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Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 1):061122. Epub 2012 Dec 17.

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

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Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications, Nanjing 210003, China.


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

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