23 citations · 65 across the 19 of their papers we have counts for
4 papers · 1 filter
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…
On gaps in the spectra of quasiperiodic Schrödinger operators with discontinuous monotone potentials
Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg
We show that, for one-dimensional discrete Schrödinger operators, stability of Anderson localization under a class of rank one perturbations implies absence of intervals in spectra…
Sharp arithmetic localization for quasiperiodic operators with monotone potentials
Svetlana Jitomirskaya, Ilya Kachkovskiy
We prove the universality of sharp arithmetic localization for all one-dimensional quasiperiodic Schrödinger operators with anti-Lipschitz monotone potentials.