Geometric Mean Density Of States In The One-dimensional Non-uniform System

In this paper, by using the ratio of geometric mean DOS and arithmetic mean DOS R, the localization properties of eigenstates, and the relation between metal-insulator transition and model parameter are investigated in one-dimensional non-uniform and (or) disorder systems. At the same time, we also investigate the localization properties of two interacting spinless bosons with on-site interaction. These investigation provide us a new quantity (the ratio of geometric mean DOS and arithmetic mean DOS) to understand the localization property for particles in 1D non-uniform systems.Firstly, The essential conception and research methods are introduced in non-uniform system. Secondly, by using the ratio R, we study numerically the localization properties of eigenstates for five kinds of one-dimensional determined and random potentials models. The extended and localized states can be distinguished by the ratio. From the varying curve of < R > vs system parameters, we can easily find sharp transition, corresponding to metal-insulator transition. It provides that the ratio may be a new index for a metal-insulator transition. Thirdly, making use of the correlative knowledge of Green function, we find the relation of the local density of states (LDOS) and the eigenstates in two interacting particles systems. So we can obtain LDOS. By using the ratio R and the spectrum averaged ratio < R >, we study the effect of the on-site interaction U on the localization properties in 1D disordered and quasiperiodic potential systems, respectively. We find that as long as there are localized eigenstates at single-particle models, the delocalization (localization) effect happens for small interactions (large interactions), while for extended states, the interaction always induces the localization effect in two interacting particles systems.