One-dimensional models of disordered quantum wires: general formalism

In this work we describe, compile and generalize a set of tools that can be used to analyse the electronic properties (distribution of states, nature of states, ...) of one-dimensional disordered compositions of potentials. In particular, we derive an ensemble of universal functional equations which characterize the thermodynamic limit of all one-dimensional models and which only depend formally on the distributions that define the disorder. The equations are useful to obtain relevant quantities of the system such as density of states or localization length in the thermodynamic limit

Projective dynamics and first integrals

We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemannian manifolds. We set the ground for a new and simple theory of the integrable systems having only quadratic first integrals. This theory begins with two centered quadrics related by central projection, each quadric being a model of a space of constant curvature. Finally, we present an extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure