The investigation of real-time dynamics of charged and neutral quantum excitation propagating through macromolecular systems is receiving growing attention due to its potentially countless applications in nano-scale (opto-)electronics and in biophysics. Several key issues have not been fully clarified yet, including the role played by molecular thermal fluctuations and the possible correlations between the degree of quantum coherence and the efficiency of the transport process. In order to gain some insight, we developed a rigorous and systematic framework describing quantum transport, based on a field-theoretic formalism.

Recent technological advances in quantum simulators have proven that synthetic materials are very well suited to study and realise many condensed matter models. However, many of these synthetic systems are characterized by neutral particles that do not couple to real gauge fields. In order to simulate interesting electromagnetic phenomena, such as the topological insulators, or the Landau levels, there is the need for the implementation of artificial gauge fields. In particular, the topological insulators are very interesting both from the point of view of fundamental physics and concrete applications. They are bulk insulating materials that carry a certain number of edge states which are topologically protected against small perturbations of the system. An example of a topological insulator is the integer quantum Hall effect. While there have been many works studying topological physics with quantum artificial systems, little attention was dedicated to the interplay of topology and the purely classical world. Only in the last couple of years, pioneering efforts to encode a non-trivial topology in the dynamical matrix or into the Hamiltonian of a system have proven that the hallmarks of a topological insulator are not the prerogative of quantum mechanics, but can be also observed with a classical system governed by Newton’s equations. The first part of this thesis is therefore based on our studies dedicated to the implementation of a classical analogue of the integer quantum Hall system, by realizing the Harper-Hofstadter model for classical frequency-modulated coupled harmonic oscillators. The achievement of an artificial gauge field allows also for the deeper study of magnetic effects such as Landau levels. In graphene, an inhomogeneous strain of the lattice is equivalent to an artificial pseudo-magnetic field, and the low-energy spectrum shows the formation of relativistic pseudo-Landau levels. The second part of the thesis is therefore focussed on the photonics honeycomb lattice geometry and our theoretical proposal for a configuration based on an intrinsically driven-dissipative system in which to probe the physics of the Landau levels, and especially the spatial structure of their wavefunctions. Finally, we have also studied spin-orbit coupling in a mechanical system of masses and springs induced by pre-tensioned springs that split the longitudinal and transverse couplings in the honeycomb geometry. We have presented the experimental results of a simple mechanical benzene composed of six pendula connected with pre-tensioned springs, to verify that the eigenmodes of this system are well described by our theory in the presence of spin-orbit coupling.

In this work an improved methodology for the study of hydrogen storage material (HSM) is presented, for the characterization of smaller samples of HSM at increased accuracy. It includes: the realization of innovative differential instrument; a novel approach to the detailed micro kinetic modelling; increase the comprehension of absorption and desorption mechanisms; support research efforts in this topic. As side results, a macro and lumped model for the design of generic hydrogen storage tank are developed and validated. The study of a novel IDA (Isochoric Differential apparatus) is presented, describing all the steps from the initial theoretical approach, to the detailed design and the definition of an experimental proceeding. It includes the necessary technical improvements to increase the measure uncertainty compared to the classical SIevert. Novel microkinetic modelling for HSM is explained as variation of classic nucleation and growth model (JMAK model). The nuclei’s growth is assumed to be limited by surface or even by radius of powder’s particles. Micro modelling is applied on Mg-based material, introducing high accurate kinetic measures obtained by IDA. This leads to extrapolate information about kinetic parameters and kinetic mechanisms of hydrogen sorption. The obtained micro modelling is used as core for the development of a model at a higher scale (macro) which keeps in consideration also heat and hydrogen diffusion in porous materials typical in hydrogen storage tank. Experimental data collected by a prototipal realization of hydrogen storage tank are used to validate macro modelling. Moreover, a lumped model is developed with the scope to built a numerical tool able to give preliminary indications on proper design/layout of hydrogen storage tank, based on hydrogen flow, temperature or pressure requirements. Lumped modelling is finally compared with results by the numerical simulation of validated macro model. Finally, micro kinetic model is applied on high accuracy sorption data (by IDA) on innovative catalysed Mg-material. Material is produced by a novel approach, where catalyst, Nb2O5, is deposited by PVD techniques at extremely low concentration on the surface of powder to exploit its higher catalyst proprieties.

