Disorder, Chaos and Correlations in Quantum Systems

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The field of mesoscopic physics has had significant progress during the past few years. The theoretical progress has been driven by the statistical approach to sample fluctuations in the ensemble of small disordered systems. As the sizes of the systems are made smaller and smaller, eventually they approach the electron mean free path. Then the motion of an electron becomes ballistic. On the other hand, due to the complex geometry, this motion can still be chaotic. Such a system is similar in many respects to other systems (atomic or nuclear) which display quantum chaos. For analytical calculations disordered systems turn out to be simpler than chaotic ballistic ones because of the additional ensemble averaging. The idea of this research is to use disordered systems as a laboratory for the investigation of quantum chaos. In a diffusive regime we plan to derive relations and develop analytical methods which can be extended to general cases. Theoretical studies will also be carried out on problems of persistent currents in isolated rings and the magnetic susceptibility of isolated metallic grains - problems closely connected to quantum chaos. We will take into account interactions between electrons since existing one-electron theories are in substantial disagreement with experiment. %%% The field of mesoscopic physics is a very current one which deals with basic problems in fundamental physics and yet has important ramifications for microelectronics. The present research will theoretically deal with a number of problems in mesoscopic physics. In particular, the research will study the onset of quantum chaos in these systems. Clearly, besides its fundamental importance, the conditions under which a microelectronic system becomes chaotic, or unstable, is of interest to the computer and communications industry.