O fenômeno de permeabilidade refere-se à capacidade com que um fluido é transportado através de um meio poroso, impulsionado por gradiente de pressão entre material e meio externo. Agentes de degradação são conduzidos ao interior de argamassas e concretos impelidos através desse tipo de fenômeno. Por isso, considera-se a permeabilidade como um dos principais parâmetros referentes à durabilidade e vida útil de materiais cimentíceos. Além disso, como esse tipo de avaliação está relacionada às condições estruturais dos vazios capilares de meios porosos, esse tipo de medida pode prover um indicativo das condições da estrutura porosa das argamassas no momento do ensaio, servindo ainda como método de controle de qualidade e avaliação dos processos de produção. Portanto, um novo procedimento de medida de permeabilidade ao ar, em regime de escoamento transiente, foi desenvolvido para avaliação de argamassas de revestimento através do método de vaccum-decay. O potencial do processo não se restringe apenas na determinação dos parâmetros clássicos de permeabilidade propostos por Henry Darcy, mas na avaliação das curvas de recuperação de pressão que fornecem um indicativo das condições microestruturais de diferentes estados da estrutura de meios porosos. Além disso, trata-se de um ensaio portátil, não destrutivo e de baixo custo de implementação para avaliação de argamassas de revestimento in situ. Para isto, neste trabalho foram avaliadas diferentes formulações de argamassas de revestimento tanto em ambiente laboratorial quanto in situ, em comparação ao método de Cembureau (referência), e se existe relação entre as duas diferentes condições apresentadas. A profundidade alcançada por esse tipo de ensaio superficial é uma dúvida recorrente deste e outros ensaios da mesma natureza, e por isso foi considerado no desenvolvimento do plano experimental. Ainda, as diferentes direções do fluxo de ar durante a medida podem influenciar as determinações das permeabilidades para diferentes configurações de experimentos realizados, e também foram considerados no desenvolvimento do método. / The phenomenon of permeability refers to the ability with which a fluid is transported through a porous medium, driven by pressure gradient between the material and the external environment. Degradation agents are conducted to the interior of mortar and concrete driven through such a phenomenon. Therefore, it is the permeability as a key parameters for durability and shelf life of cementitious materials. Moreover, as this type of evaluation is related to structural conditions of the empty capillary porous media, this type of measurement can provide an indication of the conditions of the porous structure of mortar at the time of trial, still serving as a method of quality control and evaluation production processes. Therefore, a new procedure for measuring air permeability in transient flow regime was developed for evaluation of mortar coating by the method of vacuum-decay. The potential of the process is not restricted only to the determination of the classical parameters of permeability proposed by Henry Darcy, but in assessing the recovery curve of pressure that provide a clear picture of states in different microstructural conditions of the structure of porous media. Moreover, it is a portable test, nondestructive and low cost of implementation for evaluation of mortar coating in situ. For this reason, this study evaluated different formulations of mortar coating in laboratory environment and in situ, compared to the Cembureau method (reference), and if there is a relationship between two different conditions presented. The depth reached by this type of test surface is a recurring question of this and other tests of the same nature, and so was considered in developing of this experimental plan. Still, the different directions of air flow during the measurement can influence the determination of permeability for different configurations of the experiments, and were also considered in developing the method.