The aim of this thesis is to study renormalization of Wick polynomials of quantum Boson fields in locally covariant algebraic quantum field theory in curved spacetime. Vector fields are described as sections of natural vector bundles over globally hyperbolic spacetimes and quantized in a locally covariant framework through the known functorial machinery in terms of local *-algebras. These quantized fields may be defined on spacetimes with given classical background fields, also sections of natural vector bundles: The most obvious one is the metric of the spacetime itself, but we encompass also the case of generic spacetime tensors as background fields. In our framework also physical quantities like the mass of the field or the coupling to the curvature are viewed as background fields. Wick powers of the quantized vector field are then axiomatically defined imposing in particular local covariance, scaling properties and smooth dependence on smooth perturbation of the background fields. A general classification theorem is established for finite renormalization terms (or counterterms) arising when comparing different solutions satisfying the defining axioms of Wick powers. The result is then specialized to the case of spacetime tensor fields. In particular, the case of a vector Klein-Gordon field and the case of a scalar field renormalized together with its derivatives are discussed as examples. In each case, a more precise statement about the structure of the counterterms is proved. The finite renormalization terms turn out to be finite-order polynomials tensorially and locally constructed with the backgrounds fields and their covariant derivatives whose coefficients are locally smooth functions of polynomial scalar invariants constructed from the so-called marginal subset of the background fields. Our main technical tools are based on the Peetre-Slov\'ak theorem characterizing differential operators and on the classification of smooth invariants on representations of reductive Lie groups.

Time-resolved fluorescence measurements enable the study of structure of molecular systems and dynamical processes inside them. This is possible because of a very high sensitivity of fluorescence lifetime to the physical and chemical properties of micro-environment in which fluorophores are situated. However, proper detection of the fluorescence lifetime is a challenging task, due to the fact that the fluorescence decay time of commonly used fluorophores lies in a nanosecond range. This puts strict requirements on the parameters of the fluorescence detectors. The features of single-photon avalanche diodes (SPAD) make these optical detectors a good alternative to conventional photomultiplier tubes and micro-channel plates. CMOS technology allows cointegration of a SPAD and electronic circuits on the same substrate and provides advantages in time resolution and noise characteristics. Monolithic integration of signal processing circuits and detectors on the same chip allows using such detectors without additional external hardware. New SPAD sensors with improved characteristics are produced every year. However, the designers consider various performance metrics while the importance of each particular detector characteristic depends on its application. Therefore, the validation and optimization of SPAD characteristics should be performed in a close connection with the analysis of a specific system, wherein this detector will be used. This work was aimed at developing of a model able to describe a typical fluorescence experiment with SPAD-based detector. The model simulates all essential parts of the fluorescence experiment starting from the light emission, through photo-physical processes occurring inside a bio-sample, to a detector itself and read-out electronics. The ability of the developed model to simulate various light sources (laser and micro-LED), fluorescence measurement techniques (time-correlated single photon counting and time-gating) was verified. The simulated results were in good agreement with the experimental data and the model proved its flexibility. Furthermore, the model provided the explanation of the distortions in experimental fluorescent curves measured under a very high ambient light when pile-up effects appear. Finally, a set of virtual experiments were established to investigate the influence of noisy pixels in SPAD array on a lifetime estimation and to study the feasibility of time-filtering instead of conventional optical filtering. Simulation results are in good agreement with data available in literature.

In this thesis we investigate the properties of impurities immersed in a dilute Bose gas at zero temperature using quantum Monte-Carlo methods. The interactions between bosons are modeled by a hard sphere potential with scattering length a, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length b can be varied by adjusting the well depth. We calculate the binding energy, the effective mass and the pair correlation functions of a impurity along the attractive and the repulsive polaron branch. In particular, at the unitary limit of the impurity-bosons interaction, we find that the binding energy is much larger than the chemical potential of the bath signaling that many bosons dress the impurity thereby lowering its energy and increasing its effective mass. We characterize this state by calculating the bosons-boson pair correlation function and by investigating the dependence of the binding energy on the gas parameter of the bosonic bath. We also investigate the ground-state properties of M impurities in a Bose gas at T=0. In particular, the energy and the phase diagram by using both quantum Monte-Carlo and mean field methods.

