One consequence of the presence of impurities, and in general nonhomogeneous systems, is on the transport properties of a given system. Often the impurities are inserted in a material randomly which leads to various effects of disorder and change of resistivity of the material. In this chapter the transport in mesoscopic systems is first considered and the origin of resistance in a ballistic conductor due to contacts, the thermal transport of phonons, and the importance of Umklapp processes and the existence of persistent currents are discussed. The Landauer transport theory is introduced and the transfer matrix method to analyze transport is presented. The theory of Anderson localization, where an insulating regime is obtained from a metallic regime is considered, for different dimensions, as a result of randomness in a system. Also, quasidisordered systems are considered together with a brief digression through fractality. The scaling theory of localization is introduced. As another example of the effects of disorder we consider a spin system in the presence of a random magnetic field, and using spin coherent states the change in critical temperature due to disorder is estimated.

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Nonhomogeneous Systems: Transport and Disorder

  • Pedro D. Sacramento

摘要

One consequence of the presence of impurities, and in general nonhomogeneous systems, is on the transport properties of a given system. Often the impurities are inserted in a material randomly which leads to various effects of disorder and change of resistivity of the material. In this chapter the transport in mesoscopic systems is first considered and the origin of resistance in a ballistic conductor due to contacts, the thermal transport of phonons, and the importance of Umklapp processes and the existence of persistent currents are discussed. The Landauer transport theory is introduced and the transfer matrix method to analyze transport is presented. The theory of Anderson localization, where an insulating regime is obtained from a metallic regime is considered, for different dimensions, as a result of randomness in a system. Also, quasidisordered systems are considered together with a brief digression through fractality. The scaling theory of localization is introduced. As another example of the effects of disorder we consider a spin system in the presence of a random magnetic field, and using spin coherent states the change in critical temperature due to disorder is estimated.