• Corpus ID: 118610508

Support set of random wave-functions on the Bethe lattice

@article{Luca2013SupportSO,
  title={Support set of random wave-functions on the Bethe lattice},
  author={Andrea De Luca and Antonello Scardicchio and Vladimir E. Kravtsov and Boris L. Altshuler},
  journal={arXiv: Statistical Mechanics},
  year={2013}
}
We introduce a new measure of ergodicity, the support set $S_\varepsilon$, for random wave functions on disordered lattices. It is more sensitive than the traditional inverse participation ratios and their moments in the cases where the extended state is very sparse. We express the typical support set $S_{\varepsilon}$ in terms of the distribution function of the wave function amplitudes and illustrate the scaling of $S_{\varepsilon}\propto N^{\alpha}$ with $N$ (the lattice size) for the most… 

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References

Physical review 109 , 1492 ( 1958 ) . 3 A . Einstein
  • Annals of physics
  • 2006