The motion of a particle in a random potential in two or more dimensions is chaotic, and the trajectories in deterministically chaotic systems are effectively random. It is therefore no surprise that there are links between the quantum properties of disordered systems and those of simple chaotic systems. The question is, how deep do the connec- tions go? And to what extent do the mathematical techniques designed to understand one problem lead to new insights into the other? The canonical problem in the theory of disordered mesoscopic systems is that of a particle moving in a random array of scatterers. The aim is to calculate the statistical properties of, for example, the quantum energy levels, wavefunctions, and conductance fluctuations by averaging over different arrays; that is, by averaging over an ensemble of different realizations of the random potential. In some regimes, corresponding to energy scales that are large compared to the mean level spacing, this can be done using diagrammatic perturbation theory. In others, where the discreteness of the quantum spectrum becomes important, such an approach fails. A more powerful method, devel- oped by Efetov, involves representing correlation functions in terms of a supersymmetric nonlinear sigma-model. This applies over a wider range of energy scales, covering both the perturbative and non-perturbative regimes. It was proved using this method that energy level correlations in disordered systems coincide with those of random matrix theory when the dimensionless conductance tends to infinity.
The classical Taylor's formula of advanced calculus is generalized, extending the notion of the differentiability class Cm, with applications to maxima and minima and to sufficiency of jets.
Housing provision is a major dilemma for local authorities. There is currently a huge demand for more housing, while increasing environmental, economic and political pressures must be considered when local authorities develop their policies. This remarkable volume investigates how local authorities formulate their housing strategies. It questions whether the local authority can be seen as a single entity in terms of housing or whether it is fragmented into separate departments. Incorporating in-depth empirical research from England and Wales, the book discusses whether the process of developing housing policy and allocating land needs to be more integrated, and whether key players such as speculative house-builders should be involved in the development of policy. Analyzing which information sources influence the local authority's land allocations and housing strategies, the volume debates whether they provide the most useful data and suggests alternative information sources that may assist in better land allocation policies.