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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, etc) 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.