The laser driven ion acceleration is a burgeoning field of resarch and is attracting a growing number of scientists since the first results reported in 2000 obtained irradiating thin solid foils by high power laser pulses. The growing interest is driven by the peculiar characteristics of the produced bunches, the compactness of the whole accelerating system and the very short accelerating length of this all-optical accelerators. A fervent theoretical and experimental work has been done since then. An important part of the theoretical study is done by means of numerical simulations and the most widely used technique exploits PIC codes (“Particle In Cell'”). In this thesis the PIC code AlaDyn, developed by our research group considering innovative algorithms, is described. My work has been devoted to the developement of the code and the investigation of the laser driven ion acceleration for different target configurations. Two target configurations for the proton acceleration are presented together with the results of the 2D and 3D numerical investigation. One target configuration consists of a solid foil with a low density layer attached on the irradiated side. The nearly critical plasma of the foam layer allows a very high energy absorption by the target and an increase of the proton energy up to a factor 3, when compared to the ``pure'' TNSA configuration. The differences of the regime with respect to the standard TNSA are described The case of nearly critical density targets has been investigated with 3D simulations. In this case the laser travels throughout the plasma and exits on the rear side. During the propagation, the laser drills a channel and induce a magnetic vortex that expanding on the rear side of the targer is source of a very intense electric field. The protons of the plasma are strongly accelerated up to energies of 100 MeV using a 200PW laser.

In the present thesis I focused on the study of the phenomenology arising from a class of string models called sequestered compactifications, which were born with the aim of getting low-energy SUSY from strings. This is not an easy task if combined with cosmological constraints, since the mechanism of moduli stabilization fixes both the scale of supersymmetric particles and the scale of moduli, which tend to be of the same order. However, if on the one hand supersymmetric particles with TeV mass are desired in order to address the electroweak hierarchy problem, on the other hand the cosmological moduli problem requires the moduli to be heavier than 100 TeV. The specific setup of sequestered compactifications makes this hierarchy achievable, at least in principle: as in these models the visible sector is located on a stack of D3-branes at singularities, a physical separation between the visible degrees of freedom and the SUSY-breaking sources takes place. Such decoupling translates into a hierarchy between the scale of SUSY-breaking and the spectrum of supersymmetric particles. Interestingly, moduli are the four-dimensional manifestation of the existence of extra-dimensions. Since they are only gravitationally coupled, they could decay late in the history of the universe, affecting in a significant way its cosmological evolution. Possible deviations of the cosmological observables from the values predicted by the standard Hot Big Bang Theory constitute an interesting alternative for the discovery of new physics beyond the Standard Model, which is complementary to the particle physics search. For this reason in addition to SUSY-breaking in sequestered models, I also studied several cosmological scenarios arising from them, such as production of non-thermal dark matter and dark radiation, reheating from moduli decay and inflation.

The world is stochastic and chaotic, and organisms have access to limited information to take decisions. For this reason, brains are continuously required to deal with probability distributions, and experimental evidence confirms that they are dealing with these distributions optimally or close to optimally, according to the rules of Bayesian probability theory. Yet, a complete understanding of how these computations are implemented at the neural level is still missing. We assume that the “computational” goal of neurons is to perform Bayesian inference and to represent the state of the world efficiently. Starting from this assumption, we derive from first principles two distinct models of neural functioning, one in single neuron and one in neural populations, which explain known biophysics and molecular processes of neurons. The models we propose suggest a new original interpretation for various neural quantities. Action potentials, which are usually considered the paramount form of communication between neurons, in our model of single neuron dynamics are reinterpreted as an internal communication channel. On the contrary, intracellular calcium concentration is interpreted as the most explicit representation of the external world inside the neuron. Specifically, we propose that calcium level represents the log-odds probability ratio of a particular hidden state in the world. Furthermore, we reinterpret synaptic vesicle release as a sampling process, which simulates the external world given all the available information. Finally, the neural population dynamics we propose interpret spontaneous neural activity as a process of sampling from the prior world statistics. This enables the system to implement a Markov Chain Monte Carlo algorithm that produces inference by sampling. The proposed models generate various observable predictions, which match experimental results about synaptic vesicle release, short-term synaptic potentiation, ions channels open probability, intracellular calcium dynamics and propagation, spike rate adaptation and neural receptive fields.

Quantum physics lends a view of space-time geometry as an emergent structure that shows classical features only at some observational level. The space-time manifold can be viewed as a purely theoretical arena, where quantum states and observables are defined, with the additional freedom of changing coordinates. We focus on spherically symmetric quantum sources, and determine the probability they are black holes. The gravitational radius is promoted to quantum mechanical operator acting on the ``horizon wave-function''. This formalism is applied to several sources with mass around the fundamental scale, as natural candidates of quantum black holes. This horizon quantum mechanics supports some features of BEC models of black holes. The Klein-Gordon equation for a toy graviton field coupled to a static matter current classically reproduces the Newtonian potential, while the corresponding quantum state is given by a coherent superposition of scalar modes. When N such bosons are self-confined in a volume of the size of the Schwarzschild radius, the horizon shows that their radius corresponds to a proper horizon whose related uncertainty is connected to the typical energy of Hawking modes: it is suppressed as N increases, contrarily to a single very massive particle. The spectrum of these systems is formed by a discrete ground state and a continuous Planckian distribution at the Hawking temperature representing the radiation. Assuming the internal scatterings give rise to the Hawking radiation, the N-particle state can be collectively described by a single-particle wave-function. The partition function follows together with the usual entropy law, with a logarithmic correction related to the Hawking component. The backreaction of radiating modes is also shown to reduce the Hawking flux, and eventually stop it.

In the first part of this thesis we study the Aubry-André model for interacting fermions. We numerically describe its phase diagram at half filling, performing both DMRG and QMC simulations. We show the existence of a localized phase and other three regimes: luttinger liquid, charge density wave and productstate. We study the properties of the excited states of the Hamiltonian, looking for a many-body mobility edge in the spectrum, i.e. an energy threshold that separates localized from ergodic states. Analyzing many indicators we prove its existence. Finally we propose a quench-spectroscopy method for detecting the mobility edge dynamically. In the second part we study the expansion dynamics of two bosons in a one-dimensional lattice as ruled by the Bose-Hubbard model Hamiltonian, both in the attractive and repulsive regime. Using the Bethe Ansatz we identify the bound states effects and how the two-particles state evolves in time. We show that, independently from the initial state, there exists a strong relation between the expansion velocity and the presence of bound states in the spectrum. Moreover, we discuss the role of the lattice in the system expansion. In the third part we study the time evolution of the entanglement entropy in the Ising model, when it is dynamically driven across a quantum phase transition with different velocities. We computed the time-evolution of the half chain entanglement entropy and we found that, depending on the velocity at which the critical point is reached, it displays different regimes: an adiabatic one when the system evolves according to the instantaneous ground state; a a sudden quench regime when the system remains frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations. Moreover, we discuss the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.

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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.