Semiclassical theory of systems with spin-orbit interaction is formulated in terms of path integrals using coherent-state representation. Gutzwiller’s trace formula which expresses the density of states through the parameters of classical periodic orbits is derived in the limits of weak and strong coupling, and in the limit of large spin. An application to quantum dots with Rashba spin-orbit interaction is discussed. Nous discutons le comportement dúne variété élastique dans un potentiel aléatoire, comme prototype de système désordonné. Ce modèle décrit des systèmes physiques aussi divers que les ondes de densité de charge, les parois de domaines magnétiques, les polymères dirigés (équivalent à l’équation KPZ), le décrochage dúne ligne de contact, etc… Le défi théorique est que la méthode de perturbation standard mène à des résultats absurdes. Pour y échapper, il faut suivre toute la distribution du désordre (renormalisation dite fonctionnelle). Nous décrivons des succès récents, en théorie de perturbation au delà dúne boucle, en focusant sur la dynamique hors équilibre. To obtain a first principle derivation of the conformal field theory describing the edge excitations in a quantum Hall system has been a long standing problem. After reviewing the subject and the main challenges there, we present a microscopic derivation of the field theory of edge excitations (the so-called chiral Luttinger liquid theory) for the Laughlin states. Starting from the wave function describing an arbitrary incompressibly deformed Laughlin state, and using the description of the boundary of the quantum Hall droplet in terms of harmonic moments, we quantize these deformations by defining the explicit action of the creation (annihilation) operators of edge excitations on the many-electron wave-functions. In this way we obtain the low-energy projections of local operators, and derive the quantum field theory of edge excitations directly from quantum mechanics of electrons. We also comment that in the thermodynamic limit the incompressibly deformed Laughlin state is described by the dispersionless Toda hierarchy. Similar techniques have been recently used in the description of the Laplacian growth (Hele-Shaw) problem. We will discuss the predictions of the theory of parton saturation/Color Glass Condensate for particle production in p(d)A collisions. We concentrate on the nuclear modification factor R^pA for gluon production. We show that at moderately high energy/rapidity the nuclear modification factor R^pA exhibits Cronin enhancement. As the energy/rapidity increases, R^pA decreases. At sufficiently high energy/rapidity R^pA becomes less than 1 for all values of p_T indicating the onset of suppression of gluon production due to quantum small-x evolution effects. Our predictions are supported by the recently reported BRAHMS collaboration data on particle production at forward rapidity in dAu collisions at RHIC. .

Institute for Solid State Physics, University of Karlsruhe