Desde 1989, entre las labores realizadas por la Misión Arqueológica Española en Siria se encontraba un programa de prospección y estudio del territorio, en el cual se enmarcaban los yacimientos donde se estaba excavando (Tell Qara Qūzāq y Tell Jamīs). Este programa abarcaba una amplia zona de terreno y también un extenso marco cronológico. Aprovechando esta investigación arqueológica en el Éufrates se pudo constatar la existencia de numerosas cuevas labradas, de índole funeraria algunas y monacales otras.A raíz de esta línea de investigación inicial, esta Tesis ve la luz desde el Instituto del Próximo Oriente Antiguo que me ofreció la posibilidad de estudiar directamente todos los restos de época romana y bizantina que se habían localizado en sus continuas excavaciones y prospecciones en Siria, concretamente en el entorno de Qara Qūzāq. / Since 1989, among the works carried out by the Spanish Archaeological Mission in Syria, was an program of surveys and study of the territory in which there was digging (Tell Qara Quzaq and Tell Jamis). This program didn't only include a wide land area but also an extensive chronological horizon. This way, taking advantage of this archaeological research in the Euphrates you could verify the existence of numerous figured caves, of funeral nature some and monkish others. Soon after this line of initial research, this Thesis sees the light from the Instituto del Próximo Oriente Antiguo (IPOA) that offered me the possibility to study directly and in more intensity all the remains of Roman and Byzantine time that had been located in its continuous excavations and surveys in Syria, concretely in Qara Quzaq's environment, main centre of the archaeological mission from where the IPOA acted in this region.

In this thesis I investigate several aspects of local quantum criticality, a concept of key importance in a number of physical contexts ranging from critical heavy fermion compounds to quantum dot systems. Quantum critical points are associated with second order phase transitions at zero temperature. In contrast to their finite-temperature counterparts, the zero-point motion cannot be neglected near a quantum critical point. As a result, the incorporation of quantum dynamics leads to an effective dimension larger than the spatial dimension of the system for the order parameter fluctuations within the Ginzburg-Landau-Wilson treatment of criticality. This so-called quantum-to-classical mapping works well for the critical properties in insulating systems but apparently fails in systems containing gapless fermions. This has been experimentally most clearly been demonstrated within a particular class of intermetallic compounds called heavy fermions. A particular way in which the Ginzburg-Landau-Wilson paradigm fails is for critical Kondo destruction that seems to underlie the unconventional quantum criticality seen in the heavy fermions. I focus on studying the properties of critical Kondo destruction and the emergence of energy-over-temperature-scaling in systems without spatial degrees of freedom, i.e., so-called quantum impurity systems. In particular, I employ large-N techniques to address critical properties of this class of quantum phase transitions in and out of equilibrium. As quantum critical systems are characterized by a scale-invariant spectrum with many low-lying excitations, it may appear that any perturbation can lead to a response beyond the linear response regime. Understanding what governs the non-linear response regime near quantum criticality is an interesting area. Here, I first present a path integral version of the Schrieffer-Wolff transformation which relates the functional integral form of the partition function of the Anderson model to that of its effective low-energy model. The equivalence between the low-energy sector of the Anderson model in the Kondo regime and the spin-isotropic Kondo model is usually established via a canonical transformation performed on the Hamiltonian, followed by a projection. The resulting functional integral assumes the form of a spin path integral and includes a geometric phase factor, i.e. a Berry phase. The approach stresses the underlying symmetries of the model and allows for a straightforward generalization of the transformation to more involved models. As an example of the efficiency of the approach I apply it to a single electron transistor attached to ferromagnetic leads and derive the effective low-energy model of such a magnetic transistor. As Kondo screening is a local phenomenon, it and its criticality can be studied using the appropriate impurity model. A general impurity model to study critical Kondo destruction is the pseudogap Bose-Fermi Kondo model. Here, I concentrate on the multi-channel version of the model using the dynamical large-N study. This model allows to study the non-trivial interplay between two different mechanisms of critical Kondo destruction. The interplay of two processes that can each by itself lead to critical Kondo destruction. The zero-temperature residual entropy at various fixed points for the model is also discussed. The two channel Anderson model exhibits several continuous quantum phase transitions between weak- and strong-coupling phases. The non-crossing approximation (NCA) is believed to give reliable results for the standard two-channel Anderson model of a magnetic impurity in a metal. I revisit the reliability of the NCA for the standard two channel Anderson model (constant conduction electron density of states) and investigate its reliability for the two-channel pseudogap Anderson model. This is done by comparing finite-temperature, finite-frequency solutions of the NCA equations and asymptotically exact zero-temperature NCA solutions with numerical renormalization-group calculations. The phase diagram of this model is well established. The focus here will be on the dynamical scaling properties obtained within the NCA. Finally, I study the thermal and non-thermal steady state scaling functions and the steady-state dynamics of the pseudogap Kondo model. This model allows us to study the concept of effective temperatures near fully interacting as well as weak-coupling fixed points and compare the out-of-equilibrium scaling properties of critical Kondo destruction to those of the traditional spin-density wave (SDW) scenario. The differences I identify can be experimentally probed. This may be helpful in identifying the nature of the quantum critical points observed in certain heavy fermion compounds.