426 citations · 1.4k across the 22 of their papers we have counts for
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cond-mat.dis-nn2007★ 54 cited
Fractal Weyl law for quantum fractal eigenstates
D. L. Shepelyansky
The properties of the resonant Gamow states are studied numerically in the semiclassical limit for the quantum Chirikov standard map with absorption. It is shown that the number of…
cond-mat.dis-nn2007★ 426 cited
Destruction of Anderson localization by a weak nonlinearity
A. S. Pikovsky, D. L. Shepelyansky
We study numerically a spreading of an initially localized wave packet in a one-dimensional discrete nonlinear Schrödinger lattice with disorder. We demonstrate that above a certai…
cond-mat.dis-nn2005★ 1 cited
Phonon modes in the Frenkel-Kontorova chain: exponential localization and the number theory properties of frequency bands
O. V. Zhirov, G. Casati, D. L. Shepelyansky
We study numerically phonon modes of the classical one-dimensional Frenkel-Kontorova chain, in the regime of pinned phase characterized by the phonon gap and devil's staircase, as…