In this work we discuss the role of topological degrees of freedom in very low-energy hadronic processes (vacuum polarization and vacuum birefringence). We also present an approach which enables to investigate the microscopic dynamics of non-perturbative processes: this is achieved by constructing an effective statistical theory for topological vacuum gauge configurations, by means of Lattice QCD simulations.

In this thesis I theoretically study the dynamic and ground state properties of ultracold dipolar Fermi gases. The mean-field approach based on the Thomas-Fermi energy functional is applied to consider the dynamic properties of bilayer harmonically trapped dipolar Fermi gases. The fixed-node Diffusion Monte Carlo method (FNDMC) is used instead to investigate the ground-state properties of two dimensional dipolar Fermi gases. This technique is also applied to the problem of one impurity in a bilayer configuration with dipolar fermions.

The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this thesis we explore the properties of spin-orbit-coupled Bose-Einstein condensates with equal Rashba and Dresselhaus strengths. These systems present a rich phase diagram, which exhibits a tricritical point separating a single-minimum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the system. In particular, the excitation spectrum exhibits intriguing features, including the suppression of the sound velocity, the emergence of a roton minimum in the plane-wave phase, and the appearance of a double gapless band structure in the stripe phase. Finally, we discuss a combined procedure to make the stripes visible and stable, thus allowing for a direct experimental detection.

The thesis is devoted to my Ph.D. research activities during last three years within the CMS collaboration. My primary field of interest was the investigation of the Higgs sector of the Standard Model and in connection with Beyond-Standard-Model New Physics searches.

This work is mainly divided in two parts and deals with some aspects of quantum field theory in curved space-time and some open problems related with the cosmological history of our Universe.

In this thesis, we used CMOS-like technologies to produce improved, hierarchical multifunctional bioinspired surfaces. Different natural surfaces have been surveyed including well-known lotus leaf, sharkskin, back of the Namib Desert beetle, butterfly wings, and legs of water-walking insects. The lotus leaf features superhydrophobicity, which leads to low adhesion and self-cleaning. Sharkskin is composed of ripples that manage to reduce skin-friction and thus drag resistance. The Namib Desert beetle, harvests water from the heterogeneous pattern having hydrophilic/hydrophobic bumps on his back. Butterfly wings have re-entrant structures that manage to reach superhydrophobicity from a hydrophilic substrate. Hairy legs of water-walking insects are superhydrophobic with low adhesion that allows them to fight and jump on water. In chapter 1, we have undertaken a review of bioinspired surfaces that emulate the abilities of such natural surfaces. Then, in chapter 2 we have described the innovative CMOS-like techniques used for generating several hierarchical and re-entrant microstructures. Chapter 3 depicts the analysis of surfaces with hierarchical structures generated with a fast and easy process; this latter forms a second hierarchical level composed of random pyramidal elements using wet etching. Surfaces realized with this process manage to reach remarkably high contact angle and low contact angle hysteresis. Additionally, in this chapter we have introduced an analytical model to study the stability of Cassie-Baxter state over Wenzel state for these hierarchical surfaces. In chapter 4 the fabrication and analysis of surfaces composed of controlled hierarchical levels, which combine sharkskin with single-level lotus leaf-inspired pillared structures are reported. These particular hierarchical surfaces are demonstrated to hold high superhydrophobic properties along with low skin-friction. The superhydrophobicity of these surfaces has been characterized in a series of tests on an inclined plane. The data extrapolated from this measurement was used to evaluate the total dissipated energy of the sliding drop. Combining the data collected during this experiment with contact angle and contact angle hysteresis measurements we propose a global parameter that evaluates the superhydrophobic “level†of a surface. Furthermore, in chapter 5 similar hierarchical surfaces have also been tested for water harvesting together with single-level pillared surfaces that feature heterogeneous chemistry with hydrophilic/hydrophobic spot on every single pillar. In chapter 6 a series of tests have also been performed on butterfly-inspired surfaces. Although the substrate of such surfaces is hydrophilic, thanks to the re-entrant structures the surfaces reach high level of hydrophobicity. An implemented mathematical model and experimental test confirm the stability of this hydrophobic state. In chapter 7, we describe two sets of surfaces inspired by the hairy legs of water walking insect the first is composed of stretchable pyramidal-pillars and the second of truncated-conical silicon pillars. The ability of sharp structures to easily detach from water surfaces is exploited to change the contact angle value of a water drop deposed on this fast type of stretchable micropatterned surface. A mathematical model has been implemented and experimental tests have been carried out to evaluate the stability of the water-air composite interface on both types of microstructured surfaces. In particular, in the polymeric surfaces elasto-capillarity seams to influence the metastability of the Cassie-Baxter state.

