3 citations · 9 across the 6 of their papers we have counts for
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Sharp arithmetic delocalization for quasiperiodic operators with potentials of semi-bounded variation
Svetlana Jitomirskaya, Ilya Kachkovskiy
We obtain the sharp arithmetic Gordon's theorem: that is, absence of eigenvalues on the set of energies with Lyapunov exponent bounded by the exponential rate of approximation of f…
On spectral bands of discrete periodic operators
Nikolay Filonov, Ilya Kachkovskiy
We consider discrete periodic operator on with respect to lattices of full rank. We describe the class of lattices for which the operator ma…
Perturbative diagonalisation for Maryland-type quasiperiodic operators with flat pieces
Ilya Kachkovskiy, Stanislav Krymski, Leonid Parnovski +1
We consider quasiperiodic operators on with unbounded monotone sampling functions ("Maryland-type"), which are not required to be strictly monotone and are allowed to…
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…
Localization for quasiperiodic operators with unbounded monotone potentials
Ilya Kachkovskiy
We establish non-perturbative Anderson localization for a wide class of 1D quasiperiodic operators with unbounded monotone potentials, extending the classical results on Maryland m…