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The aim of this article is to give a pedagogical introduction to the exact equilibrium and nonequilibrium properties of free fermionic quantum spin chains. In a first part we present in full details the canonical diagonalisation procedure and review quickly the equilibrium dynamical properties. The phase diagram is analysed and possible phase transitions are discussed. The two next chapters are concerned with the effect of aperiodicity and quenched disorder on the critical properties of the quantum chain. The remaining part is devoted to the nonequilibrium dynamical behaviour of such quantum chains relaxing from a nonequilibrium pure initial state. In particular, a special attention is made on the relaxation of transverse magnetization. Two-time linear response functions and correlation functions are also considered, giving insights on the nature of the final nonequilibrium stationnary state. The possibility of aging is also discussed.

The aim of this article is to give a pedagogical introduction to the exact equilibrium and nonequilibrium properties of free fermionic quantum spin chains. In a first part we present in full details the canonical diagonalisation procedure and review quickly the equilibrium dynamical properties. The phase diagram is analysed and possible phase transitions are discussed. The two next chapters are concerned with the effect of aperiodicity and quenched disorder on the critical properties of the quantum chain. The remaining part is devoted to the nonequilibrium dynamical behaviour of such quantum chains relaxing from a nonequilibrium pure initial state. In particular,<br />a special attention is made on the relaxation of transverse magnetization. Two-time linear response functions and correlation functions are also considered, giving insights on the nature of the final nonequilibrium stationnary state. The possibility of aging is also discussed.

L'auto-organisation des organismes vivants est d'une complexité et d'une efficacité étonnantes. Plus précisément, les systèmes biologiques abritent un nombre gigantesque de réactions très spécifiques qui nécessitent que la bonne biomolécule se retrouve à la bonne place, dans le bon ordre et en un temps suffisamment court pour permettre le fonctionnement cellulaire, et au-delà la vie cellulaire. D'un point de vue dynamique, cela pose la question fondamentale de savoir comment les biomolécules trouvent efficacement leur(s) cible(s) spécifique(s), ou encore, quels types de forces rassemblent tous ces partenaires de réaction spécifiques dans un environnement aussi dense et ionisé que les micro-environnements cellulaires. Dans cette thèse, nous explorons la possibilité que des biomolécules puissent interagir à travers des interactions électromagnétiques de longue-portée telles que ces dernières sont prédites à partir des premiers principes de la physique; ''longue-portée'' signifiant que les interactionsen question sont actives sur des distances bien plus larges que les dimensions typiques des molécules mises en jeu (i.e., plus grandes qu'environ 50 angströms dans les systèmes biologiques). Après avoir posé les fondements théoriques concernant les interactionsde longue-portée potentiellement actives sur de longue distances dans un contexte biologique, nous étudions la posssibilité de détecter leur éventuelle contribution à partir de dispositifs expérimentaux qui sont accessibles de nos jours. Sur ce dernier point, des résultats préliminaires encourageants tant sur le plan théorique qu'expérimental sont présentés. / Self-organization of living organisms is of an astonishing complexity and efficiency. More specifically, biological systems are the site of a huge number of very specific reactions thatrequire the right biomolecule to be at the right place, in the right order and in a reasonably short time to sustain cellular function and ultimately cellular life. From the dynamic point of view, this raises the fundamental question of how biomolecules effectively find their target(s); in other words, what kinds of forces bring all these specific cognate partners together in an environment as dense and ionized as cellular micro-environments. In the present thesis, we explore the possibility that biomolecules interact through long-range electromagnetic interactions as they are predicted from the first principles of physics; "long-range" meaning that the mentioned interactions are effective over distances much larger than the typical dimensions of the molecules involved (i.e., larger than about 50 angströms in biological systems).After laying the theoretical foundations about interactions that are potentially active over long distances in a biological context, we investigate the possibility of detecting their contribution from experimental devices which are nowadays available. On the latter point, encouraging preliminary results both at the theoretical and experimental levels are exposed.