In this work we investigate the existence of resonances for two-centers Coulomb systems with arbitrary charges in two and three dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schrödinger operator. After giving a description of the bifurcation of the classical system for positive energies, we construct the resolvent kernel of the operators and we prove that they can be extended analytically to the second Riemann sheet. The resonances are then defined and studied with numerical methods and perturbation theory.

This thesis addresses the issue of generating texts in the style of an existing author, that also satisfy structural constraints imposed by the genre of the text. Although Markov processes are known to be suitable for representing style, they are difficult to control in order to satisfy non-local properties, such as structural constraints, that require long distance modeling. The framework of Constrained Markov Processes allows to precisely generate texts that are consistent with a corpus, while being controllable in terms of rhymes and meter. Controlled Markov processes consist in reformulating Markov processes in the context of constraint satisfaction. The thesis describes how to represent stylistic and structural properties in terms of constraints in this framework and how this approach can be used for the generation of lyrics in the style of 60 differents authors An evaluation of the desctibed method is provided by comparing it to both pure Markov and pure constraint-based approaches. Finally the thesis describes the implementation of an augmented text editor, called Perec. Perec is intended to improve creativity, by helping the user to write lyrics and poetry, exploiting the techniques presented so far.

This work deals with the theory of Relativity and its diffusion in Italy in the first decades of the XX century. Not many scientists belonging to Italian universities were active in understanding Relativity, but two of them, Max Abraham and Tullio Levi-Civita left a deep mark. Max Abraham engaged a substantial debate against Einstein between 1912 and 1914 about electromagnetic and gravitation aspects of the theories. Levi-Civita played a fundamental role in giving Einstein the correct mathematical instruments for the General Relativity formulation since 1915. This work, which doesn't have the aim of a mere historical chronicle of the events, wants to highlight two particular perspectives: on one hand, the importance of Abraham-Einstein debate in order to clarify the basis of Special Relativity, to observe the rigorous logical structure resulting from a fragmentary reasoning sequence and to understand Einstein's thinking; on the other hand, the originality of Levi-Civita's approach, quite different from the Einstein's one, characterized by the introduction of a method typical of General Relativity even to Special Relativity and the attempt to hide the two Einstein Special Relativity postulates.

In the race to obtain protons with higher energies, using more compact systems at the same time, laser-driven plasma accelerators are becoming an interesting possibility. But for now, only beams with extremely broad energy spectra and high divergence have been produced. The driving line of this PhD thesis was the study and design of a compact system to extract a high quality beam out of the initial bunch of protons produced by the interaction of a laser pulse with a thin solid target, using experimentally reliable technologies in order to be able to test such a system as soon as possible. In this thesis, different transport lines are analyzed. The first is based on a high field pulsed solenoid, some collimators and, for perfect filtering and post-acceleration, a high field high frequency compact linear accelerator, originally designed to accelerate a 30 MeV beam extracted from a cyclotron. The second one is based on a quadruplet of permanent magnetic quadrupoles: thanks to its greater simplicity and reliability, it has great interest for experiments, but the effectiveness is lower than the one based on the solenoid; in fact, the final beam intensity drops by an order of magnitude. An additional sensible decrease in intensity is verified in the third case, where the energy selection is achieved using a chicane, because of its very low efficiency for off-axis protons. The proposed schemes have all been analyzed with 3D simulations and all the significant results are presented. Future experimental work based on the outcome of this thesis can be planned and is being discussed now.

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In principle, the lattice of elementary propositions of a generic quantum system admits a representation in real, complex or quaternionic Hilbert spaces as established by Solèr’s theorem (1995) closing a long standing problem that can be traced back to von Neumann’s mathematical formulation of quantum mechanics. However up to now there are no examples of quantum systems described in Hilbert spaces whose scalar field is different from the set of complex numbers. We show that elementary relativistic systems cannot be described by irreducible strongly-continuous unitary representations of SL(2, C) on real or quaternionic Hilbert spaces as a consequence of some peculiarity of the generators related with the theory of polar decomposition of operators. Indeed such a ”naive” attempt leads necessarily to an equivalent formulation on a complex Hilbert space. Although this conclusion seems to give a definitive answer to the real/quaternionic-quantum-mechanics issue, it lacks consistency since it does not derive from more general physical hypotheses as the complex one does. Trying a more solid approach, in both situations we end up with three possibilities: an equivalent description in terms of a Wigner unitary representation in a real, complex or quaternionic Hilbert space. At this point the ”naive” result turns out to be a definitely important technical lemma, for it forbids the two extreme possibilities. In conclusion, the real/quaternionic theory is actually complex. This improved approach is based upon the concept of von Neumann algebra of observables. Unfortunately, while there exists a thorough literature about these algebras on real and complex Hilbert spaces, an analysis on the notion of von Neumann algebra over a quaternionic Hilbert space is completely absent to our knowledge. There are several issues in trying to define such a mathematical object, first of all the inability to construct linear combination of operators with quaternionic coeffients. Restricting ourselves to unital real *-algebras of operators we are able to prove the von Neumann Double Commutant Theorem also on quaternionc Hilbert spaces. Clearly, this property turns out to be crucial.

