Abstract
We consider the 1d Schrödinger operator with random decaying potential and compute the 2nd term asymptotics of the density of states, which shows substantial differences between the cases \(\alpha > \frac{1}{2}\), \(\alpha < \frac{1}{2}\) and \(\alpha = \frac{1}{2}\).
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Acknowledgements
The author would like to thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme “Periodic and Ergodic Spectral Problems” supported by EPSRC Grant Number EP/K032208/1, and also to the referee for many useful comments. This work is partially supported by JSPS KAKENHI Grant Number 26400145.
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Nakano, F. Fluctuation of Density of States for 1d Schrödinger Operators. J Stat Phys 166, 1393–1404 (2017). https://doi.org/10.1007/s10955-017-1728-8
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DOI: https://doi.org/10.1007/s10955-017-1728-8