Neste trabalho analisamos algumas consequências físicas de uma cosmologia acelerada com interação no chamado setor cósmico escuro (energia escura + matéria escura fria). A componente de energia escura é representada por uma densidade de energia do vácuo que varia com o tempo e cuja lei de decaimento tem a seguinte forma: $\\Lambda = \\Lambda_0 + {3\\alpha}/{a^{2}}$, onde $\\Lambda_0$ é o termo de vácuo usual, $\\alpha$ é um parâmetro livre e $a(t)$ o fator de escala. Nesse contexto discutimos a tensão existente entre os dados de Supernovas (que preferem um Universo fechado, $\\Omega_{\\kappa} > 0$) e os dados da radiação cósmica de fundo que favorecem um Universo espacialmente plano ($\\Omega_{\\kappa} = 0$). Considerando que o termo variável simula uma curvatura (pois ambos possuem a mesma dependência no fator de escala), mostramos que sua contribuição atua no sentido de aliviar a tensão SNe Ia-CMB existente no modelo de concordância cósmica padrão ($\\Lambda CDM$, $\\alpha=0$). O modelo resolve o problema da idade do Universo e para $a>>1$, tal como ocorre com $\\Lambda CDM$, também evolui para um estágio de Sitter. O parâmetro $\\alpha$ é limitado através de uma análise estatística conjunta envolvendo dados de Supernovas, CMB ({\\it shift parameter}) e oscilações acústicas dos bárions (BAO). Separando o termo de vácuo em duas componentes ($\\Omega_{\\Lambda 0}$ e $\\Omega_{\\alpha 0}$) um teste $\\chi^{2}$ fornece os seguintes valores para o modelo plano: $\\Omega_{m0} = 0,27 \\pm 0,02$, $\\Omega_{\\Lambda 0} = 0,74 \\pm 0,02$ e $\\Omega_{\\alpha 0} = -0,01 \\pm 0,03$. / In this work we analyze some physical consequences of an accelerating cosmology endowed with interaction in the cosmic dark sector (dark energy + cold dark matter). The dark energy component is represented by a time-dependent vacuum energy whose decay law has the following form: $\\Lambda = \\Lambda_0 + {3\\alpha}/{a^{2}}$, where $\\Lambda_0$ is the standard vacuum term, $\\alpha$ is a free parameter and $a(t)$ is the scale factor. In this context we discuss the existing tension between Supernovas (SNe Ia, which prefer a closed Universe, $\\Omega_{\\kappa} > 0$) and the cosmic background radiation (CMB) data (which are favoring a spatially flat Universe, $\\Omega_{\\kappa} = 0$). By considering that the variable $\\Lambda$-term mimics a curvature (since both terms have the same dependence on the scale factor), we show that its contribution helps to alleviate the tension SNe Ia-CMB existing in the standard cosmic concordance model. The present model solves the age of the Universe problem and for $a>>1$, it also evolves to a de Sitter model as occur with the $\\Lambda CDM$ scenario. The contribution of the $\\alpha$ parameter is limited through a joint statistical analysis involving Supernovas, CMB ({\\it shift parameter}) and baryon acoustic oscillations (BAO). By separating the variable vacuum term in two components ($\\Omega_{\\Lambda 0}$ e $\\Omega_{\\alpha 0}$), a $\\chi^{2}$ test furnishes the following values for the free parameters of the flat model: $\\Omega_{m0} = 0,27 \\pm 0,02$, $\\Omega_{\\Lambda 0} = 0,74 \\pm 0,02$ and $\\Omega_{\\alpha 0} = -0,01 \\pm 0,03$.

Neste trabalho analisamos algumas consequências físicas de uma cosmologia acelerada com interação no chamado setor cósmico escuro (energia escura + matéria escura fria). A componente de energia escura é representada por uma densidade de energia do vácuo que varia com o tempo e cuja lei de decaimento tem a seguinte forma: $\\Lambda = \\Lambda_0 + {3\\alpha}/{a^{2}}$, onde $\\Lambda_0$ é o termo de vácuo usual, $\\alpha$ é um parâmetro livre e $a(t)$ o fator de escala. Nesse contexto discutimos a tensão existente entre os dados de Supernovas (que preferem um Universo fechado, $\\Omega_{\\kappa} > 0$) e os dados da radiação cósmica de fundo que favorecem um Universo espacialmente plano ($\\Omega_{\\kappa} = 0$). Considerando que o termo variável simula uma curvatura (pois ambos possuem a mesma dependência no fator de escala), mostramos que sua contribuição atua no sentido de aliviar a tensão SNe Ia-CMB existente no modelo de concordância cósmica padrão ($\\Lambda CDM$, $\\alpha=0$). O modelo resolve o problema da idade do Universo e para $a>>1$, tal como ocorre com $\\Lambda CDM$, também evolui para um estágio de Sitter. O parâmetro $\\alpha$ é limitado através de uma análise estatística conjunta envolvendo dados de Supernovas, CMB ({\\it shift parameter}) e oscilações acústicas dos bárions (BAO). Separando o termo de vácuo em duas componentes ($\\Omega_{\\Lambda 0}$ e $\\Omega_{\\alpha 0}$) um teste $\\chi^{2}$ fornece os seguintes valores para o modelo plano: $\\Omega_{m0} = 0,27 \\pm 0,02$, $\\Omega_{\\Lambda 0} = 0,74 \\pm 0,02$ e $\\Omega_{\\alpha 0} = -0,01 \\pm 0,03$. / In this work we analyze some physical consequences of an accelerating cosmology endowed with interaction in the cosmic dark sector (dark energy + cold dark matter). The dark energy component is represented by a time-dependent vacuum energy whose decay law has the following form: $\\Lambda = \\Lambda_0 + {3\\alpha}/{a^{2}}$, where $\\Lambda_0$ is the standard vacuum term, $\\alpha$ is a free parameter and $a(t)$ is the