92 citations · 184 across the 10 of their papers we have counts for
10 papers
Anderson transition for Google matrix eigenstates
O. V. Zhirov, D. L. Shepelyansky
We introduce a number of random matrix models describing the Google matrix G of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix…
Wigner crystal in snaked nanochannels: outlook
O. V. Zhirov, D. L. Shepelyansky
We study properties of Wigner crystal in snaked nanochannels and show that they are characterized by a conducting sliding phase at low charge densities and an insulating pinned pha…
Two-dimensional ranking of Wikipedia articles
A. O. Zhirov, O. V. Zhirov, D. L. Shepelyansky
The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists {\it ab aeterno}. Wikipedia, a free online encyclopaedia, becomes…
Quantum compacton vacuum
O. V. Zhirov, A. S. Pikovsky, D. L. Shepelyansky
We study the properties of classical and quantum compacton chains by means of extensive numerical simulations. Such chains are strongly nonlinear and their classical dynamics remai…
Quantum Dynamics Against a Noisy Background
Valentin V. Sokolov, Oleg V. Zhirov, Yaroslav A. Kharkov
By the example of a kicked quartic oscillator we investigate the dynamics of classically chaotic quantum systems with few degrees of freedom affected by persistent external noise.…
Google matrix, dynamical attractors and Ulam networks
D. L. Shepelyansky, O. V. Zhirov
We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite size matrix approximan…