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.

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).

Sistemi riconfigurabili a basso consumo per applicazioni di monitoraggio distribuito

The term Ambient Intelligence (AmI) refers to a vision on the future of the information society where smart, electronic environment are sensitive and responsive to the presence of people and their activities (Context awareness). In an ambient intelligence world, devices work in concert to support people in carrying out their everyday life activities, tasks and rituals in an easy, natural way using information and intelligence that is hidden in the network connecting these devices. This promotes the creation of pervasive environments improving the quality of life of the occupants and enhancing the human experience. AmI stems from the convergence of three key technologies: ubiquitous computing, ubiquitous communication and natural interfaces. Ambient intelligent systems are heterogeneous and require an excellent cooperation between several hardware/software technologies and disciplines, including signal processing, networking and protocols, embedded systems, information management, and distributed algorithms. Since a large amount of fixed and mobile sensors embedded is deployed into the environment, the Wireless Sensor Networks is one of the most relevant enabling technologies for AmI. WSN are complex systems made up of a number of sensor nodes which can be deployed in a target area to sense physical phenomena and communicate with other nodes and base stations. These simple devices typically embed a low power computational unit (microcontrollers, FPGAs etc.), a wireless communication unit, one or more sensors and a some form of energy supply (either batteries or energy scavenger modules). WNS promises of revolutionizing the interactions between the real physical worlds and human beings. Low-cost, low-computational power, low energy consumption and small size are characteristics that must be taken into consideration when designing and dealing with WSNs. To fully exploit the potential of distributed sensing approaches, a set of challengesmust be addressed. Sensor nodes are inherently resource-constrained systems with very low power consumption and small size requirements which enables than to reduce the interference on the physical phenomena sensed and to allow easy and low-cost deployment. They have limited processing speed,storage capacity and communication bandwidth that must be efficiently used to increase the degree of local ”understanding” of the observed phenomena. A particular case of sensor nodes are video sensors. This topic holds strong interest for a wide range of contexts such as military, security, robotics and most recently consumer applications. Vision sensors are extremely effective for medium to long-range sensing because vision provides rich information to human operators. However, image sensors generate a huge amount of data, whichmust be heavily processed before it is transmitted due to the scarce bandwidth capability of radio interfaces. In particular, in video-surveillance, it has been shown that source-side compression is mandatory due to limited bandwidth and delay constraints. Moreover, there is an ample opportunity for performing higher-level processing functions, such as object recognition that has the potential to drastically reduce the required bandwidth (e.g. by transmitting compressed images only when something ‘interesting‘ is detected). The energy cost of image processing must however be carefully minimized. Imaging could play and plays an important role in sensing devices for ambient intelligence. Computer vision can for instance be used for recognising persons and objects and recognising behaviour such as illness and rioting. Having a wireless camera as a camera mote opens the way for distributed scene analysis. More eyes see more than one and a camera system that can observe a scene from multiple directions would be able to overcome occlusion problems and could describe objects in their true 3D appearance. In real-time, these approaches are a recently opened field of research. In this thesis we pay attention to the realities of hardware/software technologies and the design needed to realize systems for distributed monitoring, attempting to propose solutions on open issues and filling the gap between AmI scenarios and hardware reality. The physical implementation of an individual wireless node is constrained by three important metrics which are outlined below. Despite that the design of the sensor network and its sensor nodes is strictly application dependent, a number of constraints should almost always be considered. Among them: • Small form factor to reduce nodes intrusiveness. • Low power consumption to reduce battery size and to extend nodes lifetime. • Low cost for a widespread diffusion. These limitations typically result in the adoption of low power, low cost devices such as low powermicrocontrollers with few kilobytes of RAMand tenth of kilobytes of program memory with whomonly simple data processing algorithms can be implemented. However the overall computational power of the WNS can be very large since the network presents a high degree of parallelism that can be exploited through the adoption of ad-hoc techniques. Furthermore through the fusion of information from the dense mesh of sensors even complex phenomena can be monitored. In this dissertation we present our results in building several AmI applications suitable for a WSN implementation. The work can be divided into two main areas:Low Power Video Sensor Node and Video Processing Alghoritm and Multimodal Surveillance . Low Power Video Sensor Nodes and Video Processing Alghoritms In comparison to scalar sensors, such as temperature, pressure, humidity, velocity, and acceleration sensors, vision sensors generate much higher bandwidth data due to the two-dimensional nature of their pixel array. We have tackled all the constraints listed above and have proposed solutions to overcome the current WSNlimits for Video sensor node. We have designed and developed wireless video sensor nodes focusing on the small size and the flexibility of reuse in different applications. The video nodes target a different design point: the portability (on-board power supply, wireless communication), a scanty power budget (500mW),while still providing a prominent level of intelligence, namely sophisticated classification algorithmand high level of reconfigurability. We developed two different video sensor node: The device architecture of the first one is based on a low-cost low-power FPGA+microcontroller system-on-chip. The second one is based on ARM9 processor. Both systems designed within the above mentioned power envelope could operate in a continuous fashion with Li-Polymer battery pack and solar panel. Novel low power low cost video sensor nodes which, in contrast to sensors that just watch the world, are capable of comprehending the perceived information in order to interpret it locally, are presented. Featuring such intelligence, these nodes would be able to cope with such tasks as recognition of unattended bags in airports, persons carrying potentially dangerous objects, etc.,which normally require a human operator. Vision algorithms for object detection, acquisition like human detection with Support Vector Machine (SVM) classification and abandoned/removed object detection are implemented, described and illustrated on real world data. Multimodal surveillance: In several setup the use of wired video cameras may not be possible. For this reason building an energy efficient wireless vision network for monitoring and surveillance is one of the major efforts in the sensor network community. Energy efficiency for wireless smart camera networks is one of the major efforts in distributed monitoring and surveillance community. For this reason, building an energy efficient wireless vision network for monitoring and surveillance is one of the major efforts in the sensor network community. The Pyroelectric Infra-Red (PIR) sensors have been used to extend the lifetime of a solar-powered video sensor node by providing an energy level dependent trigger to the video camera and the wireless module. Such approach has shown to be able to extend node lifetime and possibly result in continuous operation of the node.Being low-cost, passive (thus low-power) and presenting a limited form factor, PIR sensors are well suited for WSN applications. Moreover techniques to have aggressive power management policies are essential for achieving long-termoperating on standalone distributed cameras needed to improve the power consumption. We have used an adaptive controller like Model Predictive Control (MPC) to help the system to improve the performances outperforming naive power management policies.