scale factor. In this context we discuss the existing tension between Supernovas (SNe Ia, which prefer a closed Universe, $\\Omega_{\\kappa} > 0$) and the cosmic background radiation (CMB) data (which are favoring a spatially flat Universe, $\\Omega_{\\kappa} = 0$). By considering that the variable $\\Lambda$-term mimics a curvature (since both terms have the same dependence on the scale factor), we show that its contribution helps to alleviate the tension SNe Ia-CMB existing in the standard cosmic concordance model. The present model solves the age of the Universe problem and for $a>>1$, it also evolves to a de Sitter model as occur with the $\\Lambda CDM$ scenario. The contribution of the $\\alpha$ parameter is limited through a joint statistical analysis involving Supernovas, CMB ({\\it shift parameter}) and baryon acoustic oscillations (BAO). By separating the variable vacuum term in two components ($\\Omega_{\\Lambda 0}$ e $\\Omega_{\\alpha 0}$), a $\\chi^{2}$ test furnishes the following values for the free parameters of the flat model: $\\Omega_{m0} = 0,27 \\pm 0,02$, $\\Omega_{\\Lambda 0} = 0,74 \\pm 0,02$ and $\\Omega_{\\alpha 0} = -0,01 \\pm 0,03$.

O fenômeno de permeabilidade refere-se à capacidade com que um fluido é transportado através de um meio poroso, impulsionado por gradiente de pressão entre material e meio externo. Agentes de degradação são conduzidos ao interior de argamassas e concretos impelidos através desse tipo de fenômeno. Por isso, considera-se a permeabilidade como um dos principais parâmetros referentes à durabilidade e vida útil de materiais cimentíceos. Além disso, como esse tipo de avaliação está relacionada às condições estruturais dos vazios capilares de meios porosos, esse tipo de medida pode prover um indicativo das condições da estrutura porosa das argamassas no momento do ensaio, servindo ainda como método de controle de qualidade e avaliação dos processos de produção. Portanto, um novo procedimento de medida de permeabilidade ao ar, em regime de escoamento transiente, foi desenvolvido para avaliação de argamassas de revestimento através do método de vaccum-decay. O potencial do processo não se restringe apenas na determinação dos parâmetros clássicos de permeabilidade propostos por Henry Darcy, mas na avaliação das curvas de recuperação de pressão que fornecem um indicativo das condições microestruturais de diferentes estados da estrutura de meios porosos. Além disso, trata-se de um ensaio portátil, não destrutivo e de baixo custo de implementação para avaliação de argamassas de revestimento in situ. Para isto, neste trabalho foram avaliadas diferentes formulações de argamassas de revestimento tanto em ambiente laboratorial quanto in situ, em comparação ao método de Cembureau (referência), e se existe relação entre as duas diferentes condições apresentadas. A profundidade alcançada por esse tipo de ensaio superficial é uma dúvida recorrente deste e outros ensaios da mesma natureza, e por isso foi considerado no desenvolvimento do plano experimental. Ainda, as diferentes direções do fluxo de ar durante a medida podem influenciar as determinações das permeabilidades para diferentes configurações de experimentos realizados, e também foram considerados no desenvolvimento do método. / The phenomenon of permeability refers to the ability with which a fluid is transported through a porous medium, driven by pressure gradient between the material and the external environment. Degradation agents are conducted to the interior of mortar and concrete driven through such a phenomenon. Therefore, it is the permeability as a key parameters for durability and shelf life of cementitious materials. Moreover, as this type of evaluation is related to structural conditions of the empty capillary porous media, this type of measurement can provide an indication of the conditions of the porous structure of mortar at the time of trial, still serving as a method of quality control and evaluation production processes. Therefore, a new procedure for measuring air permeability in transient flow regime was developed for evaluation of mortar coating by the method of vacuum-decay. The potential of the process is not restricted only to the determination of the classical parameters of permeability proposed by Henry Darcy, but in assessing the recovery curve of pressure that provide a clear picture of states in different microstructural conditions of the structure of porous media. Moreover, it is a portable test, nondestructive and low cost of implementation for evaluation of mortar coating in situ. For this reason, this study evaluated different formulations of mortar coating in laboratory environment and in situ, compared to the Cembureau method (reference), and if there is a relationship between two different conditions presented. The depth reached by this type of test surface is a recurring question of this and other tests of the same nature, and so was considered in developing of this experimental plan. Still, the different directions of air flow during the measurement can influence the determination of permeability for different configurations of the experiments, and were also considered in developing the method.