The present work provides a geometric approach to the calculus of variations in the presence of non-holonomic constraints. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The usual classification of the evolutions into normal and abnormal ones is also discussed, showing the existence of a universal algorithm assigning to every admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. A gauge-invariant formulation of the variational problem, based on the introduction of the bundle of affine scalars over the configuration manifold, is then presented. The analysis includes a revisitation of Pontryagin Maximum Principle and of the Erdmann-Weierstrass corner conditions, a local interpretation of Pontryagin's equations as dynamical equations for a free (singular) Hamiltonian system and a generalization of the classical criteria of Legendre and Bliss for the characterization of the minima of the action functional to the case of piecewise-differentiable extremals with asynchronous variation of the corners.

My PhD thesis is focused on geometric Hamiltonian formulation of Quanum Mechanics and its interplay with standard formulation. The main result is the construction of a general prescription to set up a quantum theory as a classical-like theory where quantum dynamics is given by a Hamiltonian vector field on a complex projective space with Kähler structure. In such geometric framework quantum states are represented by classical-like Liouville densities. After a complete characterization of classical-like observables in a finite-dimensional quantum theory, the observable C*-algebra is described in geometric Hamiltonian terms. In the final part of the work, the classical-like Hamiltonian formulation is applied to the study of composite quantum systems providing a notion of entanglement measure.

Made available in DSpace on 2016-05-17T16:50:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-03-16. Added 1 bitstream(s) on 2016-05-17T16:54:31Z : No. of bitstreams: 1 000855888.pdf: 673100 bytes, checksum: f6c50190e13c6931b1a9076b72d32787 (MD5) / Apresentamos nesta dissertação uma revisão dos conceitos de geometria diferencial, onde estamos interessados em definir campos vetoriais que geram transformações de um parâmetro, formas diferenciais, variedades simpléticas e fibrados. Além disso, detalhamos o conceito de cohomologia de De Rham, o qual nos fornece uma ferramenta algébrica fundamental para analisar propriedades topológicas das variedades. A combinação desses conceitos, os quais suportam o nosso trabalho, permite-nos desenvolver teorias de localização equivariante de integrais definidas sobre espaços de fase clássicos, os quais também podem ser uma órbita co-adjunta. A localização é possível devido ao teorema de Duistermaat-Heckman, o qual nos permite escrever integrais como uma soma, ou integral, sobre o conjunto dos pontos críticos do espaço. Em seguida fazemos uma extensão para teorias de localização de integrais funcionais, onde é preciso definir o espaço dos loops. Nesse contexto aplicamos a formulação de localização equivariante tendo como base a conjectura de Atiyah-Witten para teorias supersimétricas, onde derivamos o teorema de índice de Atiyah-Singer para um operador de Dirac. O teorema de índice é aplicado no cálculo da anomalia quiral / We present in this dissertation a conceptual review of differential geometry, where we are interested in defining vector fields which are one-parameter transformation generators, differential forms, symplectic manifolds, and fiber bundles. In addition, we detail the concept about De Rham's cohomology, which provides us a fundamental algebraic tool to analyze topological properties of manifolds. The combination of these concepts, which are the background material of our work, allows us to develop equivariant localization theories of integrals defined on classical phase spaces, which can also be a co-adjoint orbit. The localization is possible because of the Duistermaat-Heckman theorem, which allows us to write integrals on the whole space just as a sum, or integral, on a critical points set. Further more, we do an extension to functional integrals localization theories, where it is needed to define loop spaces. In this context we apply equivariant localization formulation having the bases of Atiyah-Witten conjecture to supersymmetric theories, where we derive the Atiyah-Singer index theorem for a Dirac operator. The index theorem is applied to chiral anomaly calculation