Resonant Tunneling In The Disordered Systems

The concepts of disordered systems and the research methods are introduced in this thesis. Thetransport properties of the nonlinear random dimer model and the three models of pairing ladders arestudied here. The contents of this thesis are introduced as follows:In chapter1, we introduce the basic concepts of the disordered systems and the Anderson tightbinding model. The scaling theory and the conductance，which are used to describe the transportproperties of disordered systems, are also presented in this chapter. We simply introduce thedevelopment of the nonlinear disordered theory and the two related models of nonlinear systems.Then, the homogeneous balance method and the recurrence method, that are commonly used innumerical calculation, are carefully shown here. We also present the concepts and basic properties ofthe transfer matrix.Chapter2is the first content of our research. We study the transport properties of the nonlinearrandom dimer model in one-dimensional correlated disordered nonlinear chains by using therecurrence of the nonlinear Schrodinger equation. Our results show that there is a resonance state inthe system; the results are different between the square of the transmitted amplitude and that of theincident amplitude being a fixed value; we point out that only when the square of the incidentamplitude is set to be a fixed value the transport properties effected by the nonlinear parameter can betruly reflected.Chapter3is the second content of our research. By using the transfer-matrix technique we studythree models of pairing ladders. It is found that there are three resonant states in the ladder when thetwo types of atoms are both random dimers (RD) in the same chain. And no extended state exists inthe ladder when only one type of atom is RD distributed or two types of atoms are both randomdistributed in the same chain.In chapter4we simply summarize the thesis.