Metastable states are classically stable at zero temperature but can decay due to quantum tunneling. The rate of this process is exponentially small and it may be computed in Euclidean space in the Coleman-de Luccia formalism. The exponential suppression is determined by the Euclidean action computed on a trajectory with definite boundary conditions, known as Coleman-de Luccia instanton, or bounce. In some theories, the bounce may not exist or its on-shell action may be ill-defined or infinite, thus hindering the vacuum decay process. The issue of vacuum stability is, in fact, not just speculation: the Standard Model vacuum state is itself metastable. The Higgs field may tunnel outside its potential well, with catastrophic consequences for all observers. Luckily, the typical lifetime of such a state is predicted to be very long. Still, unknown high energy physics can change it by several orders of magnitude, and particle physics theories as well as cosmological models that predict large decay rates are ruled out thanks to the anthropic principle. Moreover, gravitational effects play an important role in this process, especially in the early Universe. It is thus important to examine in detail vacuum decay phenomena in gravitational settings and to keep the underlying field theory as general as possible. This thesis aims at exploring existence conditions for the Coleman-de Luccia instanton in gravitational settings. The first two chapters are dedicated to outlining the basic formalism and describing preexisting results about vacuum decay in cosmology. The Euclidean path integral approach for decay rate calculations, which was first discussed by Callan and Coleman, is introduced in Chapter 1. A quantum mechanical description of the problem is formulated and then extended to field theory. A detailed analysis of bounce calculations and their physical interpretation as bubbles of true vacuum follows. The Higgs field stability within the Standard Model is also addressed. Gravitational effects on the vacuum decay process are considered in Chapter 2, by focusing on the decay from Minkowski and de Sitter space, as they have important cosmological consequences respectively in the current Universe (due to the smallness of the cosmological constant) and at early times. The implications on Higgs decay are discussed in both settings. The last two chapters are dedicated to new results. Vacuum decay in field theories with a scalar field and quadratic gravity is investigated. An Einstein-Hilbert term, a non-minimal coupling, and a quadratic Ricci scalar are considered while keeping the scalar field potential general. The focus is on decay from Minkowski and de Sitter space, due to their importance in cosmology. Scalar fields with Einstein-Hilbert gravity are discussed in Chapter 3, by showing that the bounce at large Euclidean radii has an analytical form that is almost entirely independent of the potential, which is called the "asymptotic bounce". Bounds on the Hubble parameter in the de Sitter case are also explored, by giving an analytical explanation to numerical evidence present in the literature. These properties are used, in Chapter 4, to test for stabilization of the false vacuum state in quadratic gravity. Conclusions follow.