The experimental achievement of Bose-Einstein condensation and Fermi degeneracy with ultracold gases boosted tremendous progresses both in theoretical methods and in the development of new experimental tools. Among them, intriguing possibilities have been opened by the implementation of optical lattices: periodic potentials for neutral atoms created by interfering laser beams. Degenerate gases in optical lattices can be forced in highly anisotropic traps, reducing the effective dimensionality of the system. From a fundamental point of view, the behavior of matter waves in reduced dimensions sheds light on the intimate properties of interparticle interactions. Furthermore, such reduced-dimensional systems can be engineered to quantum-simulate fasci- nating solid state systems, like bidimensional crystals, in a clean and controllable environment. Motivated by the exciting perspectives of this field, we devote this Thesis to the theoretical study of two systems where matter waves propagate in reduced dimensions. The long-range and anisotropic character of the dipole-dipole interaction critically affects the behavior of dipolar quantum gases. The continuous experimental progresses in this flourishing field might lead very soon to the creation of degenerate dipolar gases in optical potentials. In the first part of this Thesis, we investigate the emergence of a single dipolar-induced resonance in the two-body scattering process in quasi-one dimensional geometries. We develop a two-channel approach to describe such a resonance in a highly elongated cigar-shaped harmonic trap, which approximates the single site of a quasi-one-dimensional optical lattice. At this stage, we develop a novel atom-dimer extended Bose-Hubbard model for dipolar bosons in this quasi-one-dimensional optical lattice. Hence we investigate the T = 0 phase diagram of the model by exact diagonalization of a small-sized system, highlighting the effects of the dipolar-induced resonance on the many-body behavior in the lattice. In the second part of the Thesis, we present a general scheme to realize cold-atom quantum simulators of bidimensional atomic crystals, based on the possibility to independently trap two different atomic species. The first one constitutes a two-dimensional matter wave which interacts only with the atoms of the second species, deeply trapped around the nodes of a two-dimensional optical lattice. By introducing a general analytic approach, we investigate the matter-wave transport properties. We propose some illustrative applications to both Bravais (square, triangular) and non-Bravais (graphene, kagomeÌ ) lattices, studying both ideal periodic systems and experimental- sized, eventually disordered, ones. The features of the artificial atomic crystal critically depend on the two-body interspecies interaction strength, which is shown to be widely tunable via 0D-2D mixed-dimensional resonances. Keywords: matter waves, reduced dimensions, dipolar-induced resonances, mixed-dimensional resonances, extended Bose-Hubbard model, atomic artificial crystals.

In this thesis we investigate the properties of mixtures of Bose gases in one dimensions at zero temperature using quantum Monte-Carlo methods. First we investigate the limiting case of an impurity interacting with an atomic bath. We characterize the impurity, by calculating its effective mass, binding energy as well as the contact parameter between the impurity and the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. Then we describe uniform balanced mixtures with repulsive interactions. We investigate the miscibility phase diagram of the two components and find that correlations do not alter the phase diagram predicted by mean-field theories. We investigate the Andreev-Bashkin effect , a non-dissipative drag between the the two components of the gas and find that the drag becomes very large in the strongly interacting regime. In non-homogeneous systems we also investigate the frequency of the spin-dipole mode. Finally we describe mixtures with attractive inter-species interactions, where one can obtain a liquid ground state because of the competition between the inter-species attraction and intra-species repulsion. We characterize the the liquid and we find that the liquid state can be formed if the ratio of coupling strengths between inter-species attractive and intra-species repulsive interactions exceeds a critical value.