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Numerical methods for the dispersion analysis of Guided Waves

The use of guided ultrasonic waves (GUW) has increased considerably in the fields of non-destructive (NDE) testing and structural health monitoring (SHM) due to their ability to perform long range inspections, to probe hidden areas as well as to provide a complete monitoring of the entire waveguide. Guided waves can be fully exploited only once their dispersive properties are known for the given waveguide. In this context, well stated analytical and numerical methods are represented by the Matrix family methods and the Semi Analytical Finite Element (SAFE) methods. However, while the former are limited to simple geometries of finite or infinite extent, the latter can model arbitrary cross-section waveguides of finite domain only. This thesis is aimed at developing three different numerical methods for modelling wave propagation in complex translational invariant systems. First, a classical SAFE formulation for viscoelastic waveguides is extended to account for a three dimensional translational invariant static prestress state. The effect of prestress, residual stress and applied loads on the dispersion properties of the guided waves is shown. Next, a two-and-a-half Boundary Element Method (2.5D BEM) for the dispersion analysis of damped guided waves in waveguides and cavities of arbitrary cross-section is proposed. The attenuation dispersive spectrum due to material damping and geometrical spreading of cavities with arbitrary shape is shown for the first time. Finally, a coupled SAFE-2.5D BEM framework is developed to study the dispersion characteristics of waves in viscoelastic waveguides of arbitrary geometry embedded in infinite solid or liquid media. Dispersion of leaky and non-leaky guided waves in terms of speed and attenuation, as well as the radiated wavefields, can be computed. The results obtained in this thesis can be helpful for the design of both actuation and sensing systems in practical application, as well as to tune experimental setup.

Origin and variability of PM10 and atmospheric radiotracers at the WMO-GAW station of Mt. Cimone (1998-2011) and in the central Po Valley

Particulate matter is one of the main atmospheric pollutants, with a great chemical-environmental relevance. Improving knowledge of the sources of particulate matter and of their apportionment is needed to handle and fulfill the legislation regarding this pollutant, to support further development of air policy as well as air pollution management. Various instruments have been used to understand the sources of particulate matter and atmospheric radiotracers at the site of Mt. Cimone (44.18° N, 10.7° E, 2165 m asl), hosting a global WMO-GAW station. Thanks to its characteristics, this location is suitable investigate the regional and long-range transport of polluted air masses on the background Southern-Europe free-troposphere. In particular, PM10 data sampled at the station in the period 1998-2011 were analyzed in the framework of the main meteorological and territorial features. A receptor model based on back trajectories was applied to study the source regions of particulate matter. Simultaneous measurements of atmospheric radionuclides Pb-210 and Be-7 acquired together with PM10 have also been analysed to acquire a better understanding of vertical and horizontal transports able to affect atmospheric composition. Seasonal variations of atmospheric radiotracers have been studied both analysing the long-term time series acquired at the measurement site as well as by means of a state-of-the-art global 3-D chemistry and transport model. Advection patterns characterizing the circulation at the site have been identified by means of clusters of back-trajectories. Finally, the results of a source apportionment study of particulate matter carried on in a midsize town of the Po Valley (actually recognised as one of the most polluted European regions) are reported. An approach exploiting different techniques, and in particular different kinds of models, successfully achieved a characterization of the processes/sources of particulate matter at the two sites, and of atmospheric radiotracers at the site of Mt. Cimone.