Une étude analytique et numérique de vortex métastables couplés gravitationnelle- ment et formés dans un modèle abélien de Higgs modifié est menée. Les concepts de désintégration du faux vide et de solitons topologiques sont revus. Le modèle à l’étude est comparé à d’autres modèles dans lesquels sont aussi formés des vortex. Les solutions classiques correspondant au vortex sont trouvées numériquement. Leur sensibilité au couplage gravitationnel est mise en évidence. Les zones de stabilité dans l’espace des paramètres sont également définies. Un profil dit thin-wall du vortex survient dans la limite d’un grand champ magnétique dans le coeur du vortex. La désintégration du vortex, possible en raison du vrai vide à l’intérieur de celui-ci, est dans ce cas analysée analyti- quement. Dans cette limite, l’exposant lié au taux de désintégration du vortex vaut la moitié de celui associé à la désintégration du faux vide sans vortex. Ce résultat tient peu importe la force du couplage gravitationnel. Ainsi, même une faible densité de vortex pouvant induire la désintégration du faux vide accélère grandement le processus de transition de phase et détermine le temps de vie du faux vide. Quelques commentaires concernant la limite faible gravité de l’action en théorie des champs sont ajoutés pour compléter l’étude. / Metastable vortices formed in a modified abelian Higgs model with gravity are studied both analytically and numerically. Concepts of false vacuum decay and topological solitons are reviewed. The model studied is compared to other models in which vortices are also formed. Classical solutions corresponding to a vortex are found numerically. Their sensitivity to gravitational coupling is highlighted. Zones of stability in parameter space are shown. A so-called “thin-wall” limit of the vortex is obtained for high magnetic flux whithin the vortex’s core. In that case, vortex disintegration, possible because of the true vacuum present inside the vortex, can be studied analytically. In this limit, the exponent associated to vortex tunneling decay rate is half the one associated with ordinary false vacuum decay. This results holds regardless of the gravitational coupling strength. Then, even a small density of vortices accelerates importantly the phase transition from false to true vacuum and determine the false vacuum lifetime. Comments on weak gravity limit of the action in field theory are made to complete this study.

Dans ce mémoire, on étudie la désintégration d’un faux vide, c’est-à-dire un vide qui est un minimum relatif d’un potentiel scalaire par effet tunnel. Des défauts topologiques en 1+1 dimension, appelés kinks, apparaissent lorsque le potentiel possède un minimum qui brise spontanément une symétrie discrète. En 3+1 dimensions, ces kinks deviennent des murs de domaine. Ils apparaissent par exemple dans les matériaux magnétiques en matière condensée. Un modèle à deux champs scalaires couplés sera étudié ainsi que les solutions aux équations du mouvement qui en découlent. Ce faisant, on analysera comment l’existence et l’énergie des solutions statiques dépend des paramètres du modèle. Un balayage numérique de l’espace des paramètres révèle que les solutions stables se trouvent entre les zones de dissociation, des régions dans l’espace des paramètres où les solutions stables n’existent plus. Le comportement des solutions instables dans les zones de dissociation peut être très différent selon la zone de dissociation dans laquelle une solution se trouve. Le potentiel consiste, dans un premier temps, en un polynôme d’ordre six, auquel on y rajoute, dans un deuxième temps, un polynôme quartique multiplié par un terme de couplage, et est choisi tel que les extrémités du kink soient à des faux vides distincts. Le taux de désintégration a été estimé par une approximation semi-classique pour montrer l’impact des défauts topologiques sur la stabilité du faux vide. Le projet consiste à déterminer les conditions qui permettent aux kinks de catalyser la désintégration du faux vide. Il appert qu’on a trouvé une expression pour déterminer la densité critique de kinks et qu’on comprend ce qui se passe avec la plupart des termes. / In this thesis, we study the tunneling decay of the false vacuum, that is, a vacuum that is a relative minimum of a scalar potential. Topological defects in 1+1 dimension, called kinks, appear when the potential possesses a minimum that spontaneously breaks a discrete symmetry. In 3+1 dimensions, these kinks become domain walls. For instance, they appear in magnetic materials in condensed matter. A model with two coupled scalar fields will be studied, as well as the solutions to the equations of motion that arise from it. We will then analyze how the energy of the static solutions depend on the parameters of the model. A numerical survey of parameter space reveals that the stable solutions are located between dissociation zones, areas in parameter space where stable solutions no longer exist. The behavior of the unstable solutions in the dissociation zones can be very different depending on which dissociation zone a solution is found near the dissociation zone. The potential first consists in a sixth-order polynomial, to which is added a quartic polynomial multiplied by a coupling term, and is chosen such that the extremities of the kink are at distinct false vacua. The decay rate has been estimated by a semiclassical approximation to show the impact of topological defects on the stability of the false vacuum. The project consists in determining the conditions that allow the kinks to catalyze false vacuum decay. It appears that we found an expression for the critical kink density and that we understand what happens with most terms.

