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.

Interspecies study of the enteric nervous system and related pathologies

The enteric nervous system (ENS) modulates a number of digestive functions including well known ones, i.e. motility, secretion, absorption and blood flow, along with other critically relevant processes, i.e. immune responses of the gastrointestinal (GI) tract, gut microbiota and epithelial barrier . The characterization of the anatomical aspects of the ENS in large mammals and the identification of differences and similarities existing between species may represent a fundamental basis to decipher several digestive GI diseases in humans and animals. In this perspective, the aim of the present thesis is to highlight the ENS anatomical basis and pathological aspects in different mammalian species, such as horses, dogs and humans. Firstly, I designed two anatomical studies in horses:  “Excitatory and inhibitory enteric innervation of horse lower esophageal sphincter”.  “Localization of 5-hydroxytryptamine 4 receptor (5-HT4R) in the equine enteric nervous system”. Then I focused on the enteric dysfunctions, including:  A primary enteric aganglionosis in horses: “Extrinsic innervation of the ileum and pelvic flexure of foals with ileocolonic aganglionosis”.  A diabetic enteric neuropathy in dogs: “Quantification of nitrergic neurons in the myenteric plexus of gastric antrum and ileum of healthy and diabetic dogs”.  An enteric neuropathy in human neurological patients: “Functional and neurochemical abnormalities in patients with Parkinson's disease and chronic constipation”. The physiology of the GI tract is characterized by a high complexity and it is mainly dependent on the control of the intrinsic nervous system. ENS is critical to preserve body homeostasis as reflect by its derangement occurring in pathological conditions that can be lethal or seriously disabling to humans and animals. The knowledge of the anatomy and the pathology of the ENS represents a new important and fascinating topic, which deserves more attention in the veterinary medicine field.

Theoretical and experimental study of novel hybrid composite and metal-composites interfaces

The growing demand for lightweight solutions in every field of engineering is driving the industry to seek new technological solutions to exploit the full potential of different materials. The combination of dissimilar materials with distinct property ranges embodies a transparent allocation of component functions while allowing an optimal mix of their characteristics. From both technological and design perspectives, the interaction between dissimilar materials can lead to severe defects that compromise a multi-material hybrid component's performance and its structural integrity. This thesis aims to develop methodologies for designing, manufacturing, and monitoring of hybrid metal-composite joints and hybrid composite components. In Chapter 1, a methodology for designing and manufacturing hybrid aluminum/composite co-cured tubes is assessed. In Chapter 2, a full-field methodology for fiber misalignment detection and stiffness prediction for hybrid, long fiber reinforced composite systems is shown and demonstrated. Chapter 3 reports the development of a novel technology for joining short fiber systems and metals in a one-step co-curing process using lattice structures. Chapter 4 is dedicated to a novel analytical framework for the design optimization of two lattice architectures.