Maximally-localized generalized Wannier functions for composite energy bands

We discuss a method for determining the optimally-localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ``generalized Wannier functions'' we mean a set of localized orthonormal orbitals spanning the same space as the specified set of Bloch bands. Although we minimize a functional that represents the total spread sum_n [ _n - _n^2 ] of the Wannier functions in real space, our method proceeds directly from the Bloch functions as represented on a mesh of k-points, and carries out the minimization in a space of unitary matrices U_mn^k describing the rotation among the Bloch bands at each k-point. The method is thus suitable for use in connection with conventional electronic-structure codes. The procedure also returns the total electric polarization as well as the location of each Wannier center. Sample results for Si, GaAs, molecular C2H4, and LiCl will be presented.Comment: 22 pages, two-column style with 4 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#nm_wan

Concurring urbanizations? Understanding the simultaneity of sub-and re-urbanization trends with the help of migration figures in Berlin

Most classical models of urban development conceptualize suburbanization and reurbanization as opposing processes of in-and out-migration. The article at hand starts from the understanding that this linear interpretation of migration figures falls short of the mark. Drawing on different approaches to op-erationalize reurbanization, case-specific migration-data from Berlin illustrates a population development where decline and revival do not exclusively happen at either the urban core or the city’s fringes, but can be observed throughout the city region. The paper concludes that seemingly contradicting urban dynamics, such as population gains and losses in different parts of a diversified spatial system such as the city region result from the same land and housing market processes which favour and disadvantage different social groups and neighbourhoods, respectively. This observation calls for a dismissal of mono-linear policy approaches in urban governance and planning, so as to address both macro-and micro-scale disparities in a fair manner and to prevent the neglect of the latter