We analyze ground state properties of few-nucleons systems and $^{16}$O using \eftnopi (Pionless Effective Field Theory) at \ac{LO}. This is the first time the theory is extended to many-body nuclear systems. The free constants of the interaction are fitted using both experimental data and \ac{LQCD} results. The nuclear many-body Schr\"odinger equation is solved by means of the Auxiliary Field Diffusion Monte Carlo method. A linear optimization procedure has been used to recover the correct structure of the ground state wavefunction. {\eftnopi} as revealed to be an appropriate theory to describe light nuclei both in nature, and in the case where heavier quarks are used in order to make \ac{LQCD} calculation feasible. Our results are in good agreement with experiments and \ac{LQCD} predictions. In our \ac{LO} calculation, $^{16}$O appears to be unstable against breakup into four $^4$He for the quark masses considered.

The dynamics of systems out of equilibrium, such as the phase transition process, are very rich, and related to largely scalable problems, from very small ultracold gases to large expanding galaxies. Quantum low-dimensional systems show interesting features, notably different from the canonical three-dimensional case. Bose-Einstein condensates are very good platforms to study macroscopic quantum phenomena. These three points describe well the motivation behind the study presented in this work. In this thesis, some dynamical problems of trapped and uniform condensates are studied, both at zero and finite temperature. In particular, we focus on the analysis of the propagation of linear and nonlinear excitations in a quasi-1D and in quasi-2D systems. In the first case, we are able to correctly describe the dynamics of a solitonic vortex in an elongated condensate, as measured by Serafini et al. [Phys. Rev. Lett. 115, 170402 (2015)]. In the second case, we reproduce the decay rate of a phase-imprinted soliton (collaboration with Birmingham), and assess its dependence on the temperature. We also replicate the propagation speed of sound waves over a wide range of temperatures as in Ville et al. [arXiv:1804.04037] (collaboration with Collà ̈ge de France). The result of this analysis is included in Ota et al. [arXiv:1804.04032], which is currently under revision. In uniform low-dimensional systems Bose-Einstein condensation is technically not possible, and in two dimensions it is replaced by the Berezinskii-Kosterlitz-Thouless superfluid phase transition. We study its critical properties by analysing the spontaneous generation of vortices during a quench, produced via the Kibble-Zurek mechanism. This procedure predicts, for any dimension, the scaling for the density of defects formed during a fast transition, when the system is not adiabatically following the control parameter, and regions of phase inhomogeneity are formed. We address the role of reduced dimensionality on this process. All finite temperature simulations are performed by means of the stochastic (projected) Gross-Pitaevskii equation, a model fully incorporating density and phase fluctuations for weakly interacting Bose gases.