In 1981, Unruh suggested the possibility of simulating the dynamics of quantum fields in curved spacetimes using sound-waves propagating in moving fluids: a supersonic flow would indeed influence the dynamics of sound similarly to what happens to light when it’s dragged by the spacetime geometry in strong gravity environments. This simple yet groundbreaking observation has lead to the beginning of a whole new field of research, nowadays known as Analog Gravity. Due to their superfluid character, intrinsic quantum nature and impressive experimental tunability, Bose-Einstein condensates represent one of the most promising platforms to realize analog spacetimes, including black-hole geometries with horizons and ergoregions, as well as of time-dependent configurations relevant to cosmology. In this Thesis we go beyond the standard single-component BEC and focus on two-component mixtures of atomic condensates, possibly in the presence of a coherent coupling between the two-components: the availability of various branches of elementary excitations with different sound speed and effective mass may in fact lead to advantages in the implementation of interesting geometries and, eventually, to the exploration of a broader spectrum of physical processes. We first consider black-hole related phenomena (Hawking radiation and rotational superradiance) that have already been analysed with single-component systems, generalising the results to mixtures; we then proceed to tackle a problem (the decay from the false vacuum) which instead requires the additional degrees of freedom that only a mixture displays.

The physics of ultracold atomic gases has been the subject of a long standing theoretical and experimental research over the last half century. The development of evaporative cooling techniques and the realization of the first Bose-Einstein Condensate (BEC) in 1995 gave a great advantage to the field. A great experimental knowledge of the fundamental properties of BECs, such as long-range coherence, superfluidity and topological excitations, has now been acquired. On top of these advances, current research on ultracold atoms is also focusing on quantum simulations, which aim at building analogue models of otherwise difficult to compute physical systems in the lab. In this context, BECs, with their enhanced coherence, many-body dynamics and superfluid character offer a powerful platform for advances in the field. Shortly after the first realization of a BEC, research started also investigating the physics of quantum mixtures of a BECs, either composed of different atomic species or isotopes, or of atoms occupying different hyperfine states. The latter are known as spin mixtures, or spinor condensates. The presence of multiple components interacting through mutual contact interactions enriches the physics of the condensate, introducing ground states with magnetic ordering as well as spin dynamics, which can be order of magnitudes less energetic than the density one. On top of this, hyperfine states can be coherently coupled with an external resonant radiation. Interesting physics arises when the strength of the coupling is comparable with the energy of spin excitations, an example of which is given by the emergence of the internal Josephson effect. This regime has been the subject of intense theoretical studies in the past twenty years, however its experimental realization on ultracold atomic platforms have been proven to be challenging, with experiments strongly limited by coherence times of few tens of milliseconds. In fact, the small energy scale of spin excitations reflects in a high sensitivity coupling to environmental magnetic noise, which affects the resonant condition. The experimental apparatus on which I worked during my Ph.D. solve this problem employing a magnetic shield that surrounds the science chamber, attenuating external magnetic fields by 6 orders of magnitudes. During my Ph.D., I investigated the properties of a coherently coupled mixture of BEC of Sodium 23, performing different experiments in two atomic configurations. The first configuration consist of a mixture of hyperfine states, namely the |F=1, mF = -1> and |F=1, mF = +1>, coupled by a two-photon transition, which is characterized by miscibility in the ground state. Another configuration was instead realized working with a strongly immiscible mixture of |F=1, mF=-1> and |F=2, mF = -2>, realized through with a one photon transition. My first experiment was devoted to the characterization of different methods of manipulation of the coupled miscible mixture in an elongated quasi-1D geometry. In Local Density Approximation (LDA), The dynamics of the system, depends on the atom number difference, the relative phase, and coupling to mean field energy ratio, can be fully described as an internal Josephson junction. We characterized this dynamics on a sample an inhomogeneous spatial profile, developing three different protocols for state manipulations. In a second experiment, I developed a protocol to generate Faraday waves in an unpolarized miscible mixture. Faraday waves are classical non-linear waves characterized