Holographic models of out-of-equilibrium systems

What happens to a physical system that is initially in equilibrium and is kicked out of equilibrium at a given instant? This is the main question that I have tried to answer during my PhD. Often, the system will evolve to a new equilibrium state at a certain temperature. This is called the thermalization of the system. A specic example where this question is relevant, are the collisions of heavy atomic nuclei with high energies. After such a collision the system will evolve to the so called quark-gluon plasma. This is an exotic state of matter where the quarks and gluons, which under normal conditions are locked in the protons and neutrons of the atomic nucleus, can move freely and form a collective state. Another example can be found in the disturbance of superconducting materials. It is dicult to study these systems with conventional methods. During my PhD, I have used tools that originated in string theory, our best candidate to reconcile the theory of general relativity with quantum mechanics. In particular, I used the \AdS/CFT correspondence". This conjecture states that a quantum system in 4 dimensions (3 spacelike and 1 timelike) corresponds to a system with gravity in 5 dimensions (4 spacelike and 1 timelike). Since the 4-dimensional system seems to live on the boundary of the 5-dimensional spacetime, we say that the duality is `holographic'. All the information of the 5-dimensional bulk spacetime is encoded on its boundary. It turns out that this correspondence between two dierent descriptions, allows us to model the thermalization of a quantum mechanical system by the gravitational collapse of matter and the subsequent formation of a black hole in a higher dimensional space. To study the formation of a black hole, we used both analytical and numerical methods. In this way we could model the disturbance of a quantum material and study the timeevolution of the spectral function during the thermalization process. The spectral function is a measurable quantity that indicates the density of the electron states. Our result interpolated between the initial and nal equilibrium state. On the other hand, we also focussed on more realistic holographic models of the nuclear interactions. To mimic the collision of heavy atomic nuclei, we perturbed these models by a sudden injection of energy. We observed that depending on the initial conditions the system would sometimes evolve to a new equilibrium state, but that it could also continue to oscillate quasi-periodically in time. Finally we studied a problem of a more fundamental nature. The higher dimensional spacetime that appears in the AdS/CFT correspondence is an anti-de-Sitter spacetime. This spacetime has the same number of symmetries as the Minkowski spacetime that appears in the theory of special relativity, but has a negative curvature. Recently there were numerical indications that arbitrarily weak perturbations of this spacetime can lead to the formation of a black hole. We have tried to gain some analytical insight in the processes that are involved in this eect.