The study of experimental recording of dynamical systems often consists in the analysis of signals produced by that system. Time series analysis consists of a wide range of methodologies ultimately aiming at characterizing the signals and, eventually, gaining insights on the underlying processes that govern the evolution of the system. A standard way to tackle this issue is spectrum analysis, which uses Fourier or Laplace transforms to convert time-domain data into a more useful frequency space. These analytical methods allow to highlight periodic patterns in the signal and to reveal essential characteristics of linear systems. Most experimental signals, however, exhibit strange and apparently unpredictable behavior which require more sophisticated analytical tools in order to gain insights into the nature of the underlying processes generating those signals. This is the case when nonlinearity enters into the dynamics of a system. Nonlinearity gives rise to unexpected and fascinating behavior, among which the emergence of deterministic chaos. In the last decades, chaos theory has become a thriving field of research for its potential to explain complex and seemingly inexplicable natural phenomena. The peculiarity of chaotic systems is that, despite being created by deterministic principles, their evolution shows unpredictable behavior and a lack of regularity. These characteristics make standard techniques, like spectrum analysis, ineffective when trying to study said systems. Furthermore, the irregular behavior gives the appearance of these signals being governed by stochastic processes, even more so when dealing with experimental signals that are inevitably affected by noise. Nonlinear time series analysis comprises a set of methods which aim at overcoming the strange and irregular evolution of these systems, by measuring some characteristic invariant quantities that describe the nature of the underlying dynamics. Among those quantities, the most notable are possibly the Lyapunov ex- ponents, that quantify the unpredictability of the system, and measure of dimension, like correlation dimension, that unravel the peculiar geometry of a chaotic system’s state space. These methods are ultimately analytical techniques, which can often be exactly estimated in the case of simulated systems, where the differential equations governing the system’s evolution are known, but can nonetheless prove difficult or even impossible to compute on experimental recordings. A different approach to signal analysis is provided by information theory. Despite being initially developed in the context of communication theory, by the seminal work of Claude Shannon in 1948, information theory has since become a multidisciplinary field, finding applications in biology and neuroscience, as well as in social sciences and economics. From the physical point of view, the most phenomenal contribution from Shannon’s work was to discover that entropy is a measure of information and that computing the entropy of a sequence, or a signal, can answer to the question of how much information is contained in the sequence. Or, alternatively, considering the source, i.e. the system, that generates the sequence, entropy gives an estimate of how much information the source is able to produce. Information theory comprehends a set of techniques which can be applied to study, among others, dynamical systems, offering a complementary framework to the standard signal analysis techniques. The concept of entropy, however, was not new in physics, since it had actually been defined first in the deeply physical context of heat exchange in thermodynamics in the 19th century. Half a century later, in the context of statistical mechanics, Boltzmann reveals the probabilistic nature of entropy, expressing it in terms of statistical properties of the particles’ motion in a thermodynamic system. A first link between entropy and the dynamical evolution of a system is made. In the coming years, following Shannon’s works, the concept of entropy has been further developed through the works of, to only cite a few, Von Neumann and Kolmogorov, being used as a tool for computer science and complexity theory. It is in particular in Kolmogorov’s work, that information theory and entropy are revisited from an algorithmic perspective: given an input sequence and a universal Turing machine, Kolmogorov found that the length of the shortest set of instructions, i.e. the program, that enables the machine to compute the input sequence was related to the sequence’s entropy. This definition of the complexity of a sequence already gives hint of the differences between random and deterministic signals, in the fact that a truly random sequence would require as many instructions for the machine as the size of the input sequence to compute, as there is no other option than programming the machine to copy the sequence point by point. On the other hand, a sequence generated by a deterministic system would simply require knowing the rules governing its evolution, for example the equations of motion in the case of a dynamical system. It is therefore through the work of Kolmogorov, and also independently by Sinai, that entropy is directly applied to the study of dynamical systems and, in particular, deterministic chaos. The so-called Kolmogorov-Sinai entropy, in fact, is a well-established measure of how complex and unpredictable a dynamical system can be, based on the analysis of trajectories in its state space. In the last decades, the use of information theory on signal analysis has contributed to the elaboration of many entropy-based measures, such as sample entropy, transfer entropy, mutual information and permutation entropy, among others. These quantities allow to characterize not only single dynamical systems, but also highlight the correlations between systems and even more complex interactions like synchronization and chaos transfer. The wide spectrum of applications of these methods, as well as the need for theoretical studies to provide them a sound mathematical background, make information theory still a thriving topic of research. In this thesis, I will approach the use of information theory on dynamical systems starting from fundamental issues, such as estimating the uncertainty of Shannon’s entropy measures on a sequence of data, in the case of an underlying memoryless stochastic process. This result, beside giving insights on sensitive and still-unsolved aspects when using entropy-based measures, provides a relation between the maximum uncertainty on Shannon’s entropy estimations and the size of the available sequences, thus serving as a practical rule for experiment design. Furthermore, I will investigate the relation between entropy and some characteristic quantities in nonlinear time series analysis, namely Lyapunov exponents. Some examples of this analysis on recordings of a nonlinear chaotic system are also provided. Finally, I will discuss other entropy-based measures, among them mutual information, and how they compare to analytical techniques aimed at characterizing nonlinear correlations between experimental recordings. In particular, the complementarity between information-theoretical tools and analytical ones is shown on experimental data from the field of neuroscience, namely magnetoencefalography and electroencephalography recordings, as well as mete- orological data.

The work presents the recent developments in Quantum Monte Carlo calculations for nuclear systems including strange degrees of freedom. The Auxiliary Field Diffusion Monte Carlo algorithm has been extended to the strange sector by the inclusion of the lightest among the hyperons, the Λ particle. This allows to perform detailed calculations for Λ hypernuclei, providing a microscopic framework for the study of the hyperon-nucleon interaction in connection with the available experimental information. The extension of the method for strange neutron matter, put the basis for the first Diffusion Monte Carlo analysis of the hypernuclear medium, with the derivation of neutron star observables of great astrophysical interest.