Author

B. Altshuler

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Preprint Aug 2026

Semi-localized ground state in a 1D system with long-range hopping

We study the localization of a quantum particle in a one-dimensional disordered system with long-range hopping amplitudes $t(r)\propto r^{-a}$. In contrast to the standard one-dimensional Anderson model ($a\to\infty$), in which all states are localized and the localization length is minimal at the band edge, the long-r...

M. Bahovadinov, Faridun N. Jalolov, V. E. Kravtsov et al. · 1 citation

Preprint Jul 2026

Semi-fractality and localization on a chiral Cayley tree

We study a quantum particle hopping on an infinite Cayley tree with nearest-neighbor hopping amplitudes drawn from a distribution singular as $|t|^{-a}$ near weak links and no on-site disorder. Because the graph is bipartite, the model has chiral symmetry, which strongly affects the statistics of eigenstates at the cen...

Carlo Vanoni, V. E. Kravtsov, B. Altshuler · 1 citation