only in the monomer activity, the model is exactly solvable.