by a regular pattern, that originate in classical and quantum fluids via a parametric excitation in the fluid. Interestingly enough, this process resembles the phase of reheating of the early universe, where the oscillation of the inflaton field is thought to have excited particles out of the vacuum. In analogy with this phenomenon, the oscillation of the inflaton field can be simulated with the periodic modulation of the trapping potential. On top of this, in a spin mixture, the parametric modulation can excite either in-phase (density) modes or out-of-phase (spin) modes, as two possible elementary excitations are present in the system. By extracting the spatial periodicity of the generated pattern at different modulation frequencies, I was then able to measure the dispersion relations for both density and spin modes of the system. In the presence of the coherent coupling, when spin excitations becomes gapped, we further demonstrate the scaling of the gap with the strength of the coupling radiation. The third experiment I realized concerned the characterization of the magnetic ground state of a spatially extended immiscible mixture in the presence of the coherent coupling. The Hamiltonian of such a system is formally equivalent to a continuous version of the transverse field Ising model, which describes magnetic materials at zero temperature. In this mapping, a nonlinear interaction term arises from the ratio between the self-interaction energy and the strength of the coupling, which acts as the transverse field. As the ratio between the two quantities is varied above and below one, the ground state of the system spontaneously changes from a paramagnetic phase to an ordered ferromagnetic phase, featuring two equivalent and opposite magnetizations, a signature of the occurrence of a second order quantum phase transition (QPT). Furthermore, in the magnetic model, the degeneracy between the two ferromagnetic ground states can be broken by introducing an additional longitudinal field. In the atomic case, the role of this additional field is taken by the detuning between the coupling radiation and the resonant transition frequency of non-interacting atoms. I characterized the QPT developing protocols to manipulate the spin mixture in its spatially extended ground state, varying the longitudinal field. Leveraging on the inhomogeneity of a BEC trapped in the harmonic potential, a smooth variation of the spin self-interaction energy occurs spontaneously in space, introducing different magnetic regimes at fixed coupling strength. These protocols gave access to a characterization of static properties typical of magnetic materials, such as the presence of an hysteresis cycle. The occurrence of the phase transition was instead validated by a measurement of the magnetic susceptibility and corresponding fluctuations, which both show a divergence when crossing the QPT critical point. At last, I developed a protocol to smoothly manipulate the position of magnetic domain walls, the least energetic excitations in a ferromagnet. While the previous study focused on static properties, the last experimental investigation presented in this thesis was devoted to the study of the dynamics of the metastable ferromagnetic region of the BEC. As a result of the presence of an hysteresis cycle, it is possible to engineer states of the ferromagnetic energy landscape that are homogeneously prepared either in the global minimum, with trivial dynamics, or in the metastable, higher energy, local minima. In the latter case, a classical system should eventually decay towards the global minimum, driven by temperature fluctuations which overtop the energy barrier separating the two minima. For a quantum system described by a field theory, such as a ferromagnetic BEC, the decay towards the global minimum occurs by tunneling through the barrier, triggered by quantum fluctuations. The event of tunneling is known as False Vacuum Decay (FVD), and is of outstanding relevance also for high energy physics and cosmology, were the first theoretical models were developed. In the FVD model, the decay towards the global minimum, the true vacuum, is a stochastic process that occurs only if a resonant bubble of true vacuum is formed. Once formed, the bubble will eventually expand throughout the whole system, as the true vacuum is energetically favorable. The probability for such a bubble to form can be approximately calculated analytically in 1D, and should depend exponentially on the height of the barrier the field has to tunnel through. Due to the exponentially long time scale of the process, experimental observations of FVD were still lacking. Thanks to the enhanced coherence time of the superfluid ferromagnetic mixture, and to the precise control of the barrier height through the detuning from atomic resonance, we were able to observe the event of bubble nucleation in a ferromagnetic BEC. To corroborate the observation, I measured the characteristic timescale of the decay for different values of the control parameters. Results were successfully compared first with numerical simulation, and then validated by instanton theory.