10 citations · 17 across the 4 of their papers we have counts for
4 papers
Ballistic transport for one-dimensional quasiperiodic Schrödinger operators
Lingrui Ge, Ilya Kachkovskiy
In this paper, we show that one-dimensional discrete multi-frequency quasiperiodic Schrödinger operators with smooth potentials demonstrate ballistic motion on the set of energies…
On the relation between strong ballistic transport and exponential dynamical localization
Ilya Kachkovskiy
We establish strong ballistic transport for a family of discrete quasiperiodic Schrödinger operators as a consequence of exponential dynamical localization for the dual family. The…
Anderson localization for two interacting quasiperiodic particles
Jean Bourgain, Ilya Kachkovskiy
We consider a system of two discrete quasiperiodic 1D particles as an operator on and establish Anderson localization at large disorder, assuming the potentia…
A Hilbert-Schmidt analog of Huaxin Lin's Theorem
Nikolay Filonov, Ilya Kachkovskiy
The paper is devoted to the following question: consider two self-adjoint -matrices , , , such that their commutator is…