General Relativity is known to suffer from singularities at short distances, which indicates the breakdown of its predictability, for instance at the center of black holes, and in the very early universe. This is one of the main reason to look for a Quantum Theory of Gravity, that would describe spacetime geometry as a quantum field, and possibly cure these classical singularities. However, no consensus on the topic has yet been reached, as many different approaches have been proposed, but none has yet received an experimental confirmation. This is in part due to the extraordinary small scale at which quantum gravitational effects are expected to become dominant, and to the technical difficulty to make unambiguous predictions. For this reason, many works have focused on the so-called effective approaches in which the possible high energy corrections to General Relativity are classified, and their theoretical and ob- servational predictions derived, with the idea that among these modifications, some could come as the semi-classical limits of quantum gravity theories. A way to discriminate between the different proposals is precisely the absence of singular geometries in their solutions. In the first two Chapters of this thesis, we will present such an effective approach, in which the action of General Relativity is modified at high energy by non-polynomial curvature invariants, which are constructed in such a way that the dynamical spherically symmetric sector of these theories (which contain both cosmological and non-rotating black hole spacetimes) yield second order field equations. These properties of the non-polynomial invariants follow from a peculiar algebraic identity satisfied by the Cotton tensor in this class of geometries. As we will see in the last two Chapters, having second order dynamical spherically symmetric field equations is necessary in order to recover some quantum corrected geometries that have been found from more fundamental approaches like Loop Quantum Cosmology and Asymptotic Safety, within its Einstein-Hilbert truncation. The existence of such gravitational models provides an interpretation of two-dimensional Horn- deski theory as describing the dynamical spherically symmetric sector of specific higher dimensional non-polynomial gravity theories. Therefore, it allows to have some concrete d-dimensional formu- lations of the two-dimensional Einstein-Dilaton and Lovelock Designer effective approaches that have been studied extensively, in particular to find and study the properties of non-singular black holes. This enables us to propose two four-dimensional effective-like actions, which are constructed in such a way that their dynamical spherically symmetric sectors decompose in the same way as those of General Relativity and Gauss-Bonnet gravity. In the remaining Chapters, we essentially investigate the solutions and properties of these theories. It is shown that the first one leads to regular (A)dS-core black hole solutions, with the correct quantum correction to their Newton potentials and logarithmic correction to their entropies. The charged generalization is considered, and a way to avoid the mass inflation instability of their inner horizons is found, provided that a bound between the mass and the charge is satisfied. In Chap. 4, we establish a reconstruction procedure able to find theories admitting as solutions the Modesto semi-polymeric black hole, as well as the D’Ambrosio-Rovelli and Visser-Hochberg geometries. All these black holes are regular and derived or inspired by quantum gravity results. They have many properties in common, as for example the fact that they automatically regularize the Coulomb singularity of a static electric field. Finally, the last Chapter is devoted to the theory whose dynamical spherically symmetric sector is a generalization of the one of Gauss-Bonnet gravity. It is shown that the Loop quantum cosmology bounce universe and some Asymptotic Safety black holes can be reconstructed from two members of these theories. In particular, the associated black hole solutions of the first are regular, and the associated cosmological solution of the second is as well, and describe a universe which is eternal in the past, and behaves as de Sitter spacetime in the limit of infinite past. Some generalizations of these results are provided, and the Mimetic gravity formulations of the cosmological solutions are found.

The behavior of surface tension within the random first-order theory (RFOT) of glass transition is studied in a glass-forming liquid model by means of ad-hoc numerical methods. The spinodal point for RFOT excitations turns out to be well defined as a function of the energy of inherent structures (IS), i.e. the minima of potential energy which underlie the equilibrium configurations. The corresponding spinodal temperature, although not sharply defined, lies definitely above the mode coupling one. The role played by surface tension within the context of dynamical heterogeneities is also studied by means of a dynamic algorithm in which the overlap with the initial configuration is constrained along equilibrium dynamics. Indications are found that, in the proximity of the mode coupling temperature, a phase-separation between high and low overlap regions occurs, driven by surface tension. The existence of a positive surface tension between amorphous excitations, in the proximity of the mode-coupling temperature, is therefore observed for both static and dynamic excitations.