Augmented Space Recursion


The aim of this project is to study  the properties of electrons and phonons in  disordered solids, in particular in random, substitutional alloys. When an experimentalist measures these properties we would have expected that every different sample should show different results. That this is not so, when one is measuring global (and not local) properties is due to the assumption of spatial ergodicity

What this assumption involves is the following argument : let us consider a disordered system of size NxNxN. A specific random arrangement of potentials in it is called a  configuration. If we now divide the system into MxMxM subsystems, there will be (N/M)3 of them. We now make N become infinitely large in such a way that M also becomes infinite, then we can assume that each of the subsystems represent a configuration of the full system and the global property measured on the full system is an average over  the subsystems, i.e. the configurations of the full system.

We may then compare the experimental results with configuration averaged global properties of the disordered system.  

The aim of the augmented space method is to propose an accurate and feasible method for calculation of configuration averaged properties of disordered systems.

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