Preface: phys. stat. sol. (b) 241/9
Authors: Morawetz Klaus 
Published: June 2004

“Modelling and Simulation in Molecular Systems, Mesoscopic Structures, and Material Science” was the title of a workshop held at the University of Technology in Chemnitz from 21 to 23 April 2004. This workshop coincided with the 50th birthday of Michael Schreiber. Therefore, the idea to publish a special issue is supported by two good reasons. First, a topical collection is appropriate for giving an overview about a field and to initiate further studies. This is one intention of the present issue. Second, the birthday is a suitable occasion for reflecting on the status of the different fields where Michael Schreiber has been active himself. Motivated by the characteristic name of the workshop (MS4), which expresses the broad range of his activities, the contributions are grouped into three main chapters: Disorder and Interaction, Phase Transitions and Criticality, and Transport Properties.

The first part starts with the currently intensively discussed topic of composite Fermions in the paper by B. Kramer et al. This method of rewriting correlations as new quasiparticles has amongst other things the merit of explaining such exciting phenomena as the fractional quantum Hall effect. The methodological questions of Ward identities, causality, and conservation laws are the focus of the systematic investiga‐tion in the second article by V. Janis et al. which concentrates on the problem of disorder and configura‐tional averaging. The interplay between disorder and correlation is treated in the third contribution by C. Schuster et al., where different theoretical methods are tested on the problem of Friedel oscillations within the one‐dimensional Heisenberg and Hubbard model. In the next contribution, M. Berciu et al. focus on localization as one consequence of disorder. The localized and extended electronic states are treated, together with the magnetic degrees of freedom, like spin waves. One of the astonishing consequence of localiza‐tion is the observation of resonant Rayleigh backscattering. This is investigated by random matrix theory in the next article by E. Runge et al. and extended to exciton transitions in semiconductor nanostructures. In order to characterize localization, A. Eilmes et al. consider the two‐dimensional Anderson model in the following article with special focus on the critical exponents for the localization length. The chapter on disorder ends with a contribution by A. Aldea et al. where the disorder effects are investigated in twodimensional systems with perpendicular magnetic fields such that the interplay between Landau levels and localized states can be considered.

The second chapter in the collection is devoted to critical phenomena and phase transitions. It starts with an overview of the most prominent example of critical phenomena, high‐Tc superconductivity. A. Sherman presents a review on magnetic and spectral properties of cuprate perovskites within t – J models. The long‐range hopping problem and the extraction of critical exponents are the topic of the contribution by E. Cuevas, who calculated the level spacing distribution as well as the correlation dimen‐sion in the strong coupling limit. The critical points and the thermodynamics of quenched spatial disordered systems are then treated by T. Vojta et al. Here it is shown that different parts of a system might undergo phase transitions controlled by different parameter values. Different microstructures are important when phenomena like the growth of crystals are considered. Consequently the latter problem is treated in the next contribution by H. Emmrich et al., who develop an analytical solution and compare it to simulations in order to provide insights into the universality of diffusion‐limited crystal growth. That the applications of critical phenomena are quite versatile is demonstrated in a short paper by J. St�ring et al. who show how statistical methods can be employed to optimize networks of wireless communication. This chapter on critical phenomena ends with a methodological investigation by U. Grimm. This concerns the often applied random matrix theory, and a method to calculate the level spacing distribution by using coupled differential equations.

The third chapter is devoted to transport. It starts with an article about conductance fluctuations by M. Ortuno et al. These quantum fluctuations are considered in localized systems which is directly related to the topics in the first chapter. M. Schr�der et al. present in the next article a method to propagate wave functions by approximating them by multi‐dimensional wave packets. In contrast to variational methods, this method is based on stochastic calculus. In the case where only a few electrons are transferred, as in the reaction of donor‐acceptor complexes and molecular wires, a unified description is presented in the contribution by V. May et al. The transfer rate and the stationary current are calculated and their depend‐ence on the length of the molecular system is shown. The method of Green's functions based on local orbitals is used in the next article by M. Albrecht et al. to calculate molecular charge transport. This results into a Landauer theory for the calculation of the transmission coefficient. The special role of elec‐tron‐electron interaction in the transport properties of disordered wires is considered by H. Mori et al. Here the interplay of interaction and disorder is investigated and the different roles of interaction for the localization phenomena are discussed. We close this chapter on transport by an investigation of electronic transport through nanoparticle arrays. The self‐assembled nanoparticle structures are considered within the contri‐bution by K. Nicolic whose structures represent very promising nanoelectronic devices.

The broad‐range approaches and applications selected in these three chapters demonstrate the exciting interplay between structure, disorder, and correlations and suggest the kind of future developments which are to be expected within this field. Finally, in the name of all authors and workshop participants: Happy birthday to Michael Schreiber and all best wishes for exciting future scientific activities!