23 citations · 65 across the 19 of their papers we have counts for
22 papers
Smooth perturbation theory and generic Cantor spectrum for multi-dimensional monotone quasiperiodic operators
Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg
We consider multi-dimensional quasiperiodic Schrödinger operators with monotone sawtooth-type potentials in the perturbative localization regime. We prove that a given gap is close…
On almost commuting matrices with respect to the normalized Hilbert--Schmidt norm
Mohit Bansil, Ilya Kachkovskiy
In this paper, we consider the Rosenthal -- Halmos problem of almost commuting matrices with respect to the normalized Hilbert -- Schmidt norm …
On almost commuting unitary matrices
Adam Dor-On, Lucas Hall, Ilya Kachkovskiy
A question going back to Halmos asks when two approximately commuting matrices of a certain kind are close to exactly commuting matrices of the same kind. It has long been known th…
Absence of flat bands for discrete periodic graph operators with generic potentials
Matthew Faust, Ilya Kachkovskiy
We show that Schrödinger-type operators on discrete connected periodic graphs do not have flat bands for generic potentials.
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…
Perturbative diagonalization and spectral gaps of quasiperiodic operators on with monotone potentials
Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg
We obtain a perturbative proof of localization for quasiperiodic operators on with one-dimensional phase space and monotone sampling functions, in the regime of smal…