Comparison of Shannon information entropies in position and momentum space for an electron in one-dimensional nonuniform systems

摘要

We investigate numerically the position- and momentum-space Shannon information entropies, Sβnx and Sβnp ,nrespectively, of energy eigenstates |βu0002 for an electron in four kinds of one-dimensional (1D) nonuniform systems,ni.e., the Harper model, the slowly varying potential ones, the complex quasiperiodic potential ones, and thenrandom-dimer potential ones. In the former three models, electronic localization properties are well-defined. Fornthem, we find it interesting that, Sβnx is greater than, equal to, and less than Sβnp for delocalized, critical, and localizednstates in position-space, respectively, which can be used as signatures of the transition from a delocalized phase tona localized ones. With the criterion, we analyze the random-dimer potential model. We give another perspectivenand propose a consistent interpretation of discrepancies about the random-dimer potential model. Therefore, allnthese provide us a simple method to discern the nature of states in these 1D nonuniform systems.